Study StudyMaterial Material PHYSICS(042) for Class XII PHYSICS(042) for Class XII for the for the Academic year 20152016 Academic year 20152016
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KENDRIYA VIDYALAYA SANGATHAN ZONAL INSTITUTE OF EDUCATION AND TRAIING, MYSORE
Study Material
PHYSICS(042) for Class XII for the Academic year 20152016
Prepared/Revised by
Mr. K ARUMUGAM PGT (PHYSICS), Faculty, KVS ZIET Mysore
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OUR PATRONS R PATRPATRPAPATRON SPATRONSwledgemen श्री संतोष कुमार मल्ल,आईएएस t आयुक्त Shri.ShriSantosh Kumar Mall, IAS Commissioner, KVS
श्री जी. के. श्रीवास्तव, आईएएस अपर आयुक्त (प्रशासन) G.K. Srivastava, IAS Additional Commissioner (Administration)
श्रीयू एनखवारे
अपर आयुक्त (शैक्षिक) Mr. U N Khaware Additional Commissioner (Academics)
डॉ. शचीकाांत सांयुक्त आयुक्त (प्रशशिण) Dr. Shachi Kant Joint Commissioner (Training)
श्री ए. अरूमग ु म
सांयक् ु त आयक् ु त (ववत्त) Shri M Arumugam Joint Commissioner (Finance) डा वी. ववजयलक्ष्मी संयुक्त आयुक्त (शिक्षा) Dr. V. Vijayalakshmi Joint Commissioner (Academics)
डॉ. ई. प्रभाकर सांयुक्त आयुक्त (काशमिक) Dr. E. Prabhakar Joint Commissioner (Personnel)
श्री.एस.ववजयकुमार सांयक् ु तआयक् ु त(प्रशासन)
Shri S Vijayakumar Joint Commissioner (Admn) 3
FOREWORD The seven PGTs working as members
of faculty at KVS,ZIET Mysore Mr K
Arumugam(Physics), Mr. KaluSivalingam (Maths), Mr. M Reddenna (Geo.), Mr. Murugan (History), Mr. Hari Shankar (Hindi),Mr. Joseph Paul (Econ.) and Mr. U.P Binoy (English) prepared Study Materials for Class XII for the academic year 20152016 in their respective subjects. All these study materials focus on some select aspects , namely;
Gist of lessons/chapter Marking scheme (CBSE) Important questions Solved Question papers with value point. Tips for scoring well in the examination.
The above mentioned seven members of faculty at ZIET Mysore have put in a lot of efforts and prepared the materials in a period of two months. They deserve commendations for their singleminded pursuit in bringing out these materials. The teachers of these subjects namely, Physics, Mathematics, Geography, History, Hindi, Economics and English may use the materials in the month of January& February 2016 for PreBoard Examination, revision and practice purposes. It is hoped that these materials will help the students perform better in the forthcoming Board Examinations.
INDEX
The teachers are requested to go through the materials thoroughly, and feel free to send their opinions and suggestions for the improvement of these materials to
[email protected] Dr. E.T ARASU Deputy Commissioner/ Director KVS, ZIET, Mysore
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PREFACE
It is a matter of great pleasure that after receiving encouragement from our Deputy commissioner DR. E.T Arasu I now present the thoroughly revised latest edition of STUDY MATERIAL OF CLASS XII PHYSICS based on the latest syllabus and revised question paper pattern to be followed from 2015 onwards. In this booklet according to the latest syllabus of CBSE for class XII materials were prepared. THE SALIENT FEATURES OF THIS STUDY MATERIAL ARE AS FOLLOWS;
It covers the syllabus given by CBSE for the class XII Physics Gist of each chapter Concept map of each chapter Questions and answers of 1,2 and 3 marks of each chapter Value Based questions – Chapter wise Frequently asked Board examination questionsChapter wise Marking scheme given by CBSE ( 2015) Sample Question papers for 2016 Sample Question paper with value points 5 Question paper Tips for scoring well Remedial teaching for slow learners Learning style of students Reference books and websites The material can be used for the purpose of revision All the concepts of the subject have been included in the material
This material can be used to (i) revise the syllabus (ii) to workout practice Question Papers (iii) gain conceptual clarity and (iv) know the value points for answers, besides serving as a pre – exam, eleventh hour reference material. Place: Mysore
K ARUMUGAM
Date: 18/12/2015
Faculty ZIET Mysore
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INDEX S.NO TOPIC 1 ELECTROSTATICSGIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 2 CURRENT ELECTRICITY GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 3 MAGNETIC EFFECTS OF CURRENT AND MAGNETISM GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 4 ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTGIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 5 ELECTROMAGNETIC WAVES GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 6 OPTICS GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 7 DUAL NATURE OF MATTER AND RADIATION GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 8 ATOMS NUCLEI GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 9 SOLIDS AND SEMICONDUCTORS GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 10 COMMUNICATIONS GIST OF THE LESSON, CONCEPT MAP, QUESTION AND ANSWERS, VALUE BASED QUESTIONS 11 FREQUENTLY ASKED QUESTIONS CHAPTERWISE 12 MARKING SCHEME 11 SAMPLE QUESTION PAPER FOR MARCH 2016& MODEL QUESTION PAPER WITH VALUE POINTS (4 SETS) 12 TIPS FOR SCORING WELL IN THE EXAMINATION 13 REMEDIAL TEACHING 14 LEARNING STYLE OF STUDENTS 15 LIST OF REFERENCE BOOKS AND WEBSITES
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PAGE NUMBER 724 2540 4056
5673
7479 80110 111118
119129 130152
153165 166187 188198 199216 217221 221224 225226 227
1. ELECTROSTATICS GIST Electrostatics is the study of charges at rest. Charging a body can be done by friction, induction and conduction. Properties of charges: o Like charges repel and unlike charges attract. o Charges are additive in nature i.e., Q= 𝑛𝑖=1 𝑞𝑖 o Charges are quantized. i.e., Q= ± ne [n=1,2,3,… & e=1.602 X1019 C] o Charge in a body is independent of its velocity. o Charge is conserved. To measure charge electroscopes are used. The sensitive device which is used to identify whether the body is charged or not is called electroscope.
Coulomb’s law: 𝐹 =
𝑘𝑞 1 𝑞 2 𝑟2
𝑟; k=
1
4𝜋𝜀 0
= 9 x 109 Nm2C2
Where, 𝜀0 = absolute permittivity of free space Principle of superposition: 𝐹𝑡𝑜𝑡𝑎𝑙 = sum of individual forces] qq qq 1 122 r12 1 123 r13 .... 4 r12 4 r13
𝑛 𝑖=1 𝐹𝑖
Q1Q2<0
1/r2
Q1Q2>0
[vector F
1/r 2
F
E
Q
E
Note: In the above triangle the quantity shown at the vertex, could be arrived by multiplying the quantities shown at the base, ie F=E X Q. Any one of the quantity shown at the base is given by the ratio of the quantities shown at vertex & the other quantity shown at the base, ie E=F/Q or Q= F/E. Electric field: Force experienced by a unit positive (or test) charge. It is a vector. SI unit is NC1. E
7
r
2
Applications of Gauss’ theorem for uniform charge distribution: Expression for Flux ∅
Infinite Linear 𝜆𝑙 𝜀0 𝜆 Magnitude of 2𝜋𝑟𝜀0 Field E
Charge density
𝜆=
∆𝑞 ∆𝑙
Infinite plane Thin spherical shell sheet 𝜎𝑠 𝜎4𝜋𝑟 2 𝜀0 𝜀 0
𝑄 4𝜋𝑟 2 𝜀0
𝜎 𝜀0
𝜎=
[for points on/outside the
shell] ZERO [for points inside the shell] 𝜎 4𝜋𝑟 2
∆𝑞 ∆𝑆
Properties of electric field lines: Arbitrarily starts from +ve charge and end at –ve charge Continuous, but never form closed loops Never intersect Relative closeness of the field lines represents the magnitude of the field strength. For a set of two like charges – lateral pressure in between For a set of two unlike charges – longitudinal contraction in between. Electrostatic Potential: Work done per unit positive Test charge to move it from infinity to that point in an electric field. It is a scalar. SI unit: J/C or V V = W / qo Electric potential for a point charge: 𝑉 =
8
𝑘𝑞 𝑟
Electric field is conservative. This means that the work done is independent of the path followed and the total work done in a closed path is zero.
Potential due to a system of charges: v
total
in1 kqi ri
Potential due to a dipole at a point
on its axial line: 𝑉𝑎𝑥𝑖𝑎𝑙 =
on its equatorial line:𝑉𝑒𝑞 = 0
Potential difference
𝑉𝐴 − 𝑉𝐵 = 𝑘𝑞 [
Potential energy of two charges:
U=
𝑘𝑝 𝑟2
𝑘𝑝
[or]
𝑟2
𝑐𝑜𝑠𝜃 1 𝑟𝐴
1
− ] 𝑟𝐵
𝑘𝑞1 𝑞2 𝑟
Potential energy of a dipole : U = 𝑝. 𝐸 = p E [𝑐𝑜𝑠𝜃0 𝑐𝑜𝑠𝜃1 ] Electrostatics of conductors (i) Inside a conductor Electrostatic field is zero (ii) On the surface E is always Normal (iii) No charge inside the conductor but gets distributed on the surface (iv) Charge distribution on the surface is uniform if the surface is smooth (v) Charge distribution is inversely proportional to ‘r’ if the surface is uneven (vi) Potential is constant inside and on the surface Equipotential surfaces: The surfaces on which the potential is same everywhere. Work done in moving a charge over an equipotential surface is zero. No two equipotential surfaces intersect. Electric field lines are always perpendicular to the equipotential surfaces.
As E=
𝑑𝑉 𝑑𝑟
1
If Vis constant, E∝ and if E is constant, V∝ 𝑟 𝑟
Capacitor: A device to store charges and electrostatic potential energy. 9
Q , Ratio of charge and potential difference. Scalar, V
Capacitance: C
SI unit: farad [F]
Capacitance of a parallel plate capacitor: 𝐶 =
𝜀0 × 𝐴 𝑑
Capacitance of a parallel plate capacitor with a dielectric medium in between: 𝜖𝑜 𝐴
Cm =
If t=0 =>C0 =
If t=d =>C0 =k
𝑡
(𝑑−𝑡+𝑘) 𝜖𝑜 𝐴 (𝑑) 𝜖𝑜 𝐴 (𝑑)
=>Cm = k C0
Cm
Combination
Co
of 1 c
k
capacitors:
n
1 i 1 ci
Capacitors in series:
n
Capacitors in parallel : c ci i 1
1 2
1 2
Energy stored in capacitors: U CV 2 QV
Area shaded in the graph = U = 𝑄𝑉
1 Q2 2 C
V
1 2
1
𝜎2
2
2𝜀0
Energy density :𝑈𝑑 = 𝜀0 𝐸 2 =
Introducing dielectric slab between the plates of the charged capacitor with: 10
Q
Property Charge Potential difference Electric field Capacitance
Battery connected K Q0
Battery disconnected Q0
V0
V0/K
E0
E0/K
KC0
KC0 1
Energy
1/K times 𝜀0 𝐸 2 [Energy
supplied By battery]
used for Polarization]
2
2
On connecting two charged capacitors: Common Potential: Loss of energy: ∆𝑈 =
1
K times 𝜀0 𝐸 2 [Energy is
𝑉= 1 𝐶1 ×𝐶2 2 𝐶1 +𝐶2
𝐶1 𝑉1 +𝐶2 𝑉2 𝑉1 +𝑉2
(𝑉1 − 𝑉2 )2
Van de Graff generator: isan electrostatic machine to build very high voltages. 1
1
works on the Principle𝑉(𝑟) − 𝑉(𝑅) = 𝑘𝑞 ( − ) 𝑟 𝑅 Corona discharge is the electrical discharge through the defected part of the spherical conductor, where the surface is not smooth. Hence, the hollow spherical conductor in the Van de Graff generator should have a smooth outer surface.
CONCEPT MAP
Electric Force/Field/Potential/P.E.
11
(Unit N/C or V/m)
(Unit : N)
𝐹=𝑘
𝑞1 𝑞2 𝑟2
𝐸=𝑘
𝑈=𝑘
𝑞1 𝑞2 𝑟
𝑉=𝑘
12
𝑞1 𝑟2
𝑞1 𝑟
CONCEPT MAP
Charge and it’s impact
CHARGES AND COULOMB’S LAW 13
1.
2.
3. 4.
5.
6.
7.
QUESTIONS What is the work done in moving a test charge ‘q’ through a distance of 1 cm along the equatorial axis of an electric dipole? [ Hint : on equatorial line V=0 ] Why in Millikan’s Oil Drop experiment, the charge measured was always found to be of some discrete value and not any arbitrary value? Ans: Because charge is always quantized ie., Q = n x e What is meant by electrostatic shielding? Ans: Electric filed inside a cavity is zero. Why an electric dipole placed in a uniform electric field does not undergoes acceleration? Ans: Because the net force on the dipole is zero. Fnet = 0 as F=±𝑞𝐸 Why electric field lines (i) Can never intersect one another? (ii) Cannot for closed loops sometimes? (iii) Cannot have break in between? Ans : Because (i) Electric field has an unique direction at any given point (ii) Monopoles or single isolated charges exist unlike magnetism (iii) Start from +ve charges and terminate at –ve charges (iv) Show that at a point where the electric field intensity is zero, electric potential need not be zero. Ans: If E = 0⇒ 𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 E=dV/dr What is the electric flux through the surface S in Vaccum?
1 1
1 1
1
2
2
8.
Write the expression for the electric field, charge density for a uniformly 2 charged thin spherical shell. 𝑘𝑄 𝑄 Ans: 𝐸= 2 ;𝜎 = 2 𝑟
9.
I
+σ
II
4𝜋𝑟
σ
III 14
2
10.
Write the expression for the electric field in the regions I, II, III shown in the above figure. Ans: EI =EIII = 0 EII = σ/ε0 Two free protons are separated by a distance of 1 Ao. if they are released, what is the kinetic energy of each proton when at infinite separation.[ 2 𝑒2 Hint : at inifinte distance 𝐾. 𝐸 = ] 4𝜋𝜖𝑜 𝑟
11.
12.
13.
14.
15.
How does the electric flux, electric field enclosing a given charge vary when the area enclosed by the charge is doubled? Ans: (a) ∅= constant (b) E is halved The electric field in a certain region of space is 𝐸 = 104𝑖𝑁𝐶 −1 . How much is the flux passing through an area ‘A’ if it is a part of XY plane, XZ plane, YZ plane, making an angle 300 with the axis? Ans: ΦXY =10A Vm E ∆S COSφ [φ=0] φXZ= φYZ = 0 Vm (φ =90O) =104 A cos30 O Vm An electric dipole ±4µC is kept at coordinate points (1, 0, 4) are kept at (2,1, 5), the electric field is given by 𝐸 = 20 𝑖 NC1. Calculate the torque on the dipole. Ans: Calculate first dipole moment using 𝑝 =q.2𝑎 Then calculate torque using 𝜏 = 𝑝 × 𝐸 and hence find 𝜏 =13.4 N Show diagrammatically the configuration of stable and unstable equilibrium of an electric dipole ( p ) placed in a uniform electric field ( E ). Ans:
p
p
E
E
Stable Unstable Plot a graph showing the variation of coulomb force 1 F versus 2 where r is the distance between the two 𝑟 charges of each pair of charges: (1μC, 2μC) and (2μC, 3μC) Interpret the graphs obtained. [Hint : graph can be drawn choosing –ve axis for force only] Ans: 𝑭𝑩  > 𝑭𝑨  15
2
2
2
2
A 1/r2
B F
2
16.
A thin straight infinitely long conducting wire having charge density 𝜆 is enclosed by a cylindrical surface of radius r and length l, its axis 2 coinciding with the length of the wire. Find the expression for electric flux through the surface of the cylinder. 𝜆𝑙 Ans: Using Gauss’s Law obtain: Φ = 𝜀0
17.
Calculate the force between two alpha particles kept at a distance of 2 0.02mm in air. 𝟐
Ans: 𝑭 = 𝟗 × 18.
19.
20.
𝟒×(𝟏.𝟔×𝟏𝟎−𝟏𝟗 ) 𝟏𝟎𝟗 𝟐 (𝟐×𝟏𝟎−𝟓 )
Explain the role of earthing in house hold wiring. 2 Ans: During short circuit, it provides an easy path or emergency way out for the charges flowing to the ground, preventing the accidents. What is the difference between charging by induction and charging by 2 friction? * In frictional method, transfer of charges takes place from one object to the other. * During induction, redistribution of charges takes place within the conductor. Two electric charges 3μC, 4μC are placed at the two corners of an isosceles right angled triangle of side 1 m as shown in the figure. What is the direction and magnitude of electric field at A due to the two charges? A
2 Ans: E=45×〖10〗^3 NC^(1) θ=36.9° from line AB B 4μC
21.
22.
23.
C 1m
3μC
A sensitive instrument is to be shifted from a strong electric field in its environment. Suggest a possible way. 2 [ Hint : Electrostatic shielding ] A charge +Q fixed on the Y axis at a distance of 1m from the origin and another charge +2Q is fixed on the X axis at a distance of √2 m from the origin. A third charge – Q is placed at the origin. What is the angle at 3 which it moves? Ans: Force due to both the changes are equal = KQ2& r to each other so the resultant force will make 45o with Xaxis. Two charges 5µC, 3µC are separated by a distance of 40 cm in air. Find 3 the location of a point on the line joining the two charges where the 16
electric field is zero. Ans: Solve for x from the equation: k 24.
25.
5𝑋10−6 𝑥2
=k
3𝑋10−6 (40−𝑥)2
Deduce Coulomb’s law from Gauss’ law. Ans:∅=E .S =Q/ε0 E×4πr2=Q/ε0 3 2 F=Eq0∴F=〖Qqo/(4πε0 r ) State Gauss’s law and use this law to derive the electric filed at a point 3 from an infinitely long straight uniformly charged wire. Ans: Statement E.ds
q Derivation for E =
2 r
26.
Three charges –q, Q and –q are placed at equal distances on a straight line. If the potential energy of system of these charges is zero, then what is the ratio of Q:q [ Ans : 1:4 ] ELECTRIC POTENTIAL 1.
2.
3.
3
Is it possible that the potential at a point is zero, while there is finite 1 electric field intensity at that point? Give an example. Ans: Yes , Centre of a dipole Is it possible that the electric field 𝐸 at a point is zero, while there is a 1 finite electric potential at that point. Give an example. Ans: Yes, Inside charged shell Can two equipotential surfaces intersect? Justify your answer. 1 Ans: No. Otherwise it would mean two directions for force at a point.
4.
Is potential gradient a vector or a scalar quantity? Ans: Scalar quantity
5.
Write the dimensional formula of ‘є0 ‘the permittivity of free space. 1 1 3 4 2 Ans: [M L T A ] An electric dipole is placed in an electric field due to a point charge. 1 Will there be a force and torque on the dipole? Ans: Yes, Both force and torque will act as the Electric Field is non uniform. Draw the graph showing the variation of electric potential with 1 distance from the centre of a uniformly charged shell.
6.
7.
17
1
An s V r
8.
9.
Distance
Find the ratio of the electric field lines starting from a proton kept first 1 in vacuum and then in a medium of dielectric constant 6. Ans: 6 : 1 Calculate the electric field from the equipotential surface shown 1 below. 2m 2V vV 3m
4V
6V
4m
Ans: 2 V [ E
dv , dv 2V , dr 1m] dr
10. Sketch the electric field lines, when a positive charge is kept in the 1 vicinity of an uncharged conducting plate. Ans +q

11.
  Find dipole moment. Two charges are kept as shown.
1
Ans: (0,0,2)q ……………. +q(0,0,2) 15 µc +15 µc 12. Compare the electric flux in a cubical surface of side 10 cm and a 1 spherical surface of radius 10 cm, when a change of 5µC is enclosed by them. 18
13.
14.
15.
16.
An s
Ans: Electric flux will be same in both the cases. Explain why the electric field inside a conductor placed in an external electric field is always zero. Ans: Charge lies on the surface of a conductor only Two identical metal plates are given positive charges Q1 and Q2,where Q1> Q2. Find the potential difference between them, if they are now brought together to form a parallel plate capacitor with capacitance Ans: (Q1 – Q2)/2C 27 small drops of mercury having the same radius collage to form one big drop. Find the ratio of the capacitance of the big drop to small drop. Ans: [3:1] A uniformly charged rod with linear charge density λ of length L is inserted into a hollow cubical structure of side ’L’ with constant velocity and moves out from the opposite face. Draw the graph between flux and time.
1
2
2
2
ø
O
time
17. Draw a graph showing the variation of potential with distance from the 2 positive charge to negative charge of a dipole, by choosing the midpoint of the dipole as the origin. An 2 V s
d
18. If 𝐸 = 3𝑖 +4𝑗5𝑘̂, calculate the electric flux through a surface of area 50 2 units in zx plane Ans: 200 unit 19. Name the physical quantities whose SI units are Vm, Vm1. Which of 2 these are vectors? Ans: Vm → electric flux, scalar ; Vm1→electric field, vector 20. The spherical shell of a Van de Graff generator is to be charged to a 2 19
potential of 2 million volt. Calculate the minimum radius the shell can have, if the dielectric strength of air is 0.8 kV/mm. Ans: [2.5m] 21. How will you connect seven capacitors of 2µf each to obtain an 2 effective capacitance of 10/11 µf. Ans: 5 in parallel and 2 in series 22. A proton moves with a speed of 7.45 x 105m/s directly towards a free 2 proton initially at rest. Find the distance of the closest approach for the two protons. Ans: 5.56 x 1023m 23. Three point charges of 1C, 2C & 3C are placed at the corners of an 2 equilateral triangle of side 1m. Calculate the work done to move these charges to the corners of a smaller equilateral triangle of sides 0.5m.
2C
3C
10
Ans: 9.9 x 10 J 2 24. Suggest an arrangement of three point charges, +q,+q, q separated by finite distance that has zero electric potential energy
25
A point charge Q is placed at point O as shown. Is the potential difference ( VAVB) positive, negative or zero if Q is (i) positive (ii) negative
2
26. Show that the potential of a charged spherical conductor, kept at the 3 centre of a charged hollow spherical conductor is always greater than that of the hollow spherical conductor, irrespective of the charge accumulated on it. Ans: VaVb=(q/4πє) (1/r1/R) 20
1C
(Principle of Van de Graff generator) CAPACITORS 1
2
3
What happens to the capacitance of a capacitor when a copper plate 2 of thickness one third of the separation between the plates is introduced in the capacitor? Ans: 1.5 times Co A parallel plate capacitor is charged and the charging battery is then 2 disconnected. What happens to the potential difference and the energy of the capacitor, if the plates are moved further apart using an insulating handle? Ans: Both Increases Find the equivalence capacitance between X and Y. 2 X 3 μf
4
5.
6.
3 μf
3 μf
Y
Ans: 9 μf A pith ball of mass 0.2 g is hung by insulated thread between the 2 plates of a capacitor of separation 8cm. Find the potential difference between the plates to cause the thread to incline at an angle 150 with the vertical, if the charge in the pith ball is equal to 107C. Ans: 429 V Find the capacitance of arrangement of 4 plates of Area A at distance 2 d in air as shown.
What is an equivalent capacitance of the arrangement the shown 3 below
21
7.
8.
9.
10.
If 6V cell is connected across AD. Calculate the potential difference between B&C. A parallel plate capacitor is charged to a potential difference V by d.c. source and then disconnected. The distance between the plates is then halved. Explain with reason for the change in electric field, capacitance and energy of the capacitor. Ans: Use the formulae  Electric field remains same, Capacitance doubled, Energy halved Derive an expression for capacitance of parallel plate capacitor, when a dielectric slab of dielectric constant k is partially introduced between the plates of the capacitor. A potential difference of 1200 V is established between two parallel plates of a capacitor. The plates of the capacitor are at a distance of 2 cm apart. An electron is released from the negative plate, at the same instant, a proton is released from the +ve plate. (a)How do their (i) velocity (ii) Energy compare, when they strike the opposite plates. (b) How far from the positive plate will they pass each other? Ans a. (i)42.84 (ii)equal b. 2.7cm Draw a graph to show the variation of potential applied and charge stored in a capacitor. Derive the expression for energy stored in a parallel plate capacitor from the capacitor.
3
3
3
3
V
q
11.
Find the capacitance of a system of three parallel plates each of area A 2 m2 separated by d1 and d2 m respectively. The space between them is filled with dielectrics of relative dielectric constant є1 and є2. 22
12.
13.
14.
Two parallel plate capacitors A and B having capacitance 1µF and 5 µF 3 are charged separately to the same potential 100V. They are then connected such that +ve plate of A is connected to –ve plate of B. Find the charge on each capacitor and total loss of energy in the capacitors. Ans: 400µC, 500µC and 5/3 x 10J Calculate the capacitance of a system having five equally spaced 3 plates, if the area of each plate is 0.02 m2 and the separation between the neighboring are 3 mm. in case (a) and (b)
Ans: (Hint: Capacitance of a parallel plate capacitor εoA/d ) 1.18 x 104 μ F and 2.36 x 10 μ F Net capacitance of three identical capacitors in series is 1μf. What will 2 be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations, if they are both connected to the same source. Ans: 9μf 1:9 15. Two parallel plate capacitors X and Y have the same area of plates and the same separation between them. X has air between the plates and Y contains a dielectric medium of εr=4. Calculate Capacitance of X and Y if equivalent capacitance of combination is 4 µF. (i) Potential Difference between the plates of X and Y (ii) What is the ration of electrostatic energy stored in X and Y [ Ans : 5 µF, 20 µF, 9.6 V, 2.4 V, 4:1 ]
VALUE BASED QUESTIONS 23
1. Saanvi has dry hair. A comb ran through her dry hair attract small bits of paper. She observes that Chinju with oily hair combs her hair; the comb could not attract small bits of paper. She consults her teacher for this and gets the answer. She then goes to the junior classes and shows this phenomenon as Physics Experiment to them. All the juniors feel very happy and tell her that they will also look for such interesting things in nature and try to find the answers .she succeeds in forming a Science Club in her school. How can you explain the above experiment? What according to you are the values displayed Saanvi?
2. Sneha’s mother who was illiterate was folding her synthetic saree. She saw a spark coming out of it .She got frightened and called Sneha. Sneha being a science student gave the reason behind it. After knowing the reason her mother calmed down. What is the reason for the spark? What value was displayed by Sneha?
24
2. CURRENT ELECTRICITY GIST Current carriers – The charge particles which flow in a definite direction constitutes the electric current are called current carriers. e.g.: Electrons in conductors, Ions in electrolytes, Electrons and holes in semiconductors. Electric current is defined as the amount of charge flowing through any cross section of the conductor in unit time. I = Q/t. Current density J = I/A. Ohm’s law: Current through a conductor is proportional to the potential difference across the ends of the conductor provided the physical conditions such as temperature, pressure etc. Remain constant. V α I i.e. V = IR, Where R is the resistance of the conductor. Resistance R is the ratio of V & I Resistance is the opposition offered by the conductor to the flow of current. Resistance R = ρl/A where ρ is the resistivity of the material of the conductor length and A area of cross section of the conductor. If l is increased n times, new resistance becomes n2R. If A is increased n times, new resistance becomes
1 R n2
Resistivity ρ = m/ne2τ, Where m, n, e are mass, number density and charge of electron respectively, τrelaxation time of electrons. ρ is independent of geometric dimensions. Relaxation time is the average time interval between two successive collisions Conductance of the material G =1/R and conductivity σ=1/ρ Drift velocity is the average velocity of all electrons in the conductor under the influence of applied electric field. Drift velocity Vd = (eE/m)τ also I = neAvd Mobility (μ) of a current carrier is the ratio of its drift velocity to the applied field
Vd E
Effect of temperature on resistance: Resistance of a conductor increase with the increase of temperature of conductor RT Ro (1 T ) , where α is the temperature coefficient of resistance of the conductor. α is slightly positive for metal and conductor, negative for semiconductors and insulators and highly positive for alloys.
Combination of resistors: Rseries R1 R2 ...Rn ,
25
1 RParallel
1 1 1 ... R1 R2 Rn
Cells: E.M.F of a cell is defined as the potential difference between its terminals in an open circuit. Terminal potential difference of a cell is defined as the potential difference between its ends in a closed circuit. Internal resistance r of a cell is defined as the opposition offered by the cell to the flow of current. r = 1 R E V
where R is external resistances.
Grouping of cells : nE , R nr mE ii) In parallel grouping circuit, current is given by I p where n, m are r mR
i) In series grouping circuit, current is given by I s
number of cells in series and parallel connection respectively. Kirchhoff’s Rule: i) Junction Rule:The algebraic sum of currents meeting at a point is zero.
I 0
ii) Loop rule:The algebraic sum of potential difference around a closed loop is zero V o Wheatstone bridge is an arrangement of four resistors arranged in four arms of the bridge and is used to determine the unknown resistance in terms of other three resistances. For balanced Wheatstone Bridge,
P R Q S
Wheatstone bridge is most sensitive when the resistance in the four arms are of the same order In the balanced condition of the bridge on interchanging the positions of galvanometer and battery if there is no effect on the balancing length of the bridge. Slide Wire Bridge or Metre Bridge is based on Wheatstone bridge and is used to measure unknown resistance. If unknown resistance S is in the right gap, 100 l s R l
Potentiometer is considered as an ideal voltmeter of infinite resistance. Principle of potentiometer: The potential drop across any portion of the uniform wire is proportional to the length of that portion of the wire provided steady current is maintained in it i.e. v α l Smaller the potential gradient greater will be the sensitivity of potentiometer. Potentiometer is used to (i) compare the e.m.f.s of two cells (ii) determine the internal resistance of a cell and (iii) measure small potential differences. 26
Expression for comparison of e.m.f of two cells by using potentiometer,
1 l1 where l1 , l2 are the balancing lengths of potentiometer wire for e.m.fs 1 2 l2
and 2 of two cells. Expression for the determination of internal resistance of a cell I is given by l1 l2 R l2
Where l1 is the balancing length of potentiometer wire corresponding to e.m.f of the cell, l2 that of terminal potential difference of the cell when a resistance R is connected in series with the cell whose internal resistance is to be determined
Expression for determination of potential difference V
rl . Where L Rr L
is the length of the potentiometer wire, l is balancing length, r is the resistance of potentiometer wire, R is the resistance included in the primary circuit. Joule’s law of heating states that the amount of heat produced in a conductor is proportional to (i) square of the current flowing through the conductor,(ii) resistance of the conductor and (iii) time for which the current is passed. Heat produced is given by the relation H=I2Rt Electric power: It is defined as the rate at which work is done in maintaining the current in electric circuit. P =VI = I2R =V2/R. Power P is the product of V & I Electrical energy: The electrical energy consumed in a circuit is defined as the total work done in maintaining the current in an electrical circuit for a given time. Electrical energy = VIt = I2Rt =(V2/R)t = Pt Commercial unit of energy 1KWh= 3.6×106J Colour coding : Black Brown Red OrangeYellowGreenBlue Violet Gray White 0 1 2 3 4 5 6 7 8 9 Tolerance (i) Gold 5% (ii) Silver 10% (iii) No Color 20% Example: if colour code on carbon resister is Red Yellow and Orange with tolerance colour as silver, the resistance of the giveresister is (24×103 ± 10%)Ω.
27
CONCEPT MAP
Flow of Charges
28
QUESTIONS DRIFT VELOCITY, CURRENT, POTENTIAL DIFFERENCE, OHM’S LAW AND RESISTANCE 1. How does the drift velocity of electrons in a metallic conductor vary with increase in temperature? Ans. remains the same 2. Two different wires X and Y of same diameter but of different materials are joined in series and connected across a battery. If the number density of electrons in X is twice that of Y, find the ratio of drift velocity of electrons in the two wires. Ans: Vdx/Vdy = ny/nx = ½ 3. A 4Ω non insulated wire is bent in the middle by 1800 and both the halves are twisted with each other. Find its new resistance? Ans: 1Ω 4. Can the terminal potential difference of a cell exceed its emf? Give reason for your answer. Ans: Yes, during the charging of cell. 5. Two wires of equal length one of copper and the other of manganin have the same resistance. Which wire is thicker? Ans: Manganin. 6. The VI graph for a conductor makes angle Ѳ with V axis, what is the resistance of the conductor? Ans: R = Cot Ѳ
(1)
(1)
(1)
(1)
(1)
(1)
(1)
7. It is found that 1020 electrons pass from point X towards another point Y in 0.1s. How much is the current & what is its direction? Ans: 160A; from Y to X 8. Two square metal plates A and B are of the same thickness and material. The side of B is twice that of side o fA. If the resistance of A and B are denoted by RA and RB, find RA/ RB. Ans: 1
(1)
(1)
29
9*. The VI graph of two resistors in their series combination is shown. Which one of these graphs shows the series combinations of the other two? Give reason for your answer. I Ans: 1 V 10. Plot a graph showing the variation of conductivity with the temperature T in a metallic conductor. (Ans: see fig1) R
T
(2)
D
Fig 1 fig2 11. Draw a graph to show the variation of resistance R of the metallic wire as a function of its diameter D keeping the other factor constant. (Ans: see fig2) 12. Two conducting wires X and Y of same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ratio of drift velocity of electrons in the two wires. (Ans: I nvd i.e. Vdx/Vdy = ny/nx = ½) 13 A pd of 30V is applied across a colour coded carbon resistor with rings of blue, black and yellow colours. What is the current to the resistor? Ans: R = 60 × 104Ω , I= 5× 105A 14. A nonconducting ring of radius r has charge q distribute over it. What will be the equivalent current if it rotates with an angular velocity ω? Ans: I= q/t = qω/2π. 15.* Two cells each of emf E and internal resistances r1 and r2 are connected in series to an external resistance R. Can a value of R be selected such that the potential difference of the first cell is 0. Ans: I = 2Ɛ/(R + r1 + r2) Potential diff. for first cell V1 = Ɛ – I r1 = 0 Ɛ = (2 Ɛ r1)/R + r1 + r2 Solving these we get, R = r1  r2 16. Why does Resistance increase in series combination and decrease in parallel combination 30
(2)
(2) (2)
(2)
(2)
Ans: Effective length increases in series combination (R α l). In parallel combination area of cross section increases (R α 1/A) 17. A piece of silver wire has a resistance of 1Ω. What will be the resistance of the constantan wire of one third of its length and one half of its diameter if the specific resistance of the constantan wire is 30 times than that of the silver? Ans: 40Ω 18. Calculate the current shown by the ammeter in the circuit in fig 1
(2)
(2)
5Ω 10Ω 10Ω 10Ω
10Ω + A
5Ω
I(A) 5 0
5
t(s)
10
10V
Fig 1. Fig 2. Ans: R = 2Ω and I = 5A 19. The plot in fig 2 given above shows the variation of current I through the cross section of a wire over a time interval of 10s. Find the amount of charge that flows through the wire over this time period. Ans: Area under the It graph, q = 37.5C 20. Find the resistance between the points (i) A and B and (ii) A and C in the following network 10Ω
10Ω
10Ω
A
B 10Ω
10Ω
Ans: (i) RAB = 27.5Ω C
D
10Ω
10Ω
10Ω
31
(ii) RAC = 30Ω
(2)
(2)
21. Two wires of the same material having lengths in the ratio 1:2 and diameter 2:3 are connected in series with an accumulator. Compute the ratio of p.d across the two wires Ans: R = ρl/A = 4ρl/πd2 RA/RB = 9/8 VA/VB = IARA/IBRB = 9/8 22. 4 cells of identical emf E1, internal resistance r are connected in series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with the current output. (i)What is the emf of each cell used? (ii)For what current from the cells, does maximum power dissipation occur in the circuit? (iii)Calculate the internal resistance of each cell
(2)
(3)
Ans: 4E = 5.6 E = 1.4 V When I = 1A, V = 2.8/4 = 0.7V Internal resistance, r= (E – V)/I = 0.7Ω The output power is maximum when internal resistance = external resistance = 4r.Imax = 4E/ (4r +4r) = 1A
23.* An infinite ladder network of resistances is constructed with 1Ω and 2Ω resistances shown. A 6V battery between A and B has negligible resistance. (i) Find the effective resistance between A and B.
(3)
Ans: Since the circuit is infinitely long, its total resistance remains unaffected by removing one mesh from it. Let the effective resistance of the infinite network be R, the circuit will be
𝑅=
2𝑅 𝑅+2
+ 1
𝑅 = 2Ω
24. The resistance of a tungsten filament at 150°C is 133Ω. What will be its resistance at 5000C? The temperature coefficient of tungsten is 0.00450C1 at 00C. Ans: Use Rt = R0 (1+ α t) R500 = 258Ω
32
(3)
25. The circuit shown in the diagram contains two identical lamps P and Q. (3) What will happen to the brightness of the lamps, if the resistance Rh is increased? Give reason. Ans: Brightness of P and Q decrease and increase respectively. 26. A battery has an emf E and internal resistance r. A variable resistance R is connected across the terminals of the battery. Find the value of R such that (a) the current in the circuit is maximum (b) the potential (3) difference across the terminal is maximum. (c)Plot the graph between V and R Ans: (a) I = Ɛ / (r + R) I = Imax when R =0 Imax = Ɛ /r (b)V = Ɛ R/(r + R) = Ɛ /(r/R + 1) V = Vmax when r/R + 1= minimum, r/R = o, V= Ɛ (c) V R
II. KIRCHHOFF’S RULE AND APPLICATIONS 1. Using Kirchhoff’s laws, calculate I1, I2 andI3 Ans: I1 = 48/31A I2 = 18/31A I3 = 66/31A 2. In the circuit, find the current through the 4Ω resistor.
(3)
(3) (3)
Ans: I = 1A III. WHEATSTONE BRIDGE AND POTENTIOMETER 1. The emf of a cell used in the main circuit of the potentiometer should be (1) more than the potential difference to be measured. Why? 2. The resistance in the left gap of a metre bridge is 10Ω and the balance point (1) is 45cm from the left end. Calculate the value of the unknown resistance. Ans S = 12.5Ω 3. How can we improve the sensitivity of a potentiometer? (1) 4. Why is potentiometer preferred over a voltmeter (1) 5. Write the principle of (2) 33
(i) a meter bridge. (ii) a potentiometer. 6. How does the balancing point of a Wheatstone bridge get affected (2) i) Position of cell and Galvanometer are interchanged? ii) Position of the known and unknown resistances is interchanged? 7. Explain with a neat circuit diagram, how will you compare emf of two cells using a potentiometer? 8. With the help of a circuit diagram, describe the method of finding the internal resistance of the Primary Cell using a potentiometer. (3) 9. With the help of a neat circuit diagram describe the method to determine the potential difference across the conductor using a potentiometer. (3) 10. Calculate the current drawn from the battery in the given network. Ans: I = 2A
11. Find the value of X and current drawn from the battery of emf 6V of (3) negligible internal resistance Ans: X = 6Ω and I = 1A
12. Find the value of the unknown resistance X and the current drawn by the circuit from the battery if no current flows through the galvanometer. Assume the (3) resistance per unit length of the wire is 0.01Ωcm1.
Ans: X = 3Ω 13. In the circuit shown, AB is a resistance wire of uniform cross – section in (3) which a potential gradient of 0.01V cm1 exists. (a)If the galvanometer G shows zero deflection, what is the emf Ɛ1 of the cell used? 34
(b)If the internal resistance of the driver cell increases on some account, how will it affect the balance point in the experiment? Ans: (a) PD VAB = 1.8 V (b) Balance pt. will shift towards B since V/l decreases. 14.* In a potentiometer circuit, a battery of negligible internal resistance is set up as shown to develop a constant potential gradient along the wire AB. Two cells of emfs Ɛ 1 and Ɛ 2 are connected in series as shown in the combination (1) and (2). (3) The balance points are obtained respectively at 400cm and 240cm from the point A. Find (i) Ɛ 1/ Ɛ 2 and (ii) balancing length for the cell Ɛ 1 only.
Ans : Ɛ 1 + Ɛ 2 α 400, Ɛ 1 Ɛ 2 α 240,Solving Ɛ 1/ Ɛ 2 = 4, Ɛ 1 α l1, (Ɛ1 + Ɛ 2)/ Ɛ 1= 400/l1 , l1 = 320cm 15.* A potentiometer wire of length 100cm having a resistance of 10Ω is connected in series with a resistance and cell of emf 2V of negligible internal (3) resistance. A source emf of 10mV is balanced against a length of 40cm of potentiometer wire. What is the value of the external resistance? Ans: I = E/(R + 10) = (2/R + 10) Resistance of 40cmwire is 4Ω. At J, (2/R +10) x 4 = 10 x 103 R = 790Ω 16.* In the potentiometer circuit shown, the balance point is at X. State with reason where the balance point will be shifted when (i)Resistance R is increased, keeping all parameters unchanged. (ii)Resistance S is increased keeping R constant. (iii)Cell P is replaced by another cell whose emf is lower than that of that cell Q. Ans: (i) As R is increased V/l will decrease hence X will shift towards B. (ii)No effect (iii) Balance point is not found. 35
(3)
17.* A potentiometer wire has a length L and resistance R0. It is connected to a (3) battery and a resistance combination as shown. Obtain an expression for the potential difference per unit length of the potentiometer wire. What is the maximum emf of a ‘test cell’ for which one can get a balance point on this potentiometer wire? What precautions should one take while connecting this test cell to the circuit?
Ans: Total resistance of potentiometer wire R = R0 + RS/(R+S) Current in the circuit I = E/ (R0 + (RS/R+S)) Total potential difference across AB V = I R0 = E R0/ (R0 + (RS/R+S)) Therefore, PD per unit length is V/L = E R0/L (R0 + (RS/R+S)) Max emf of a test cell should be less than V. Precaution: Positive terminal of the test cell must be connected to positive terminal of the battery. 18. The variation of potential difference V with length l in case of two potentiometers X and Y as shown. Which one of these will you prefer for comparing emfs of two cells and why?
(3)
Ans : The potentiometer Y is preferred, as it has low potential gradient (V/l) 19. Two cells of emfs Ɛ1 and Ɛ2 (Ɛ1> Ɛ2) are connected as shown in figure When a potentiometer is connected between A and B, the balancing length of the potentiometer wire is 300cm. On connecting the same potentiometer between A and C, the balancing length is 100cm. Calculate the ratio of Ɛ1 and Ɛ2. Ans: Ɛ1 α 300, Ɛ 1 – Ɛ 2 α 100, Ɛ1/Ɛ2 = 3/2 IV. ELECTRIC ENERGY AND POWER 1. What is the largest voltage you can safely put across a resistor marked 98Ω (1)
0.5W? 36
2.
Which lamp has greater resistance (i) 60W and (ii) 100W when connected to
the same supply? Ans: R = V2/P, 3.
(1)
R α 1/P, 60 lamp has more resistance
Nichrome and Cu wires of the same length and same diameter are
connected in series in an electric circuit. In which wire will the heat be produced at (2)
a higher rate? Give reason. Ans: P = I2R 4.*
P α R Heat produced is higher in Nichrome wire.
An electric bulb rated for 500W at 100V is used in circuit having a 200V
supply. Calculate the resistance R that must be put in series with the bulb, so that (2)
the bulb delivers 500W. Ans:
Resistance of bulb=V2/P = 20Ω, I = 5A, for the same power dissipation,
current should be 5A when the bulb is connected to a 200V supply. The safe resistance R’ = V’/I = 40Ω. Therefore, 20Ω resistor should be connected in series. 5.
Two bulbs are marked 220V100W and 220V50W. They are connected in
series to 220V mains. Find the ratio of heat generated in them.
(2)
Ans: H1/H2 = I2R1 /I2R2 = R1/ R2= ½ 6.*
Can a 30W, 6V bulb be connected supply of 120V? If not what will have to (3)
be done for it? Ans: Resistance of bulb R= V2/P = 36/30 = 1.2Ω
Current capacity of the bulb I =
P/V = 5A A resistance R’ to be added in series with the bulb to have current of 5 A, I = V’/R + R’ =5, R’ = 22.8Ω VALUE BASED QUESTIONS: 1. Father and a son returned home completely drenched due to heavy rain. Father advised his son not touch any electrical units with wet hands for he may get a shock; In spite of this, on immediately entering the house, the son switches 37
on the light (supply voltage is 220 V) and gets a severe shock; He was fortunate not to get electrocuted. Father, who is a Biologist, told that when the skin is dry, resistance of a human body is 105 Ω; and when the skin is wet the body resistance is 1500 Ω. What is the lesson learnt by you? Calculate the current that flow through (I) a wet body and (II) a dry body. When will we have serious consequences dry skin or wet skin? Why? (Ans: to obey elders; b) Using, I = V/R (i) 147 mA; (ii) 2.2 mA.; c) wet skin – with 147mA, when the current flows, the result is fatal) 2. Based on the previous knowledge learnt in the class,two students of class XII( A and B) were asked to conduct an experiment in the laboratory using a meter bridgeone is made of Nichrome and the other one is made of Copper, of same length and same diameter of constant potential difference. The student A could not give explanation for not achieving the result whereas student B, could get the result and was also able to explain. What made student B to perform successfully? Give the formula to calculate the rate of heat production. (ANS: a) student B had concentrated in the class room teaching and also had studied again to remember what was taught; b) Refer NCERT Text book) 3. An old woman who had suffered from a heart stroke was taken to the hospital by her grandson who is in class XII. The grandson has studied in Physics that, to save a person who is suffering from a heart stroke, regular beating of the heart is to be restored by delivering a jolt to the heart using a defibrillator, whose capacity is 70 microfarad and charged to a potential of 5000V and energy stored in 875J; 200J of energy is passed through a person’s body in a pulse lasting 2 milliseconds. The old woman gets panicked and refuses to be treated by defibrillator. Her grandson then explains to her the process that would be adopted by medical staff and how the result of that would bring her back to normalcy. The woman was then treated and was back to normal What according to you, are the values displayed by the grandson? How much power is delivered to the body to save a person’s life from heart attack? 38
(ANS: (a)Presence of mind, Knowledge of subject, Concern for his grandmother, Empathy, Helping and caring; (b) Power = energy / time; = 200/2 x 103 = 100KW) 4. On our return from an excursion trip in our school, I noticed a bird sitting on a high voltage electric wire. I curiously noticed the bird and found to my surprise that the bird flew off after sometime without any electrical shock. This incident made me think of another incident that took place near my house last week where, a boy, who climbed to take a kite, got severe jolt of electric current. I immediately approached my school Physics teacher for an explanation. My teacher explained the effect of electrical current which I told my mother that evening. What are the values associated with the above incident? What would be the explanation given by the Physics teacher? (ANS: a) observation, eagerness to learn; b) both the legs of the bird are at same voltage and hence no current passes; to receive a shock there must be a potential difference between one part of the body and another; if a person hangs from a high voltage wire without touching anything else, he can be quite safe and would not feel shock) 5. Mrs Vasundhara left her car headlights on while parking. The car would not start when she returned. Seeing her struggle, Mohit went to her help. Not knowing much about cars, he ran and brought a mechanic Raju from a garage nearby. Raju realized that the battery had got discharged as the headlight had been left on for a long time. He brought another battery and connected its terminals to the terminals of the car battery to get the engine started. Once the engine was running, he disconnected this second battery. This is known as “JUMP STARTING”. Mrs. Vasundharathanked both Mohit and Raju for helping her. (a)What values did Mohit have? (b) A storage battery of emf 8.0 volts and internal resistance 0.5 ohm is being charged by a 120 volt DC supply using a series resistor of 15.5 ohms. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit? 39
ANS: a) Helpful, aware of his weakness, decision making ability b). I= E/(R+r) =(120 – 8.00) / (15.5 +0 .5) = 7 Amp. Terminal voltage V= E + Ir = 8.00 + 7 x 0.5 = 11.5 volt. The series resistor limits the current drawn from the external source . In its absence the current will be dangerously high. 6. Rahul and Rohit bought an electric iron. They had a 2 pin plug. Rahul was keen to start using the new iron with the 2 pin plug. However, Rohit insisted that they buy a 3 pin plug before using it. Rahul got angry. Rohit patiently explained the importance of using a 3 pin plug and the earthing wire. He said that if the metallic body of the iron came in contact with the live wire at 220 volts, they would get an electric shock. If earthed, the current would go to the earth and the potential of the metallic body would not rise. The iron would then be safe to use. Hearing Rohit, Rahul calmed down and agreed. (a) What values did Rahul and Rohit have? (b) Which has greater resistance – 1 K watt electric heater or 100 watt electric bulb, both marked 220 volts? ANS: (a) Rahul is enthusiastic and flexible, Rohit is patient, knowledgeable, assertive (b) R = V2 / P R α 1 / P Hence 100W bulb has greater resistance.
3.MAGNETIC EFFECTS OF CURRENT AND MAGNETISM GIST 1. Magnetic field:It is a region around a magnet or current carrying conductor in which its magnetic influence can be felt by a magnetic needle. BiotSavart Law: dB =μ0 IdlSinθ/4πr2 μ0=4π x 107 Tm/A 40
[Direction of dB can be found by using Maxwell’s Right hand thumb rule.] 2. Applications : 1. Magnetic field at a centre of a current carrying circular coil B= μ0I/2a 2. Magnetic field at a point on the axis of current carrying coil. B= μ0Nia2/2(a2+x2)3/2 (N=no. of turns in the coil) Ampere’s circuital law: It states that the line integral of magnetic field around any closed path in vacuum/air is μ0 times the total current threading the closed path.∫ B. dl= μ0 I 3. Applications Magnetic field due to straight infinitely long current carrying straight conductor. B= μ0 I/2πr 4. Magnetic field due to a straight solenoid carrying current B= μ0n I n= no. of turns per unit length 5. Magnetic field due to toroidal solenoid carrying current.B= μ0N I / 2πr N= Total no. of turns. 6. Force on a moving charge [ Lorentz Force] In magnetic field F=q(V x B) In magnetic and electric field F=q[E+(ν x B)] Lorentz force 7. Cyclotron Principle :When a charged particle moves at right angle to a uniform magnetic field it describes circular path. An ion can acquire sufficiently large energy with a low ac voltage making it to cross the same electric field repeatedly under a strong magnetic field. Cyclotron frequency or magnetic resonance frequency ν=qB/2πm, T=2πm/Bq; ω=Bq/m Maximum velocity and maximum kinetic energy of charged particle. Vm=Bqrm/m Em=B2q2rm2 / 2m 8. Force on a current carrying conductor in uniform F= (I l x B) l=length of conductor Direction of force can be found out using Fleming’s left hand rule. Force per unit length between parallel infinitely long current carrying straight conductors. 41
9.
10.
11.
12.
F/l= μ0 I1 I2/2πd If currents are in same direction the wires will attract each other. If currents are in opposite directions they will repel each other. 1 Ampere – One ampere is that current, which when flowing through each of the two parallel straight conductors of infinite length and placed in free space at a distance of 1m from each other, produces between them a force of 2x107 N/m of their length. Torque experienced by a current loop in a uniform B. τ = NIBA Sinθ τ=MXB Where M=NIA Motion of a charge in Perpendicular magnetic field F=q(vxB),F=qvBSin90=qvB (circular path) Parallel or antiparallel field F=qvBSin0 (or) qvBSin180=0(Straightline path) If 0<θ<90 , the path is helix v Cosθ is responsible for linear motion v, v Sinθ is responsible for circular motion Hence trajectory is a helical path Moving coil galvanometer It is a sensitive instrument used for detecting small electric Currents. Principle: When a current carrying coil is placed in a magnetic field, it experiences a torque. I αθ andI = K θ where K= NAB / C Current sensitivity, I s= θ / I=NBA/K voltage sensitivity, Vs= θ /V=NBA/KR Changing N > Current sensitivity changes but Voltage Sensitivity does not change
13.
Conversion of galvanometer into ammeter A small resistance S is connected in parallel to the galvanometer coil S=IgG/( I  I g) ;
14.
Conversion of galvanometer into a voltmeter. 42
RA=GS/(G+S)
A high resistance R is connected in series with the galvanometer coil. R=( V/Ig ) –G
;
Rv=G+R
15.
Current loop as a magnetic dipole
16.
Magnetic dipole moment M =
evr 2
M=n( eh / 4πme)
Representation of uniform magnetic field.
17.
B
18.
Magnetic dipole moment of a magnetic dipole.
19.
a) M=m (2l) b) SI unit of M  ampere metre
m= pole strength.
c) The magnetic permeability of a material may be defined as the ration of magnetic induction B to the magnetic intensity H µ=B/H
43
44
22. Properties of magnetic substances DIA PARA
FERRO
1. Diamagnetic substances are those substances which are feebly repelled by a magnet. Eg. Antimony, Bismuth, Copper, Gold, Silver, Quartz, Mercury, Alcohol, water, Hydrogen, Air, Argon, etc.
Paramagnetic substances are those substances which are feebly attracted by a magnet. Eg. Aluminium, Chromium, Alkali and Alkaline earth metals, Platinum, Oxygen, etc.
Ferromagnetic substances are those substances which are strongly attracted by a magnet. Eg. Iron, Cobalt, Nickel, Gadolinium, Dysprosium, etc.
2. When placed in magnetic field, the lines of force tend to avoid the substance.
The lines of force prefer to pass through the substance rather than air.
The lines of force tend to crowd into the specimen.
3. When placed in nonuniform magnetic field, it moves from stronger to weaker field (feeble repulsion).
When placed in nonuniform magnetic field, it moves from weaker to stronger field (feeble attraction).
When placed in nonuniform magnetic field, it moves from weaker to stronger field (strong attraction).
4. When a diamagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction perpendicular to the field.
When a paramagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field.
When a paramagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field very quickly.
45
5. If diamagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects away from the centre when the magnetic poles are closer and collects at the centre when the magnetic poles are farther.
If paramagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects at the centre when the magnetic poles are closer and collects away from the centre when the magnetic poles are farther.
If ferromagnetic liquid taken in a watch glass is placed in uniform magnetic field, it collects at the centre when the magnetic poles are closer and collects away from the centre when the magnetic poles are farther.
6. Induced Dipole Moment (M) is a small – ve value.
Induced Dipole Moment (M) is a small + ve value.
Induced Dipole Moment (M) is a large + ve value.
7. Intensity of Magnetisation (I) has a small – ve value.
Intensity of Magnetisation (I) has a small + ve value.
Intensity of Magnetisation (I) has a large + ve value.
8. Intensity of Magnetisation (I) has a small – ve value.
Intensity of Magnetisation (I) has a small + ve value.
Intensity of Magnetisation (I) has a large + ve value.
9. Magnetic permeability μ is always less than unity.
Magnetic permeability μ is more than unity.
Magnetic permeability μ is large i.e. much more than unity.
10. Magnetic susceptibility cm has a small – ve value.
Magnetic susceptibility cm has a small + ve value.
Magnetic susceptibility cm has a large + ve value.
11. They do not obey Curie’s Law. i.e. their properties do not change with temperature.
They obey Curie’s Law. They lose their magnetic properties with rise in temperature.
They obey Curie’s Law. At a certain temperature called Curie Point, they lose ferromagnetic properties and behave like paramagnetic substances.
46
47
CONCEPT_MAP
Moving Charges
using
48
CONCEPT_MAP
Moving Charge and Force
QUESTIONS 49
1*
2
3
4
5
6*
7
8
9
MAGNETIC FORCE In a certain arrangement, a proton does not get deflected while passing through a magnetic field region. State the condition under which it is possible. 1 Ans: v is parallel or antiparallel to B An electron beam is moving vertically upwards. If it passes through a magnetic field directed from South to North in a horizontal plane, in what direction will the beam be deflected? 1 Ans:Towards geographical East in the horizontal plane What is the work done by the magnetic force on a charged particle moving perpendicular to the magnetic field? 1 Ans: Zero A wire of length 0.04m carrying a current of 12 A is placed inside a solenoid, making an angle of 300 with its axis. The field due to the solenoid is 0.25 T. Find the force on the wire. Ans; 0.06N 2 A circular loop of radius 0.1 m carries a current of 1A and is placed in a uniform magnetic field of 0.5T. The magnetic field is perpendicular to the plane of the loop. What is the force experienced by the loop? 2 Ans: The magnetic dipole does not experience any force in a uniform magnetic field.Hence, the current carrying loop (dipole) does not experience any net force. A proton, alpha particle and deuteron are moving in circular paths with same kinetic energies in the same magnetic fields. Find the ratio of their radii and time periods. Ans: Rp: Rα : Rd =1:1:√2 2 Tp: Tα : Td =1:2:2 An electron moving with Kinetic Energy 25 keV moves perpendicular to a uniform magnetic field of 0.2 mT. Calculate the time period of rotation of electron in the magnetic field. 2 7 Ans: T = 1.79 x 10 S A charged particle of mass ‘m’ charge ‘q’ moving at a uniform velocity ‘v’ enters a uniform magnetic field ‘B’ normal to the field direction. Deduce an expression for Kinetic Energy of the particle. Why does the Kinetic Energy of the charged particle not change when moving through the magnetic field? 3 An electron is revolving around the nucleus of an atom in an orbit of radius 0.53 Å. Calculate the equivalent magnetic moment, if the frequency of revolution of the electron is 6.8 x 10 9 MHz. Ans: pm = 9.6 x 10 24 A m2 3 50
1
2
3
4
5*
6*
7*
8
BIOTSAVART LAW AND ITS APPLICATIONS A current is set up in a long copper pipe. What is the magnetic field inside the pipe? Ans: Zero1 A wire placed along north south direction carries a current of 5 A from South to North. Find the magnetic field due to a 1 cm piece of wire at a point 200 cm North East from the piece. 2 10 Ans: 8.8 x 10 T, acting vertically downwards. How will the magnetic filed intensity at the centre of a circular coil carrying current change if the current through the coil is doubled and the radius of the coil is halved. 2 Ans: B = μ0n x 2I / 2 x (R/2) = 4B A circular coil of 500 turns has a radius of 2 m, and carries a current of 2 A. What is the magnetic field at a point on the axis of the coil at a distance equal to radius of the coil from the center? 2 Ans: B = 1. 11 x 10 4 T The strength of magnetic induction at the center of a current carrying circular coil is B1 and at a point on its axis at a distance equal to its radius from the center is B2. Find B1/B2. 2 Ans: 2 √2 A current is flowing in a circular coil of radius ‘r’ and magnetic field at its center is B0. At what distance from the center on the axis of the coil, the magnetic field will be B0/8? 2 Ans: x = √3r 𝜋 A straight wire of length′ ′𝑚, is bent into a circular shape. if the wire were 2 to carry a current of 5 A, calculate the magnetic field due to it, before bending, at a point 0.01 times the radius of the circle formed from it. Also calculate the magnetic field at the center of the circular loop formed, for the same value of current. 3 4 5 Ans: B1 = 4 x 10 T, B 2 = 1.256 x 10 T Two insulated wires perpendicular to each other in the same plane carry equal currents as shown in figure. Is there a region where the magnetic field is zero? If so, where is the region? If not, explain why the field is not zero? 3 I 51
I 9
What is the net magnetic field at point 0 for the current distribution shown here?
ans (µ0 I / 2r)=(µoi/π r)
1
2
3
3
AMPERE’S CIRCUITAL LAW AND APPLICATIONS A long straight solid metal wire of radius ‘R’ carries a current ‘I’, uniformly distributed over its circular cross section. Find the magnetic field at a distance ‘r’ from the axis of the wire (a) inside and (b) outside the wire Ans; (a) µ0µrIr/2πR2 (b) µ02I/ 4πr 2 A solenoid is 1m long and 3 cm in mean diameter. It has 5 layers of windings of 800 turns each and carries a current of 5 A. Find Magnetic Field Induction at the center of the solenoid. 2 2 Ans: 2.5 x 10 T, parallel to the axis of the solenoid. Find the value of magnetic field inside a hollow straight current carrying conductor at a distance r from axis of the loop. 2
Ans B=0
1*
FORCE BETWEEN TWO PARALLEL CURRENTS, TORQUE ON A CURRENT LOOP, MOVING COIL GALVANOMETER A rectangular loop of size 25 cm x 10 cm carrying a current of 15A is placed 52
2 cm away from a long, straight conductor carrying a current of 25 A. What is the direction and magnitude of the net Force acting on the loop? Ans: F =7.8175 x 104 N
2*
3
4*
A long straight conductor PQ , carrying a current of 60 A, is fixed horizontally. Another long conductor XY is kept parallel to PQ at a distance of 4 mm, in air. Conductor XY is free to move and carries a current ‘I’ . Calculate the magnitude and direction of current ‘I’ for which the magnetic repulsion just balances the weight of the conductor XY. 2 Ans: I = 32. 67 A, The current in XY must flow opposite to that in PQ, because only then the force will be repulsive. A circular coil of 200 turns, radius 5 cm carries a current of 2.5 A. It is suspended vertically in a uniform horizontal magnetic field of 0.25 T, with the plane of the coil making an angle of 600 with the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning. 2 Ans: 0.49Nm A Galvanometer of resistance 3663 ohm gives full scale deflection for a certain current Ig.Calculate the value of the resistance of the shunt which when joined to the galvanometer coil will result in 1/34 of the total current passing through the galvanometer. Also find the total resistance of the Galvanometer and shunt. Ans: 111 ohm, 107.7 A.
53
MAGNETISM AND MATTER 1
2
1
1 2 3
4*
5
6*
BAR MAGNET A short bar magnet has magnetic moment of 50 A m2. Calculate the magnetic field intensity at a distance of 0.2 m from its centre on (1) its axial line (2) its equitorial line. Ans: B1 = 1.25 x 10 3 T , B2 = 0.625 x 10 3 T. Calculate the torque acting on a magnet of length 20 cm and pole strength 2 x 10 5 Am, placed in the earth’s magnetic field of flux density 2 x 10 5 T, when (a) magnet is parallel to the field (b) magnet is perpendicular to the field. Ans: (a) Zero (b) 0.8 x 10 10 Nm MAGNETISM AND GAUSS LAW What is the significance of Gauss’s law in magnetism? Ans: Magnetic monopoles do not exist. THE EARTH’S MAGNETISM How the value of angle of dip varies on moving from equator to Poles? A compass needle in a horizontal plane is taken to geographic north / south poles. In what direction does the needle align? The horizontal component of earth’s magnetic field is 0.2 G and total magnetic field is 0.4 G. Find the angle of Dip. Ans: 60. 250 A long straight horizontal table carries a current of 2.5 A in the direction 100 south of west to 10 0 north of east. The ,magnetic meridian of the place happens to be 10 0 west of the geographic meridian. The earth’s magnetic field at the locations 0.33G and the angle of dip is zero. Ignoring the thickness of the cable, locate the line of neutral points. Ans: r = 1.5 cm ( BH = B cos δ, BH = µ0 I/ 2πr) The vertical component of earth’s magnetic field at a place is √3 times the horizontal component. What is the value of angle of dip at this place? Ans: 600 A ship is sailing due west according to mariner’s compass. If the declination of the place is 150east, what is the true direction of the ship? Ans: 750 west of north. IMPORTANT TERMS IN MAGNETISM 54
1
2
A magnetising field of 1600 A/m produces a magnetic flux of 2.4 x 10 5 Wb in a bar of iron of cross section 0.2 cm2. Calculate permeability and susceptibility of the bar. Ans: Permeability = 7.5 x 104 T A 1 m, Susceptibility =596.1 The maximum value of permeability of µmetal is 0.126 Tm/A. Find the maximum relative permeability and susceptibility. Ans: 105 each. MAGNETIC PROPERTIES OF MATERIALS
1
2 3 4 5 6*
7*
8
The susceptibility of magnesium at 300K is 1.2 x 105. At what temperature will the susceptibility be equal to 1.44 x 105 . Ans: 250 K An iron bar magnet is heated to 10000C and then cooled in a magnetic field free space. Will it retain its magnetism? What is the net magnetic moment of an atom of a diamagnetic material? Ans : Zero Which materials have negative value of magnetic susceptibility? Ans : Diamagnetic materials. Why permanent magnets are made of steel while the core of the transformer is made of soft iron? An iron rod of volume 104 m3 and relative permeability 1000 is placed inside a long solenoid wound with 5 turns/cm. If a current of 0.5A is passed through the solenoid , find the magnetic moment of the rod. The susceptibility of a magntic mateial is 0.9853. Identify the type of the magnetic material.Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field. Ans : paramagnetic Two similar bars, made from two different materials P and Q are placed one by one in a non uniform magnetic field. It is observed that (a) the bar P tends to move from the weak to the strong field region. (b) the bar Q tends to move from the strong to the weak field region. What is the nature of the magnetic materials used for making these two bars?
55
VALUE BASED QUESTIONS: 1. Sandeep’s mother had put lot of clothes for washing in the washing machine, but the machine did not start and an indicator was showing that the lid did not close. Sandeep seeing his mother disturbed thought that he would close the lid by force but realized that the mechanism was different. It was a magnetic system. He went to the shop and got a small magnetic door closer and put it on the lid. The machine started working. His mother was happy that Sandeep helped her to save Rs.500/ also. • What was the value developed by Sandeep? • What values did his mother impart to Sandeep? 2. Tushar was using a galvanometer in the practical class. Unfortunately it fell from his hand and broke. He was upset, some of his friends advised him not to tell the teacher but Tushar decided to tell his teacher. Teacher listened to him patiently and on knowing that the act was not intentional, but just an accident, did not scold him and used the opportunity to show the internal structure of galvanometer to the whole class. (i) What are the values displayed by Tushar. (ii) Explain the principle, Construction and working of moving coil galvanometer. 3. Two girls Pooja and Ritu were very good observers and performed in the school function using their cassette player. One day when they were performing, tape got stuck up and the music stopped. But Pooja was determined not to let down the performance so she sang the song instead of dancing and Ritu completed the dance. • What were the values displayed by Pooja and Ritu? • What kind of Ferro magnetic material is using for coating magnetic tapes used in cassette players or building memories stories in modern computers?
4. ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS 56
GIST 1 The phenomenon in which electric current is generated by varying magnetic fields is called electromagnetic induction 2 Magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as ΦB = B.A = BACosθ where θ is the angle between B and A. 3 Magnetic flux is a scalar quantity and its SI unit is weber (Wb). Its dimensional formula is [Φ] = ML2T2A1. 4 Faraday’s laws of induction states that the magnitude of the induced e.m.f in a circuit is equal to the time rate of change of magnitude flux through the circuit. 𝑑∅ ε= − 𝐵 𝑑𝑡 5 According to Lenz law, the direction of induced current or the polarity of the induced e.m.f is such that it tends to oppose the change in magnetic flux that produces it. (The negative sign in Faraday’s law indicates this fact.) 6 Lenz law obeys the principle of energy conservation. 7 The induced e.m.f can be produced by changing the (i) magnitude of B (ii) area A (iii) angle θ between the direction of B and normal to the surface area A. 8 When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a velocity v perpendicular to the field, the induced e.m.f is called motional e.m.f produced across the ends of the rod which is given by ε = Blv. 9 Changing magnetic fields can setup current loops in nearby metal bodies (any conductor). Such currents are called eddy currents. They dissipate energy as heat which can be minimized by laminating the conductor. 10 Inductance is the ratio of the flux linkage to current. 11 When a current in a coil changes it induces a back e.m.f in the same coil. 𝑑𝐼 The self induced e.m.f is given by ε = −𝐿 where L is the self𝑑𝑡 inductance of the coil. It is a measure of inertia of the coil against the change of current through it. Its S.I unit is henry (H). 12 A changing current in a coil can induce an e.m.f in a nearby coil. This relation, 𝑑𝑖 ε = −𝑀12 2, shows that Mutual inductance of coil 1 with respect to coil 𝑑𝑡 2 (M12) is due to change of current in coil 2. (M12 = M21). 13 The selfinductance of a long solenoid is given by L = µ0n2Al where A is 57
14
15
the area of crosssection of the solenoid, l is its length and n is the number of turns per unit length. The mutual inductance of two coaxial coils is given by M12 = M21 = µ0 n1n2Al where n1& n2 are the number of turns per unit length of coils 1 & 2. A is the area of crosssection and l is the length of the solenoids. Energy stored in an inductor in the form of magnetic field is U B 1 Limax 2 2
and B2 Magnetic energy density U B 2 0
16 In an A.C. generator, mechanical energy is converted to electrical energy by virtue of electromagnetic induction. * Rotation of rectangular coil in a magnetic field causes change in flux (Φ = NBACosωt). * Change in flux induces e.m.f in the coil which is given by ε= dΦ/dt = NBAωSinωt ε 𝜀= ε0Sinωt * Current induced in the coil I = ε/R = ε0Sinωt/R = I0Sinωt 17 An alternating voltage ε=ε0Sinωt, applied to a resistor R drives a current I = I0Sinωt in the resistor, I0 = ε0 /R where ε0& I0 are the peak values of voltage and current. (also represented by Vm & Im) 18 The root mean square value of a.c. may be defined as that value of steady current which would generate the same amount of heat in a given resistance in a given time as is done by the a.c. when passed through the same resistance during the same time. Irms = I0/√2 = 0.707i0 Similarly, vrms = v0/√2 = 0.707v0. For an a.c. ε = εm Sin ωt applied to a resistor, current and voltage are in phase. 19 In case of an a.c. circuit having pure inductance current lags behind e.m.f by a phase angle 90°. ε = εm Sin ωt and i = im Sin (ωtΠ/2) Im = εm/XL; XL = ωL is called inductive reactance. 20 In case of an a.c. circuit having pure capacitance, current leads e.m.f by a phase angle of 90°. ε = εmSinωt and I= ImSin(ωt+π/2) where Im = εm/XC and XC = 1/ωC is called capacitive reactance. 21 In case of an a.c. circuit having R, L and C, the total or effective 58
resistance of the circuit is called impedance (Z). Z = εm / Im = R 2 + (XC  XL )2 tanΦ =
Xc X L R
where φ is the phase
difference between current and voltage. ε = εmSinωt, I= ImSin(ωt+Φ) 23 Average power loss over a complete cycle in an LCR circuit is P = εrmsIrmsCosΦ * In a purely resistive circuit Φ = 0; P = VRMSIRMS. * In a purely inductive circuit Φ = Π/2; P = 0. * In a purely capacitive circuit Φ = Π/2; P = 0. 24 In an LCR circuit, the circuit admits maximum current if XC = XL, so that Z = 1 1 R and resonant frequency 𝜔𝑟 = 𝑎𝑛𝑑𝜗𝑅 = √𝐿𝐶
2𝜋√𝐿𝐶
25 Q factor of series resonant circuit is defined as the ratio of voltage developed across the inductance or capacitance at resonance to the applied voltage across ‘R’, 𝜔 𝐿 1 𝜔 Q= 𝑟 𝑜𝑟 also 𝑄 = 𝑟 where 2∆𝜔 is bandwidth. 𝑅
26
𝜔𝑟 𝐶𝑅
for a transformer,
2∆𝜔
Es N s i p K E p N p is
In an ideal transformer, εPIP = εSIS. i.e If NS>NP; εS>εP& IS
NS; εP>εS & IP
1 q0 dt 2 LC
CONCEPT MAP
EMI and application
59
60
61
QUESTIONS MAGNETIC FLUX, INDUCED E.M.F, 1
Two concentric circular coils are perpendicular to each other. Coil I 1 carries a current i. If this current is changed, will this induce a current in the coil II?
I
II
2
3
[No Field due to one coil is parallel to the plane of the second coil. So flux does not change.] A closed loop of wire is being moved with constant velocity without 1 changing its orientation inside a uniform magnetic field. Will this induce a current in the loop? [Ans: No there is no change in ΦB] A cylindrical bar magnet is kept along the axis of a circular coil and near it 1 as shown in the fig. Will there be any induced current at the terminals of the coil when the magnet is rotated a) about its own axis b) about an axis perpendicular to the length of the magnet?
N Fig (i)
S Fig(ii)
Ans Fig. (i) No e.m.f will be induced, as these is no change in flux. 62
Fig (ii) Yes, Φ changes continuously. So e.m.f is induced in the coil. 4
A conducting wire is kept along the N→S direction and is allowed to fall freely. Will an e.m.f be induced in the wire? (Yes) 5 A conducting wire is kept along the E→W direction and is allowed to fall freely. Will an e.m.f be induced in the wire? (Yes) 6 A vertical magnetic pole falls down through the plane of magnetic meridian. Will any e.m.f be induced between its ends? Ans: No, because the pole intercepts neither Bv or BH 7 A wheel with a certain number of spokes is rotated in a plane normal to earth’s magnetic field so that an emf is induced between the axle and rim of the wheel, keeping all other things same, number of spokes is changed. How is the e.m.f affected? (Hint: Number of spokes does not affect the net emf) 8 What are eddy currents? 9 Explain any two applications of eddy current. 10 The magnetic flux linked with a coil passing perpendicular to the plane of the coil changes with time Φ = 4t2 + 2t + 3, where “t” is the time in seconds. What is magnitude of e.m.f induced at t = 1 second? Ans: (e = dΦ/dt =
d 4t 2 2t 3 ,e = 8t +2 dt
If t = 1s
1
1
1
1
1 2 3
e= 10V)
11 A wheel fitted with spokes of radius ‘r’ is rotating at a frequency of n revolutions per second in a plane perpendicular to magnetic field B Tesla. What is the e.m.f induced between the axle and rim of the wheel [2] Φ = BA
3
e = d(BA)/dt= B dA/dt, dA/dt= Πr2x n e = B. Πr2n 12 Two coils P and S are arranged as shown in the figure. (i) What will be the direction of induced current in S when the switch is closed? (ii) What will be the direction of induced current in S when the switch is opened?
63
2
P
S
Ans: (i) anticlockwise (ii) clockwise 13 A conducting circular loop is placed in a uniform magnetic field B = 2 0.020T with its plane perpendicular to the field. Somehow, the radius of the loop starts shrinking at a constant rate of 1mm/s. Find the induced current in the loop at an instant when the radius is 2cm. Ans. (Ф= Πr2B d Ф/dt = 2ΠrB dr/dt e= 25μV 14 A 12V battery is connected to a 6Ω; 10 H coil through a switch drives a constant current in the circuit. The switch is suddenly opened. Assuming that it took 1ms to open the switch calculate the average e.m.f induced across the coil. Ans. (I initial=2A I final= 0 𝜀=Ldi/dt = 20000V) 15 A coil of mean area 500 cm2 having 1000 turns is held perpendicular to a uniform magnetic field of 0.4 G. The coil is turned through 180 o in 1/10 seconds. Calculate the average induced e.m.f. Ans. (0.04 V) 16 A conducting rod of length l with one end pivoted is rotated with a uniform angular speed ω in a Vertical plane normal to uniform magnetic field B. Deduce an expression for e.m.f induced in this rod. 17 Two identical coaxial coils carry equal currents. What will happen to the current in each loop if the loops approach each other? (2)
2
2
2
2
Ans. (Acc to Lenz’s law current in each coil will decrease) 18 Obtain the direction of induced current and e.m.f when the conductor AB is moved at right angles to a stationary magnetic field (i) in the upward direction (ii) in the downward direction. (i) B to A (ii) A to B) 64
2
B
N
S
G
A
19 A fan blade of length 0.5 m rotates perpendicular to a magnetic field of 5x10 5 T. If the e.m.f induced between the centre and the end of the blade is 10 2 V .Find the rate of rotation. Ans. (e=B dA/dt ; dt= 1/n ; n=254.7 rev/s)
3
20 The figure shows a square loop having 100 turns an area of 2.5x10 3 m2 3 and a resistance of 100Ώ . The magnetic field has a magnitude of B= 0.4 T. Find the work done in pulling the loop out of the field slowly and uniformly in 1 second. P
Q
R
* * * * * * * * * * * * *v * * *
* * * *
Also draw graph showing the variation of power delivered when the loop is moved from P to Q to R.
(1x 106J)
21 Two coils have a mutual inductance of 0.005H. The current changes in the 3 first coil according to the equation I= I0 Sin ωt where I0 =10A and ω=100∏ rad/s. Calculate the maximum value of e.m.f in the second coil. (5 π volts) 22 A long rectangular conducting loop of width L mass m and resistance R is 3 placed partly above and partly below the dotted line with the lower edge parallel to it. With what velocity it should continue to fall without any acceleration?
65
* * * * * * * * *
* * * ** * * * * *****(mg = B2l2v/r ; v=mgr/ B2l2 ) INDUCTANCE 1
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. Find the mutual inductance between them assuming R2<< R1. (M=µ0 πR22 /2R1)
2
2
Prove that the total inductance of two coils connected in parallel is
2
1 1 1 LT L1 L2
3
4
5
Two circular loops are placed with their centres at fixed distance apart. 2 How would you orient the loops to have (i) maximum (ii) minimum Mutual inductance? A coil of wire of certain radius has 600 turns and inductance of 108mH. 2 What will be the inductance of another similar coil with 500 turns? (75mH) Obtain the mutual inductance of a pair of coaxial circular coils kept 2 separated by a distance as shown in fig:
R
r
ALTERNATING CURRENT  RMS CURRENT AND VOLTAGE 66
1
Find
the
RMS
value
of
A.C
shown
in
the
figure. 1
2
The instantaneous value of e.m.f is given by ε= 300sin 314t. What is the 1 rms value of emf ? Ans: 𝜀 0=300 units 𝜀 rms=212.1 units
3
Why a 220 V AC is considered to be more dangerous than 220 V DC?
1
Ans: peak value of AC is more than rms value which is equal to 311V. 4
An AC current flows through a circuit consisting of differerent elements 1 connected in series. (i) Is the applied instantaneous voltages equal to the algebraic sum of instantaneous voltages across the series elements of the circuit? (ii) Is it true for rms voltages? Ans: (i) yes (ii) no
5
A capacitor blocks DC. Why? Ans: XC=1/(2πfC ), for D.C f=0, therefore Xc=∞
6
What is the phase relationship between e.m.f across L and C in a series 1 LCR circuit connected to an A.C source? Ans:The phase difference between VL and VC=1800
7
Two alternating currents are given by I1=I0Sinωt and I2= I0Sin(ωt+π/3). 1 Will the rms value ofI1 & I2be equal or different?
1
Ans: The rms value will be equal. 8
An alternating current is given by i=i1Cosωt+i2Sin ωt. Find the rms 2 current in the circuit.
(2) 67
Ans:√
(𝑖12 +𝑖12 ) 2
9
An alternating current having a peak value of 14A is used to heat a metal 2 wire. What is the value of steady current which can produce the same heating effect as produced by AC? Why? Ans: irms=10A 10 If a constant current of 2.8A exists in a resistor, what is the rms value of 2 current? Why? (2) Ans: 2.8A 11 Sketch a graph showing the variation of impedance of LCR circuit with 1 the frequency of applied voltage.
Z
(1) ϑ ϑr
12 If resistance R in circuit ‘a’ be decreased, what will be the direction of
2
induced current in the circuit ‘b’.
AC CIRCUITS 1
What is meant by wattless current?
1
2
Define: Q factor in LCR series circuit
1
3
Why is choke coil preferred over resistor to reduce a.c?
1
4
How do R, XL and XC get affected when the frequency of applied AC is 3 doubled? Ans: a) R remains unaffected b) XL=2πfL, so doubled c) XC=1/2πfC, so halved For circuits for transporting electric power, a low power factor implies 2
5
68
large power loss in transmission line. Why? Ans: irms 6
7
8
9
10
11
12
13
(2)
P Vrms Cos
In an AC circuit there is no power consumption in an ideal inductor. Why? Ans: P= Vrms Irms Cos π/2 =0 An LCR series circuit is connected to an AC source. Which of its components dissipates power? L or C or R? Justify your answer. Ans: Resistance, Power in L and C = 0 An electric lamp connected in series with a capacitor and an AC source is glowing with certain brightness. How does the brightness of the lamp change on reducing the capacitance? Ans: Brightness decreases. (As C decreases, XC increases. Hence Z increases and I decreases.) The power factor of an AC circuit is lagging by a factor 0.5. What does it mean? (2) Ans: CosФ=0.5, ie, Ф =600. This implies that the current lags behind applied voltage by a phase angle of 600 The peak value of an AC is 5A and its frequency is 60Hz. Find its rms value. How long will the current take to reach the peak value starting from zero? Ans: Irms= 3.5A . Time period T=(1/60)s . The current takes one fourth of the time period to reach the peak value starting from zero. t =T/4 =(1/240)s. The voltage and current in a series AC circuit are given by V= V0 Cosωt & I= I0 Sinωt. What is the power dissipated in the circuit? Ans: I=I0Sinωt & V=V0Sin(ωt+π/2), since V leads current by a phase angle π/2, it is an inductive circuit . So, P=0 When an AC source is connected to a capacitor with a dielectric slab between its plates, will the rms current increase or decrease or remain constant? Ans: The capacitance increases, decreasing the reactance Xc . Therefore the rms current increases. Can peak voltage across an inductor be greater than the peak voltage supplied to an LCR? Ans: Yes, at the time of break of a circuit, a large back e.m.f is set up across the circuit. 69
2
2
2
2
2
2
2
2
14 Write any two differences between impedance and reactance.
2
15 A 100 Ω resister is connected to 220V, 50 cycles per seconds. What is (i) peak potential difference (ii) average potential difference and (iii) rms current? Ans. 𝜀 o=311.08V, 𝜀 m =197.9V, Iv= 2.2 A 16 Define and derive the root mean square value of a.c voltage
2
3
RESONANCE in LCR Circuits 1
2
An inductor of inductance 100mH is connected in series with a 2 resistance, a variable capacitance and an AC source of frequency 2 kHz. What should be the value of the capacitance so that maximum current may be drawn into the circuit? Ans: 1/ωC=ωL ; C=1/ω2L=63nF. In the circuit shown below R represents an electric bulb. If the frequency 2 of the supply is doubled, how the valves of C and L should be changed so that the glow in the bulb remains unchanged?
Hint: 3
4
5
6
7
XL=2πfL
XC=1/2πfC
Draw phasor diagram for an LCR circuit for the cases (i) the voltage across the capacitor is greater than that across the inductor (ii) voltage across inductor is greater than that across the capacitor. Does current in AC circuit lag, lead or remain in phase with voltage of frequency υ applied to a series LCR circuit when (i) υ = υ r (ii) υ< υ r (iii) υ > υ r, where υ r resonant frequency? 11kw of electric power can be transmitted to a distant station at (i) 220V and (ii) 22kV. Which of the two modes of transmission should be preferred and why? In an AC circuit V and I are given by V=100Sin100t volts and I= 100 Sin(100t+π/3)mA respectively. What is the power dissipated in the circuit? Ans: V0=100V I0=100A Ф= π/3 P=Vrms Irms Cos Ф=2500W
2
1
2
2
The potential across a generator is 125V when it is suppling10A. When it 2 70
8
9
supplies 30A, the potential is 120V. What is the resistance of the armature and induced e.m.f? Ans: E=127.5V In an LCR circuit the potential difference between terminals of 3 inductance 60V, between terminals of capacitor 40V and between the terminals of resistor is 40V. Find the supply voltage. (3) Ans: In series LCR circuit voltage across capacitor and inductor are in opposite phase, so net voltage across the combination of L and C becomes 6030=30V. Total voltage across R and L = 50V The natural frequency of an LC circuit is 1,25,000 Hz. Then the capacitor 3 C is replaced by another capacitor with a dielectric medium k, which decreases the frequency by 25 KHz. What is the value of k? Ans: υ1=1/2π√LC υ2=1/2π√kLC k=( υ1/ υ 2)2=(1.25)2=1.56.
10 Obtain the resonant frequency and Q factor of a series LCR circuit with 3 L= 3H, C= 27µF and R= 7.4 Ώ. Write two different ways to improve quality factor of a series LCR circuit Ans: Q=45,ω0=111rad/s 11 An A.C source of voltage V= Vm Sinωt is connected onebyone to three 5 circuit elements X, Y and Z. It is observed that the current flowing in them i. is in phase with applied voltage for X ii. Lags applied voltage in phase by π /2 for elements Y. iii. Leads the applied voltage in phase by π /2 for element Z. Identify the three circuit elements. TRANSFORMER 1
Why is the core of a transformer laminated?
1
2
Why can’t a transformer be used to step up dc voltages?
1
3
The graph below shows the variation of I with t. If it is given to the primary of a transformer, what is the nature of induced e.m.f in the secondary?
3
71
I
t
(Hint: e has constant positive value in the first part and a constant negative value in the second part)
4
1. The turn ratio of a transformer is 10. What is the e.m.f in the secondary if 2V is supplied to primary? 2. A transformer has an efficiency of 80% It works at 4kW and 100V. If the secondary voltage Is240V find the primary current. (40 A ) When a voltage of 120V is given to the primary of a transformer the current in the primary is 1.85mA. Find the voltage across the secondary when it gives a current of 150mA. The efficiency of the transformer is 95% (1406V)
3
GENERATOR 1
2
3
If the speed of rotation of armature is increased twice how would it 1 affect the (a) maximum e.m.f produced (b) frequency of the e.m.f? (e=NBAω ;f=ω/2Π) 2 A coil of area 0.2m and 100 turns rotating at 50 revolutions per second 2 with the axis perpendicular to the field. If the maximum e.m.f is 7kV determine the magnitude of magnetic field. (1.1 Tesla) An ac generator consists of a coil of 50 turns and an area of 2.5m2 3 rotating at an angular speed of 60 rad/s in a uniform magnetic field of B= 0.3T between two fixed pole pieces. The resistance of the circuit including that of the coil is 500Ώ (i) What is the maximum current drawn from the generator? (ii)What is the flux through the coil when current is zero? (iii)What is the flux when current is maximum? 72
(4.5A, 375Wb, zero) VALUE BASED QUESTIONS 1. Lakshmi, Ritu and Kajal lived in a resettlement colony where they observed most houses stole power from transmission lines using hooks. They had learnt in school about fire caused due to electric short circuit. They decided to make people aware of the risks involved and also the importance of paying their electricity bills. They got all their friends and responsible elders together and with the help of the electricity board, succeeded in changing the situation. • What values did Lakshmi, Ritu and Kajal have? • A low voltage supply from which one needs high currents must have a very low internal resistance, why? • A high tension supply of say 6 KV must have a very large internal resistance. Why? 2. Rahul and Rohit bought an electric iron. They had a 2 pin plug. Rahul was keen to start using the new iron with the 2 pin plug. However, Rohit insisted that they buy a 3 pin plug before using it. Rahul got angry. Rohit patiently explained the importance of using a 3 pin plug and the earthing wire. He said that if the metallic body of the iron came in contact with the live wire at 220 volts, they would get an electric shock. If earthed, the current would go to the earth and the potential of the metallic body would not rise. The iron would then be safe to use. Hearing Rohit, Rahul calmed down and agreed. • What values did Rahul and Rohit have? • Which has greater resistance – 1 K watt electric heater or 100 watt electric bulb, both marked 220 volts? 3. Sachin had gone to meet his grandfather who was staying in a village. In the evening, they were both watching TV, when suddenly the lights went off. Grandfather told Sachin that the fuse must have blown up as all their neighbors had electricity. Luckily Sachin knew how to change a fuse. His grandfather was happy and told him that if he had been alone, he would have had to spend the night in the dark without a fan. Sachin felt and made up his mind to replace the fuse with a circuit breaker which uses a solenoid with a core so that his grandfather would not have any problems in future. • What values did Sachin have? • The main power supply of a house is through a 5 ampere fuse. How many 100 watt bulbs can be used in the house simultaneously at 220 volts?
73
5. ELECTRO MAGNETIC WAVES GIST 1. Conduction current and displacement current together have the property of continuity. 2. Conduction current & displacement current are precisely the same. 3. Conduction current arises due to flow of electrons in the conductor. Displacement current arises due to electric flux changing with time. 𝒅∅𝑬 4. 𝑰𝑫 = 𝜺𝟎 ∫ 𝒅𝒕 5. Maxwell’s equations Gauss’s Law in Electrostatics 𝑄 ∮ 𝐸 . 𝑑𝑆= 𝜀0
Gauss’s Law in Magnetism ∮ 𝐵. 𝑑𝑆=0 Faraday’s Lenz law of electromagnetic induction. 𝐵
∮ 𝐸 . 𝑑𝑙 =∫ 𝑑𝑡.𝑑𝑆 Ampere’s – Maxwell law 𝐸
∫ 𝐵 . 𝑑𝑙 =0 I + 0 0∫ 𝑑𝑡 . 𝑑𝑆 6. Electromagnetic Wave : The wave in which there are sinusoidal variation of electric and magnetic field at right angles to each others as well as right angles to the direction of wave propagation. 1 7. Velocity of EM waves in free space:𝑐 = 3x108 m/s √𝜇0𝜀0
8. The Scientists associated with the study of EM waves are Hertz,
Jagdish Chandra Bose & Marconi. 9. EM wave is a transverse wave because of which it undergoes polarization effect. 10. Electric vectors are only responsible for optical effects of EM waves. 𝐸 11. The amplitude of electric & magnetic fields are related by = 𝑐 𝐵 12. Oscillating or accelerating charged particle produces EM waves. 13. Orderly arrangement of electro magnetic radiation according to its frequency or wavelength is electromagnetic spectrum. 14. Hint to memorise the electromagnetic spectrum in decreasing order of its frequency. Gandhiji’s Xrays Used Vigorously InMedical Research 15. EM waves also carry energy, momentum and information. 74
ELECTRO MAGNETIC SPECTRUM, ITS PRODUCTION, DETECTION AND USES IN GENERAL Wave length Range Type Production Detection Uses Frequency Range Radio >0.1m Rapid Receiver’s Radio, TV 9 5 10 to 10 Hz acceleration / aerials Communication deceleration of electrons in aerials
Microwave
0.1mm 1011 to109 Klystron valve or Point contact Radar, Hz magnetron valve diodes communication
1mm to Infrared 700nm Vibration of atom 11 14 10 to10 or molecules Hz
Light
Ultraviolet
Thermopiles, Bolometer Infrared Photographic Film
TV
Green House effect, looking through haze, fog and mist, Ariel mapping.
700nm to 400nm Electron in an 14 8x10 Hz atom during transition
Eye, Photography, Photocell, Illuminations, Emit & Photographic reflect by the objects. Film
400nm 1nm 5x1014 8x1014
Preservation of food Photocell & items, Detection of photographic invisible writing, finger film print in forensic laboratory.
to Inner Shell electron in atom to moving from one energy level to a lower energy level
75
Determination of Structure of molecules & atoms.
Xrays
1nm to 10 Xray tube or 3 nm inner shell 1016 to 1021 Electrons Hz
<103nm Radioactive 18 22 10 to 10 decay of Gamma Hz nucleus ray
Photographic Study of crystal film, Geiger structure & atom, tube, fracture of bones. ionization chamber.
Nuclear reaction & the Photographic structure of atoms & film, Geiger Nuclei. tube, To destroy cancer cells. ionization chamber
76
CONCEPT MAP
Electromagnetic Waves
77
78
VALUE BASED QUESTIONS 1.
A fluorescent tube seller boasts of the quality of his fittings. He offers
cheaper fittings with beautiful choke fitted on it.The customer installs it and finds the tube working fine but giving strong humming sound . He and his wife found the hum to be tolerable but their young children said that it is too high to be tolerated. What do you think about the cause of hum? Comment on the character of the seller.
2.
Clinical microscopes are used to diagnose diseases based on blood and
urine samples.Mr. Bajaj does not believe in such tests. He prefers to go to doctors who diagnose on the basis of pulse check only. He fell ill and his temperature persisted for more than a month. Anurag a student of class twelfth resides near Mr. Bajaj house, convinced Mr. Bajaj and got his examination conducted. How X ray are produced? What are the values exhibited by Anurag?
3.
Sushma’s mother suffers from cancer of third stage. She has been advised a
therapy in which cancerous growth will be burnt by atomic radiations. She is told that her beautiful hair will fall in this therapy and she is liable to become bald. Sushma’s mother refuses the therapy which is otherwise must for her. Sushma talked to her mother explaining the need of the therapy and could convince her. What are the values exhibited by Sushma? Which electromagnetic radiation is used in cancer treatment?
79
6. OPTICS RAY OPTICS GIST 1 REFLECTION BY CONVEX AND CONCAVE MIRRORS.
Mirror formula
1 1 1 , where u is the object distance, v is v u f
the image distance and f is the focal length. v u
2
Magnification m
f v f . f f u
m is ve for real images and +ve for virtual images. REFRACTION Ray of light bends when it enters from one medium to the other, having different optical densities. Sun can be seen before actual sunrise and after actual sunset due to Atmospheric refraction An object under water ( any medium ) appears to be raised due to refraction when observed inclined n
Re al depth apparent depth
and
Shift in the position (apparent) of object is X = t { 1 – 1/n) where t is the actual depth of the medium Snell’s law states that for a given colour of light, the ratio of sine of the angle of incidence to sine of angle of refraction is a constant, when light travels from rarer to denser, Sini n2 sin r n1
Absolute refractive index is the ratio between the velocities of light in vacuum to the velocity of light in medium. For air n=1. n
3
c v
When a ray of light travels from denser to rarer medium and if the angle of incidence is greater than critical angle, the ray of light is reflected back to the denser medium. This phenomenon is called 80
Total internal reflection. SinC
4
nR nD
Diamond has a high refractive index, resulting with a low critical angle (C=24.40). This promotes a multiple total internal reflection causing its brilliance and luster. Some examples of total internal reflection are formation of mirage and working of an optical fibre. When light falls on a convex refracting surface(light travelling from rarer to denser medium), it bends and the relation between U, V and R is given by
n2 n1 n2 n1 V u R
Lens 5 mLens maker’s formula or thin lens formula is given by 1 n2 n1 1 1 f n1 R1 R2
6
For Convex Lens R1 +ve ;R2 –ve Concave lens R1ve; R2 +ve The way in which a lens behaves as converging or diverging depends upon the values of nL and nm. When two lenses are kept in contact the equivalent focal length is given by
1 1 1 & P P1 P2 F f1 f 2
.
7
The lens formula is given by
8
When light passes through a glass prism it undergoes refraction.
1 1 1 v u f
A Dm Sin 2 The expression for refractive index is n A Sin 2
As the angle of incidence increases, the angle of deviation decreases, reaches a minimum value and then increases. This minimum value is called angle of minimum deviation “Dm”.
81
9 d
i ANS WER Si
Where d is minimum, i=e, refracted ray lies parallel to the base. For a small angled prism d=(n1)A. 10 When white light (poly chromatic or composite) is passed through a glass prism, It splits up into its component colours (Monochromatic). This phenomenon is called Dispersion. m. 11 Rainbow is formed due to a combined effect of dispersion, refraction and reflection of sunlight by spherical water droplets of rain. 12 Scattering of light takes place when size of the particle is very small when compared to the wavelength of light Intensity of scattered light is I
(i) (ii) (iii) (iv)
1
4
The following properties or phenomena can be explained by scattering. Sky is blue. Sky is reddish at the time of sunrise and sunset Infrared photography used in foggy days. Yellow light used in vehicles on foggy days. Red light used in signals.
82
1
2
One half of the reflecting surface of a concave mirror is coated with black paint. How will the image be affected? Brightness decreases Why a concave mirror is preferred for shaving? Enlarged VIRTUAL
3
Mirrors in search lights are parabolic and not spherical. Why? Produce intense parallel beam) eliminating spherical aberration
4
Using the mirror formula show that a virtual image is obtained when an object is placed in between the principal focus and pole of the concave mirror. 1 1 1 1 1 u
5
Using the mirror formula show that for a concave mirror, when the object is placed at the centre of curvature, the image is formed at the centre of curvature. 6 Find the position of an object, which when placed in front of a concave mirror of focal length 20cm, produces a virtual image which is twice the size of the object. Ans. 10cm 7 Plot a graph between 1/u and 1/v for a concave mirror. What does the slope of the graph yield? Ans. Straight line, slope =u/v=1/m 8 REFRACTION AND LENSES Which of the following properties of light: Velocity, wavelength and frequency, changes during the phenomenon (i) reflection (ii) refraction Ans. (i) No change (ii) velocity, wavelength change) 9 A convex lens is combined with a concave lens. Draw a ray diagram to show the image formed by the combination, for an object placed in between f and 2f of the convex lens. Compare the Power of the convex and concave lenses so that the image formed is real. Ans: f of convex lens must be less than f of concave lens to produce real image. So power of Convex greater than that of concave) 10 Derive a relation between the focal length and radius of curvature of a Plano convex lens made of glass. Compare the relation with that of a concave mirror. What can you conclude? Justify your answer. Ans. (f=2R) both are same. But applicable always in mirrors, but for lenses only in specific cases, the relation can be applied.) 83
11 In the given figure an object is placed at O in a medium (n2>n1). Draw a ray diagram for the image formation and hence deduce a relation between u, v and R n1 n2 n1 n2 v u R
12 Show that a concave lens always produces a virtual image, irrespective of the position of the object. uf But u is ve and f is ve for concave lens u f Ans. Hence v is always ve. that is virtual v
13 Sun glasses are made up of curved surfaces. But the power of the sun glass is zero. Why? Ans. It is convex concave combination of same powers. So net power zero A convex lens is differentiated to n regions with different refractive 14 indices. How many images will be formed by the lens? Ans. n images but less sharp 15 A convex lens has focal length f in air. What happens to the focal length of the lens, if it is immersed in (i) water (n=4/3) (ii) a medium whose refractive index is twice that of glass. Ans. 4f, f 16 Calculate the critical angle for glass air surface, if a ray falling on the surface from air, suffers a deviation of 150 when the angle of incidence is 400. Find n by Snell’s law and then find c=41.140 17 Two thin lenses when in contact produce a net power of +10D. If they are at 0.25m apart, the net power falls to +6 D. Find the focal lengths of the two lenses Ans. 0.125m, 0.5m) 18 A glass prism has an angle of minimum deviation D in air. What happens to the value of D if the prism is immersed in water? Ans. Decreases 19 Draw a ray diagram for the pat followed by the ray of light passing through a glass prism immersed in a liquid with refractive index greater than glass.
84
Three rays of light red (R) green (G) and blue (B) are incident on the surface of a right angled prism as shown in figure. The refractive indices for the material of the prism for red green and blue are 1.39, 1.43 and 1.47 respectively. Trace the path of the rays through the prism. How will the situation change if the rays were falling normally on one of the faces of an equilateral prism?
(Hint Calculate the critical angle for each and if the angle of incidence on the surface AC is greater, then TIR will take place.) 20 Show that the angle of deviation for a small angled prism is directly proportional to the refractive index of the material of the prism. One of the glass Prisms used in Fresnel’s biprism experiment has refractive index 1.5. Find the angle of minimum deviation if the angle of the prism is 30. (3) (D= (n1) A, 1.50) 21 . In the given diagram, a ray of light undergoes total internal reflection at the point C which is on the interface of two different media A and B with refractive indices1.7 and 1.5 respectively. What is the minimum value of angle of incidence? Can you expect the ray of light to undergo total internal reflection when it falls at C at the same angle of incidence while entering from B to A. Justify your answer?
n2=1.5 C
n1=1.7
A
85
B
Ans. Use SinC
nr 0.88 and C=61.70 so i=61.80 no for TIR ray of light nd
must travel from denser to rarer from B to A)
22 The velocity of light in flint glass for wavelengths 400nm and 700nm are 1.80x108m/s and 1.86x108 m/s respectively. Find the minimum angle of deviation of an equilateral prism made of flint glass for the given wavelengths. (For 400nm D=520 and for 700nm D=480) 23 In the given diagram a point object is kept at the Focus F of the convex lens. The ray of light from the lens falls on the surfaces AB and BC of a right angled glass prism of refractive index 1.5 at an angle 420.Where will be the final image formed? Draw a ray diagram to show the position of the final image formed. What change do you expect in your answer if the prism is replaced by a plane mirror? A
B
F
C
C=41.80 Ans at F itself, no change
86
OPTICAL INSTRUMENTS GIST 1 Human eye: Eye lens: crystalline Cilliary muscles: lens is held in position by these. Iris: Circular contractible diaphragm with an aperture near the centre. Pupil: the circular aperture is pupil. It adjusts controlling light entering the eye. Power of accommodation: ability of pupil for adjusting focal length. Far point: the maximum distant point that an eye can see clearly. Near point: closest distant that eye lens can focus on the retina. Range of vision: distant between near point and far point. 2 Defects of vision: Myopia: image formed in front of the retina. Correctionusing concave lens.
Hypermetropia image behind the retina. Correctionusing convex lens.
Presbiopialow
power
of
accommodation.
87
Correctionbifocal
lens.
Astigmatismcornea has different curvature in different direction. Correctionusing cylindrical Lens. 3
4
88
5
Astronomical Telescope: (Image formed at infinity – Normal Adjustment) fo + fe = L
fo
Eye
fe Fo Fe
α
•
α
Po
β
Pe
I Eyepiece
Image at infinity
Objective
Focal length of the objective is much greater than that of the eyepiece. Aperture of the objective is also large to allow more light to pass through it.
6 Angular magnification or Magnifying power of a telescope in normal adjustment
7
Newtonian Telescope: (Reflecting Type) Plane Mirror Light from star
Magnifying Power: M=
Eyepiece
fo Concave Mirror
fe Eye
8 Cassegrain telescope refer from NCERT / refer Page no 83 89
QUESTIONS MICROSCOPE AND TELESCOPE *1. You are given following three lenses. Which two lenses will you use as 2 an eyepiece and as an objective to construct an astronomical telescope? Lens Power (P) Aperture (A) L1 3D 8 cm L2 6D 1 cm L3 10D 1 cm
2. 3. 4. 5.
6.
Ans The objective of an astronomical telescope should have the maximum diameter and its eyepiece should have maximum power. Hence, L1 could be used as an objective and L3 could be used as eyepiece. Draw a ray diagram of a reflecting type telescope. State two advantages of this telescope over a refracting telescope. Draw a ray diagram of an astronomical telescope in the normal adjustment position, state two drawbacks of this type of telescope. Draw a ray diagram of a compound microscope. Write the expression for its magnifying power. The magnifying power of an astronomical telescope in the normal adjustment position is 100. The distance between the objective and the eyepiece is 101 cm. Calculate the focal lengths of the objective and of the eyepiece. How does the ‘resolving power’ of an astronomical telescope get affected on (i) Increasing the aperture of the objective lens? (ii) 90
2 2 2 2
2
7.
8.
*9.
Increasing the wavelength of the light used? What are the two ways of adjusting the position of the eyepiece while 5 observing the Final image in a compound microscope? Which of these is usually preferred and why? Obtain an expression for the magnifying power of a compound microscope. Hence explain why (i) we prefer both the ‘objective’ and the ‘eyepiece’ to have small focal length? and (ii) we regard the ‘length’ of the microscope tube to be nearly equal to be separation between the focal points of its objective and its eyepiece? Calculate the magnification obtained by a compound microscope having an objective of focal length 1.5cm and an eyepiece of focal length 2.5 cm and a tube length of 30. What are the two main considerations that have to be kept in mind 5 while designing the ‘objective’ of an astronomical telescope? Obtain an expression for the angular magnifying power and the length of the tube of an astronomical telescope in its ‘normal adjustment’ position. An astronomical telescope having an ‘objective’ of focal length 2m and an eyepiece of focal length 1cm is used to observe a pair of stars with an actual angular separation of 0.75. What would be their observed angular separation as seen through the telescope? Hint observed angular separation = 0.75’ ×200 = 150’ Cassegraintelescope uses two mirrors as shown inFig. Sucha telescope is built withthe mirrors20 mm apart. If theradius of curvature of thelarge mirror is 220mmand the small mirror is 140mm,where willthe final image of anobjectat infinitybe? Thefollowingfigure shows a Cassegraintelescope consistingof a concavemirrorand a convexmirror.
Distance betweenthe objective mirrorand thesecondary mirror,d = 20 mm Radiusof curvatureof the objectivemirror,R1=220 mm 91
Hence,focallength of the objectivemirror, Radiusof curvatureof the secondarymirror,R1=140 mm
Hence,focallength of the secondary mirror, Theimage of an object placedat infinity,formed by theobjectivemirror, will actas a virtual object for thesecondary mirror. Hence,the virtualobjectdistancefor the secondarymirror,
Applyingthe mirrorformulafor the secondarymirror,we can calculate
image distance(v)as: Hence, the final image will be formed315 mmawayfrom thesecondary mirror. 5
92
DEFECTS OF VISION 1.
Amyopic person has beenusingspectacles of power −1.0 dioptre for distant vision.Duringold age healso needs to use separate reading glass of power + 2.0 dioptres. Explain whatmay have happened. Ans Thepower of the spectaclesusedby the myopic person,P = −1.0 D Focallengthof the spectacles, Hence,the farpoint of theperson is 100 cm. He might havea normalnear point of 25
cm.Whenhe
uses
the
spectacles,
the
objects
placed
atinfinity
producevirtualimages at 100 cm.He uses the abilityof accommodation of theeyelensto see theobjects placedbetween 100 cmand 25 cm. During oldage, theperson uses reading glasses of (power, P=100/50) Theability of accommodationis lost in oldage.This defect is calledpresbyopia.As a result, he is unable to seeclearly theobjects placedat 25 cm.
2.
Amanwith normal nearpoint (25 cm)reads a book withsmallprint using amagnifyingglass: a thinconvex lens of focallength 5 cm.
(a) What is theclosest and the farthestdistanceatwhichhe should keepthe lens fromthe pages so that he canread the book when viewingthrough the magnifyingglass?
93
5 5
(b)Whatis the maximum and theminimumangular magnification (magnifying power) possible using theabove simple microscope? Ans (a)Focallengthof the magnifying lass f = 5 cm Least distance of distance vision, d = 25 cm Closest objectdistance= u Image distance, v= −d = −25 cm
Accordingto thelens formula,we have: Hence,the closestdistanceat whichthe person canread thebook is 4.167 cm. For theobjectat thefarthestdistant(u’), the imagedistance According to the lens formula,we have:
Hence,the farthest distance atwhich theperson can readthe book is 5cm. (b)Maximum angular magnification is given by therelation:
94
CONCEPT MAP
Optical Instruments
95
Wave Optics GIST
96
INTERFERENCEOF WAVES
97
DIFFRACTION OF LIGHT AT A SINGLE SLIT ;
98
Width of Central Maximum: θ1
A
d
• • • • • • • • • • • • •
0 1 2 3 4 5 6 7 λ/2 8 9 10 11 12
B
Plane Wavefront
•
P1 Dark y1
θ1
•O
D
N
Bright
θ1
λ Slit
y1 = D λ / d Since the Central Maximum is spread on either side of O, the width is
Screen β0 = 2D λ / d
POLARISATION OF LIGHT WAVES : Malus’ Law: When a beam of plane polarised light is incident on an analyser, the intensity I of light transmitted from the analyser varies directly as the square of the cosine of the angle θ between the planes of transmission of analyser and polariser. (2)
99
Polarisation by Reflection and Brewster’s Law:
CONCEPT MAP WAVE NATURE OF LIGHT
100
101
QUESTIONS Huygen's Principle 1.
Draw a diagram to show the refraction of a plane wave front incident on a convex lens and hence draw the refracted wave front.
1
2.
What type of wavefront will emerge from a (i) point source, and (ii) distance light source?
1
3.
Define the term wave front? Using Huygen’s construction draw a figure showing the propagation of a plane wave reflecting at the interface of the two media. Show that the angle of incidence is equal to the angle of reflection.
3
Define the term ‘wavefront’. Draw the wavefront and corresponding rays in the case of a (i) diverging spherical wave (ii) plane wave.Using Huygen’s construction of a wavefront, explain the refraction of a plane wavefront at a plane surface and hence deduce Snell’s law. Interference 1. How does the angular separation of interference fringes change, in Young’s experiment, when the distance between the slits is increased? Answhen separation between slits (d) is increased, fringe width β decreases.
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How the angular separation of interference fringes in young would’s double slit experiment change when the distance of separation between the slits and the screen is doubled? AnsNo effect (or the angular separation remains the same)
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Indoubleslitexperiment using light of wavelength 600 nm,the angular width of afringe formedon adistant screenis 0.1º.Whatis the spacingbetweenthe two slits? Ans Thespacing between theslits is
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*4. If the path difference produced due to interference of light coming out of two slits for yellow colour of light at a point on the screen be 3λ/2, what will be the colour of the fringe at that point? Give reasons. Ans. The given path difference satisfies the condition for the minimum of intensity for yellow light, Hence when yellow light is used, a dark fringe will be formed at the given point. If white light is used, all components of white light except the yellow one would be present at that point.
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State two conditions to obtain sustained interference of light. In Young’s 102
double slit experiment, using light of wavelength 400 nm, interference fringes of width ‘X’ are obtained. The wavelength of light is increased to 600 nm and the separation between the slits is halved. In order to maintain same fringe with, by what distance the screen is to be moved? Find the ration of the distance of the screen in the above two cases. AnsRatio3:1 6.
Two narrow slits are illuminated by a single monochromatic source. Name the pattern obtained on the screen. One of the slits is now completely covered. What is the name of the pattern now obtained on the screen? Draw intensity pattern obtained in the two cases. Also write two differences between the patterns obtained in the above two cases.
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*7. In Young’s doubleslit experiment a monochromatic light of wavelength λ, is used. The intensity of light at a point on the screen where path difference is λ is estimated as K units. What is the intensity of light at a point where path difference is λ /3? AnsK/4
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*8.
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Abeam of light consistingof two wavelengths,650 nm and 520 nm, is used toobtaininterference fringesin aYoung’s doubleslitexperiment.(a)Find thedistance of thethird brightfringeon the screenfrom the centralmaximum for wavelength 650 nm.(b)What is theleastdistancefrom thecentralmaximumwherethe brightfringes due toboth the wavelengths coincide? Ansa)
b)
3 *9
A narrow monochromatic beam of light of intensity I is incident a glass plate. Another identical glass plate is kept close to the first one and parallel to it. Each plate reflects 25% of the incident light and transmits 103
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the reaming. Calculate the ratio of minimum and maximum intensity in the interference pattern formed by the two beams obtained after reflection from each plate. Ans. Let I be the intensity of beam I incident on first glass plate. Each plate reflects 25% of light incident on it and transmits 75%. Therefore, I1 =I; and I2 = 25/100I = I/4;I3 =75/100 I = 3/4I;I4 = 25/100 I3 = 1⁄4 x 3⁄4 I = 3/16 I I5= 7/100 I4= 3⁄4 x 3/16 I = 9/64 I Amplitude ratio of beams 2 and 5 is R = √ I2/I5 = √I/4 x 64/91 = 4/3 Imin/ Imax = [r1/r+1]2 = [4/31 / 4/3+1]2 = 1/49 = 1:49 *10 In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance D from the slits. If the screen is moved 5 x 102 m towards the slits, the charge in fringe width is 3 x 10 5 m. If the distance between the slit is 103 m. Calculate the wavelength of the light used. Ans. The fringe width in the two cases will be β = Dλ/d;β ‘= D’λ/d β  β’ = (DD’)λ/d; or wavelength λ = (β  β’ )d / (DD’) But DD’ = 5 x 102 m β  β’ = 3 x 105 m , d= 103m;λ = 3 x 105 x 103 / 5 x 102 = 6 x 107m= 6000A 11. Two Sources of Intensity I and 4I are used in an interference experiment. Find the intensity at points where the waves from two sources superimpose with a phase difference (i) zero (ii) π/2 (iii) π. AnsThe resultant intensity at a point where phase difference is Φ is I R = I1 +I2+2√I1I2 Cos Φ As I1 =I and I2 = 4I therefore I R = I +4I+2√1.4I Cos Φ = 5I +4I cos Φ (i) when Φ =0 , I R = 5I +4I cos 0 = 9 I;(ii) when Φ =π/2 , I R = 5I +4I cos π/2 =5I (iii) when Φ =π , I R = 5I +4I cos π = I 12. What are coherent sources of light? Two slits in Young’s double slit experiment are illuminated by two different sodium lamps emitting light of the same wavelength. Why is no interference pattern observed? (b) Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence write the expression for the fringe width. (c) If S is the size of the source and its distance from the plane of the two slits, what should be the criterion for the interference fringes to be seen? 104
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Ansc) 13. What are coherent sources? Why are coherent sources required to produce interference of light? Give an example of interference of light in everyday life. In Young’s double slit experiment, the two slits are 0.03 cm apart and the screen is placed at a distance of 1.5 m away from the slits. The distance between the central bright fringe and fourth bright fringe is 1 cm. Calculate the wavelength of light used. Ans(Numerical part)
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14. What is interference of light? Write two essential conditions for sustained interference pattern to be produced on the screen. Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits are opened and (b) one of the slit is closed. What is the effect on the interference pattern in Young’s double slit experiment when: (i) Screen is moved closer to the plane of slits? (ii)Separation between two slits is increased. Explain your answer in each case. Diffraction
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*1. Why a coloured spectrum is seen, when we look through a muslin cloth and 2 not in other clothes? Ans. Muslin cloth is made of very fine threads and as such fine slits are formed. White light passing through these silts gets diffracted giving rise to colored spectrum. The central maximum is white while the secondary maxima are coloured. This is because the positions of secondary maxima (except central maximum) depend on the wavelength of light. In a coarse cloth, the slits formed between the threads are wider and the diffraction is not so pronounced. Hence no such spectrum is seen. 2.
A parallel beam of light of wavelength 600 nm is incident normally on a slit of 2 width ‘a’. If the distance between the slits and the screen is 0.8 m and the distance of 2nd order maximum from the centre of the screen is 15 mm, calculate the width of the slit. AnsDifference between interference and diffraction: Interference is due to 105
superposition of two distinct waves coming from two coherent sources. Diffraction is due to superposition of the secondary wavelets generated from different parts of the same wavefront. Numerical: Here, λ = 600 nm = 600 × 10−19 = 6 × 10−7 m D = 0.8 m, x = 15 mm = 1.5 × 10−3 m,n = 2, a = ?
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Why light ways do not diffracted around buildings, while radiowaves diffract 2 easily? Ans For diffraction to take place the wave length should be of the order of the size of the obstacle. The radio waves (particularly short radio waves) have wave length of the order of the size of the building and other obstacles coming in their way and hence they easily get diffracted. Since wavelength of the light waves is very small, they are not diffracted by the buildings. Draw the diagram showing intensity distribution of light on the screen for 3 diffraction of light at a single slit. How is the width of central maxima affected on increasing the (i) Wavelength of light used (ii) width of the slit? What happens to the width of the central maxima if the whole apparatus is immersed in water and why? State the condition under which the phenomenon of diffraction of light takes 5 place. Derive an expression for the width of central maximum due to diffraction of light at a single slit. A slit of width ‘a’ is illuminated by a monochromatic light of wavelength 700 nm at normal incidence. Calculate the value of ‘a’ for position of * (i) first minimum at an angle of diffraction of 30° (iii) first maximum at an angle of diffraction of 30° Ansi)
ii) Polarisation 1. At what angle of incidence should a light beam strike a glass slab of refractive index √3, such that the reflected and the refracted rays are 106
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perpendicular to each other? Ansi=600 2.
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What is an unpolarized light? Explain with the help of suitable ray diagram how an unpolarized light can be polarized by reflection from a transparent medium. Write the expression for Brewster angle in terms of the refractive index of denser medium. The critical angle between a given transparent medium and air is denoted by ic, A ray of light in air medium enters this transparent medium at an angle of incidence equal to the polarizing angle(ip). Deduce a relation for the angle of refraction (rp) in terms of ic. What is meant by ‘polarization’ of a wave? How does this phenomenon help us to decide whether a given wave is transverse or longitudinal in nature?
QUESTIONS (HOTS) VERY SHORT ANSWER QUESTIONS (1 MARK) 1. Air bubble is formed inside water. Does it act as converging lens or a diverging lens? 1 Ans : [Diverging lens] 2. A water tank is 4 meter deep. A candle flame is kept 6 meter above the level. µ for water is 4 3 . Where will the image of the candle be formed?. Ans : [6m below the water level] 1
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SHORTANSWER QUESTIONS (2 MARKS) 1. Water is poured into a concave mirror of radius of curvature ‘R’ up to a height h as shown in figure 1. What should be the value of x so that the image of object ‘O’ is formed on itself? 2
Fig 1 Fig 2 2. A point source S is placed midway between two concave mirrors having equal focal length f as shown in Figure 2. Find the value of d for which only one image is formed. 2 3. A thin double convex lens of focal length f is broken into two equals halves at the axis. The two halves are combined as shown in figure. What is the focal length of combination in (ii) and (iii). 2
4. How much water should be filled in a container 21cm in height, so that it appears half filled when viewed
from the top of the container a 4 3 ? 2
5. A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in figure and emerges from the other refracting face AC as RS such 108
that AQ= AR. If the angle, of prism A= 60 and µ of material of prism is 3 then find angle . 2 Hint : This a case of min .deviation 60
SHORT ANSWER QUESTIONS (3 MARKS) 1. A converging beam of light is intercepted by a slab of thickness t and refractive index µ. By what distance will the convergence point be shifted? Illustrate the answer. 3
1 X 1 t 2. In double slit experiment SS2 is greater than SS1 by 0.25 . calculate the path difference between two interfering beam from S1 and S2 for maxima on the point P as shown in Figure. 3
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VALUE BASED QUESTIONS 1. Ravi is using yellow light in a single silt diffraction experiment with silt width of 0.6 mm. The teacher has replaces yellow light by xrays. Now he is not able to observe the diffraction pattern. He feels sad. Again the teacher replaces xrays by yellow light and the diffraction pattern appears again. The teacher now explains the facts about the diffraction and • Which value is displayed by the teacher ? • Give the necessary condition for the diffraction. 2. Aditya participated in a group discussion in his school on “Human eye and its defects” in the evening he noticed that his father is reading a book by placing it at a distance of 50 cm or more from his eye. He advised him for his eye checkup. • Suggest the focal length/power of the reading spectacle for him, so that he may easily read the book placed at 25 cm from eye. • Name the value displayed by Aditya. 3. Vinod was watching a program on the topic MOON on the Discovery channel. He came to know from the observations recorded from the surface of Moon that the sky appears dark from there. He got surprised and wanted to know the reason behind it. He discussed it with his friends, and they had the reasons as 1. Phenomenon of refraction of light 2.Phenomenon of scattering of light and explained the topic to him in detail. (i) Name the value that was displayed by Vinod (ii ) what values were displayed by his friends
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7. DUAL NATURE OF MATTER & RADIATION GIST ELECTRON EMISSION 1. There are three types of electron emission, namely, Thermionic Emission, Photoelectric Emission and Field Emission. 2. The minimum energy required by an electron to escape from the metal surface is called work function. 3. Work function is conveniently expressed in electron volts ( e V ) 4. One electron volt is the energy gained or lost by an electron while passing through a potential difference of one volt. PHOTOELECTRIC EFFECT 1. The minimum energy required by an electron to come out from metal surface is called the work function of a metal. 2. Photo electric effect is the phenomenon of electrons by metals when illuminated by light of suitable frequency 3. Photo electric current depends on i) The intensity of incident light ii) The potential difference applied between two electrodes iii) The nature of the emitter material EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT
1. The minimum negative potential given to the anode plate for which the photo electric current becomes zero is called stopping potential. 2. The stopping potential Vo depends on i) The frequency of incident light and ii) the nature of emitter material. For a given frequency of incident light, the stopping potential is independent of its intensity. 2 K max eVo =(1/2)m vmax 2. Below a certain frequency (threshold frequency) γ0 , characteristics of the metal , no photo electric emission takes place, no matter how large the intensity may be. EINSTEIN’S PHOTO ELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION 111
1. Light is composed of discrete packets of energy called quanta or photons. 2. The energy carried by each photon is E = hν, where ν is the frequency and momentum p= h/λ. The energy of the photon depends on the frequency γ of the incident light and not on its intensity. 3. Photo electric emission from the metal surface occurs due to absorption of a photon by an electron 4. Einstein’s photo electric equation: Kmax = hν – φ0 or eV0 = hν  φ0. PARTICLE NATURE OF LIGHT: THE PHOTON 1. Radiation has dual nature: wave and particle. The wave nature is revealed in phenomenon like interference, diffraction and polarization. The particle nature is revealed by the phenomenon photo electric effect. 2. By symmetry, matter also should have dual nature: wave and particle. The waves associated with the moving material particle are called matter waves or De Broglie waves. 3. The De Broglie wave length (λ) associated with the moving particle is related to its moment p as: λ =h/p = h/mv 4.An equation for the De Broglie wavelength of an electron accelerated through a potential V. Consider an electron with mass ‘m’ and charge ‘e’ accelerated from rest through a potential V. K = eV K = 1/2mv2 = p2/2m P2 = 2mK P = √2mK = √2meV λ = h/ √2meV Substituting numerical values of h, m and e λ = (1.227/√V) nm.
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CONCEPT MAP
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1* 2∗ 3 4∗ 5 6 7∗
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QUESTIONS ELECTRON EMISSION, PHOTO ELECTRIC EFFECT If the intensity of incident radiation in a photoelectric experiment is doubled what, happens to kinetic energy of emitted photo electrons? 1 10 Calculate the frequency associated with photon of energy 3.3 x 10 J? Ans: ν = 5 x 10 23Hz. 1 What is the momentum of a photon of energy 1 MeV? 1 Energy E = 1 MeV = 1.6 x 10 13J, p = E/c= 5.33x 1022 Kgm/s What happens to the velocity of emitted electrons when the wave length of incident light is decreased? 1 If the frequency of incident radiation in a photocell is increased, does it affect the stopping potential? If so how? 1 On what factor does the energy carried by a quantum of light depend? 1 The threshold wave length for photoelectric emission from a given surface is 5200Ǻ. Will photo electric emission takes place, if an ultra violet radiation of one watt power is incident on it? 1 Name the element with highest work function and also the element with lowest work function. Highest work function – Platinum ( 5.65eV ) Lowest work function – Caesium ( 2.14eV ) 2 Calculate the work function of a metal in eV if its threshold wavelength is 6800Å. Ans: Work function = hc / λ0 = 1.825eV. 2 Work function of aluminium is 4.2eV. If two photons each of energy 2.5eV are incident on its surface, will the emission of electrons take place? 2 A source of light is placed at a distance of 50cm from a photocell and the cut off potential is found to be V0. If the distance between the light source and the cell is made 20cm, what will be the new cut off potential? Ans: Stopping potential is still Vo. 2 EINSTEIN’S
PHOTO
ELECTRIC
EQUATION 114
:ENERGY
QUANTUM
OF
12 13 14 15 16
17*
18
19*
20*
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RADIATION Which of the two photons is more energetic: red light or violet light? 1 What will be the stopping potential when a photon of 25eV is incident of metal surface of work function 6eV? Ans : 19 volt 1 Why is alkali metal surfaces better suited as photosensitive surfaces?1 Blue light can eject electrons from a photosensitive surface while orange light can not. Will violet and red light eject electrons from the same surface? Two metals A & B have work functions 4eV & 10eV respectively. In which case the threshold wave length is higher? 1 A radio transmitter at a frequency of 880 kHz and a power of 10kW. Find the number of photons emitted per second. 2 Ans: n = energy emitted per second/energy of one photon = 1.716 x 1031. A parallel beam of light is incident normally on a plane surface absorbing 40% of the light and reflecting the rest. If the incident beam carries 10W of power, find the force exerted by it on the surface. 2 8 Ans : 5.33 x 10 N No photoelectrons are emitted from a surface, if the radiation is above 5000 Ǻ. With an unknown wavelength, the stopping potential is 3V. Find the wave length. 3 Ans : 2262Ǻ Illuminating the surface of a certain metal alternately with light of wave lengths0.35μm and 0.54μm, it was found that the corresponding maximum velocities of photoelectrons have a ratio 2. Find the work function of that metal. 3 Ans: 5.64eV A beam of light consists of four wavelengths 4000Ǻ, 4800Ǻ, 6000Ǻ & 7000Ǻ, each of intensity 1.5mW/m2. The beam falls normally on an area 104m2 of a clean metallic surface of work function 1.9eV.Assuming no loss of kinetic energy, calculate the number of photoelectrons emitted per second. Ans :E1 = 3.1eV, E2 = 2.58eV, E3 = 2.06eV, E4 = 1.77eV 3 Only the first three wave lengths can emit photo electrons. Number of photo electrons emitted per second = IA ( 1/E1+1/E2+1/E3 ) = 1.12 x 1012. ( Hint – convert eV into joule before substitution ) In an experiment on photo electric emission , following observations were made; ( i ) wave length of incident light = 1.98 x 107m 115
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( ii ) stopping potential = 2.5 V. Find ( a ) kinetic energy of photo electrons with maximum speed ( b ) work function & ( c ) threshold frequency 3 Ans; ( a ) Kmax = 2.5eV ( b ) work function = 3.76eV ( c ) threshold frequency = 9.1x 1014Hz WAVE NATURE OF MATTER What is the de Broglie wavelength (in Å) associated with an electron accelerated through a potential of 100 V?1 Ans: λ = 1.227 A o Matter waves associated with electrons could be verified by crystal diffraction experiments .Why? 1 Ans: The wave length of the matter waves associated with electrons has wave lengths comparable to the spacing between the atomic planes of their crystals. 1 How do matter waves differ from light waves as regards to the velocity of the particle and the wave? 1 Ans: In case of matter waves, the wave velocity is different from the particle velocity. But in case of light, particle velocity and wave velocity are same. An electron and an alpha particle have same kinetic energy. Which of these particles has the shortest de Broglie wavelength? 1 Ans: Alpha particle The de Broglie wavelength of an electron is 1 A0. Find the velocity of the electron. 1 6 Ans: 7.3 x 10 m/s Find the ratio of wavelength of a 10 k eV photon to that of a 10 keV electron. Ans: 10 ( Hint: λphoton = 1.24 A0, λelectron = 0.1227 A0 ) 2 A proton and an alpha particle are accelerated through the same potential difference. Find the ratio of the wavelengths associated with the two. 2 Ans: (Hint λ = h/ √2meV), λp : λα = 2 √2 : 1 Why macroscopic objects in our daily life do not show wave like properties? OR Why wave nature of particles is significant in the subatomic domain only? 2 Macroscopic objects in our daily life do not show wave like properties because the wave length associated with them is very small and beyond the scope of any measurement. In the sub atomic world, masses of the particles are extremely small leading to a wave length that is measurable. Show that Bohr's second postulate 'the electron revolves around the nucleus 116
10*
only in certain fixed orbits without radiating energy can be explained on the basis of de Broglie hypothesis of wave nature of electron. 2 Ans. The de Broglie wavelength for electron in orbit mvr = nh/ 2π This is Bohr's second postulate. As complete deBroglie wavelength may be in certain fixed orbits, nonradiating electrons can be only in certain fixed orbits. The deBroglie wavelength associated with an electron accelerated through a potential difference V is . What will be the deBroglie wavelength when the accelerating p.d. is increased to 4V? 2
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Determine the accelerating potential required for an electron to have a deBroglie wavelength of 1 Å 2 Ans: V = 150.6 V An electron, an alpha particle and a proton have the same kinetic energy, which one of these particles has (i) the shortest and (ii) the largest, deBroglie wavelength? 2 Ans: =
13
V 1 1 4 , 2 2 V1 2 1 2 v 2
h 2mEk
1 m
The two lines A and B shown in the graph plot the deBroglie wavelength λ as function of 1/ √V (V is the accelerating potential) for two particles having the same charge. Which of the two represents the particle of heavier mass? 2
Ans: Slope of the graph is h/√2me. Slope of A is smaller, so A represents heavier particle. 14*
Find the ratio of deBroglie wavelength of molecules of Hydrogen and Helium which are at temperatures 270C and 1270C respectively. 3 Ans: de Broglie wavelength is given by λH2 /λ He = √(m He T He/m HT H = √(8/3)
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VALUE BASED QUESTIONS 1. Rahim, a class XI student of KV, visited his uncle and hears the burglar alarm on opening the entrance door; his aunt welcomes him. He goes upstairs and asks his uncle who is a Physics Lecturer, about the principle working of a burglar alarm. He discusses this with his class mates and decides to present a program on ‘Burglar Alarm’ in the morning assembly. a) How will you define the inquisitiveness of Rahim? b) State the laws of photoelectric emission (ANS: curiosity to learn, interest in the subject, sharing knowledge; b) Refer NCERT book)
2.
In an experiment of photoelectric effect, Nita plotted graphs for
different observation between photo electric current and anode potential but her friend Kamini has to help her in plotting the correct graph. Neeta Thanked Kamini for timely help. a)
What value was displayed were Kamini and Neeta.
b)
Draw the correct graph between I and V
ANS: a) sharing and caring b) Refer NCERT
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8. ATOMS & NUCLEI GIST Thomson’s model of atom Every atom consists of fuels charged sphere in which Its drawbacks: couldn’t explain large electrons are embedded like seeds in water angle scattering & the origin of spectral melon. series. Rutherford’s model of atom i) Every atom consists of a tiny central core, called the Limitations: couldn’t explain the stability atomic nucleus, in which the entire positive of the nucleus & the emission of line charge and almost entire mass of the atom spectra of fixed frequencies. are concentrated. ii) The size of nucleus is of the order of 1015 m , which is very small as compared to the size of the atom which is of the order of 1010 m. iii)The atomic nucleus is surrounded by certain number of electrons. As atom on the whole is electrically neutral, the total negative charge of electrons surrounding the nucleus is equal to total positive charge on the nucleus. iv)These electrons revolve around the nucleus in various circular orbits as do the planets around the aun. The centripetal force required by electron for revolution is provided by the electrostatic force of attraction between the electrons and the nucleus.
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r0=2kZe2 1/2mv2 Distance of closest approach of the alpha particle in the α particle scattering experiment
b=kZe2cotθ/2 1/2mv2 Limitationsapplicable only for hydrogen like atoms & couldn’t explain the splitting of spectral lines. (not consider electro static force among the electrons)
Impact parameter of the alpha particle
Bohr’s model of atom
Orbit radius of the electron around the r=e2/4πЄ0mv2, v=2πke2 / nh, r=n2h2mke2 nucleus Energy of the electron in the nth orbit of En= me4/8Є02n2h2 = 13.6/n2 eV hydrogen atom E=2.18*1018 J / n2 Angular momentum of electron in any orbit L = mvr = nh/2π, n=1,2,3,… is integral multiple of h/2π 1/λ = R(1/n12 – 1/n22)
Wave number ν
R=1.097 * 10+7m1
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No of protons in a nucleus
Atomic Number (Z)
No. of nucleons(protons + neutrons) in a nucleus AZ R=R0 A1/3
Mass Number (A) Number of neutrons Nuclear radius
Ρ= 3m/4πR03
Nuclear density
Same Z & different A Ex, 1H2,1H3,1h1, & C12,C14,C16 Same A & different Z [ 18Ar40,20Co40] & (1H3, 2H3) Same no. of neutrons Mass of neutrons – 1H3, 2He4 E= m x c2 ( m= mass of reactants – mass of products) 1 a.m.u.= 931.5 Mev dN/dt=λN dW/dt= R= Activity unit Bq. N =N0eλt
Isotopes Isobars Isotones Map defect
m
Binding energy Eb Radioactive decay law
OR No: of nuclei remaining undecayed at any instant of time N=N0( ½)n , n = t/t1/2
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t1/2=0.693 λ τ= 1/λ Alpha,beta,gamma
Half life Mean life 3 types of radiations
Splitting of a heavy nucleus into lighter elements.This process is made use of in Nuclear reactor & Atom bomb Nuclear Reactor is based upon controlled nuclear chain reaction and has 1) Nuclear fuel 2) modulator 3) control rods 4) coolant 5) shielding
Nuclear fission
Fusing of lighter nuclei to form a heavy nucleus.This process takes place in Stars & Hydrogen bomb. Controlled Thermonuclear Fusion In a fusion reactora) high particle density is required b) high plasma temperature of 109K c) a long confinement time is required
Nuclear fusion
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CONCEPT MAP
Nuclear energy uclear Energy
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QUESTIONS ALPHA PARTICLE SCATTERING 1. What is the distance of closest approach when a 5Mev proton approaches a gold nucleus (Z=79) (1) 1 Ze 2 Ans r0= = 2.3 * 1014m. 4 F2 2. Which has greater ionizing power: alpha or beta particle? (1) BOHR’S ATOMIC MODEL 1. In Bohr’s theory of model of a Hydrogen atom, name the physical quantity which equals to an integral multiple of h/2∏? (1) Ans: Angular momentum 2. What is the relation between ‘n’ & radius ‘r’ of the orbit of electron in a Hydrogen atom according to Bohr’s theory? (1) 2 Ans: r α n 3. What is Bohr’s quantization condition? (1) *4. For an electron in the second orbit of hydrogen, what is the moment of linear momentum as per the Bohr’s model? (2) Ans: L=2(h/2∏) =h/∏ (moment of linear momentum is angular momentum) 5. Calculate the ratio of energies of photons produced due to transition of electron of hydrogen atoms from 2nd level to 1st and highest level to second level.E21 = Rhc[ 1/n12 – 1/n2] = ¾ Rhc E∞  E1 = Rhc(1/22 – 1/∞) = Rhc / 4 (3) SPECTRAL SERIES *1. What is the shortest wavelength present in the Paschen series of hydrogen spectrum? (2) Ans: n1=3, n2=infinity, λ=9/R=8204Ǻ 2. Calculate the frequency of the photon which can excite an electron to 3.4 eV from 13.6 eV. Ans: 2.5x1015Hz (2) 124
3. The wavelength of the first member of Balmer series in the hydrogen spectrum is 6563Å.Calculate the wavelength of the first member of Lyman series in the same spectrum. Ans: 1215.4Å (2) 4. The ground state energy of hydrogen atom is 13.6eV.What is the K.E & P.E of the electron in this state? (2) Ans: K.E=E=13.6 eV, P.E=2K.E=27.2 eV *5. Find the ratio of maximum wavelength of Lyman series in hydrogen spectrum to the maximum wavelength in Paschen Series? (2) Ans: 7:108 *6. The energy levels of an atom are as shown below. a) Which of them will result in the transition of a photon of wavelength 275 nm? b) Which transition corresponds to the emission of radiation maximum wavelength? (3) 0eV A 2eV B C 4.5eV D 10eV Ans: E=hc/λ=4.5eV, transition B Eα1/λ, transition A *7. The spectrum of a star in the visible & the ultraviolet region was observed and the wavelength of some of the lines that could be identified were found to be 824Å,970Å,1120Å,2504Å,5173Å &6100Å.Which of these lines cannot belong to hydrogen spectrum? (3) Ans: 970Å (3) 9. What is the energy possessed by an ē for n= ? Ans E=0 (1) 10. Calculate the ratio of wavelength of photon emitted due to transition of electrons of hydrogen atom from i) Second permitted level to first level ii) Highest permitted level to second level (3) 11 11. The radius of inner most electron orbit of H2 atom is 5.3 x 10 m. What are radii for n=2, 3, 4? Ans: rn = n2r1(3) COMPOSITION OF NUCLEUS 1. What is the relation between the radius of the atom & the mass number?(1) Ans: size α A1/3 125
2. What is the ratio of the nuclear densities of two nuclei having mass numbers in the ratio 1:4? Ans: 1:1 (1) 3. How many electrons, protons & neutrons are there in an element of atomic number (Z) 11& mass number (A) 24? Hint: ne = np =11, nn = (A – Z) = 24 11 = 13 4. Select the pairs of isotopes & isotones from the following: (2) 13 14 30 31 i. C6 ii. N7 iii. P15iv. P15 Ans: isotopesiii &iv ,isotonesi& ii 5. By what factor must the mass number change for the nuclear radius to become 1 3
twice? 2 or 2 timeA (2) 3
NUCLEAR FORCE & BINDING ENERGY. 1. What is the nuclear force? Mention any two important properties of it. (2) 2. Obtain the binding energy of the nuclei 56Fe26 &209Bi83in MeV from the following data: mH=1.007825amu,mn=1.008665amu, m(56Fe26)=55.934939amu, m(209 Bi 83)=208.980388amu, 1amu=931.5MeV 3. Which nucleus has the highest binding energy per nucleon? (3) 56 Ans: Fe →492.26MeV,8.79MeV/A Bi →1640.3MeV,7.85 MeVHence Fe26 4. From the given data, write the nuclear reaction for α decay of 238 92U and hence calculate the energy released.
238U .92
= 238.050794u
4 = 2 He
4.00260u
234 90Th =
234.04363u (3) 16 & 35 5Binding Energy of 8O 17C one 127.35 Mev and 289.3 Mev respectively. Which of the two nuclei is more stable stability & BE/N? (2) RADIOACTIVITY 1. How is a particle different from an electron? (1) 2. Draw graph between no. of nuclei undecayed with time for a radioactive substance (1) 3. Among the alpha, beta & gamma radiations, which are the one affected by a magnetic field? (1) Ans: alpha & beta 4. Why do α particles have high ionizing power? (1) Ans: because of their large mass & large nuclear cross section 5. Write the relationship between the half life & the average life of a radioactive substance. (1) Ans: T =1.44t1/2 126
6. If 70% of a given radioactive sample is left undecayed after 20 days, what is the % of original sample will get decayed in 60 days? (2) 7. How does the neutron to proton ratio affected during (i) decay ii) α decay(2) 8. A radioactive sample having N nuclei has activity R. Write an expression for its half life in terms of R & N. (2) Ans: R=Nλ, t1/2=0.693/λ =0.693N/R 9. Tritium has a half life of 12.5 years against beta decay. What fraction of a sample of pure tritium will remain undecayed after 25 years? (2) Ans: N0/4 10. What percentage of a given mass of a radioactive substance will be left undecayed after 5 halflife periods? (2) n Ans: N/N0 =1/2 =1/32 =3.125% 11. A radioactive nucleus ‘A’ decays as given below: β γ A A1 A2 If the mass number & atomic number of A1 are 180 & 73 respectively, find the mass number & atomic number of A & A2 (2) Ans: A—180 & 72, A2—176 & 71 12. Two nuclei P & Q have equal no: of atoms at t=0.Their half lives are 3 & 9 hours respectively. Compare the rates of disintegration after 18 hours from the start. (2) Ans: 3:16 *13. Two radioactive materials X1& X2 have decay constants 10λ & λ respectively. If initially they have the same no: of nuclei, find the time after which the ratio of the nuclei of X1 to that of X2 will be 1/e? Ans: N=N0eλt, t=1/9λ (3) *14. One gram of radium is reduced by 2.1mg in 5 years by decay. Calculate the halflife of Uranium. Ans: 1672 years (3) *16. At a given instant there are 25% undecayed radioactive nuclei in a sample. After 10 seconds the number of undecayed nuclei reduces to 12.5 %.calculate the i) mean life of the nuclei ii) the time in which the number of the undecayed nuclei will further reduce to 6.25 % of the reduced number. Ans: t1/2=10s, λ=.0693/s, τ=1/λ=14.43s, N=1/16(N0/8) →t=4x10=40s (3) 17. Half lives of two substances A and B are 20 min and 40 min respectively. Initially the sample had equal no of nuclei. Find the ratio of the remaining no: of nuclei of A and B after 80 min. Ans: 1:4 (3) 127
NUCLEAR REACTIONS 1. Why heavy water is often used in a nuclear reactor as a moderator? (1) 2. Why is neutron very effective as a bombarding particle in a nuclear reaction?(1) Ans: Being neutral it won’t experience any electrostatic force of attraction or repulsion. 3. Why is the control rods made of cadmium? (1) Ans: They have a very high affinity on neutrons. 4. Name the phenomenon by which the energy is produced in stars. (1) Ans: Uncontrolled Nuclear fusion 5. Name the physical quantities that remain conserved in a nuclear reaction?(1) 6. What is neutron multiplication factor? For what value of this, a nuclear reactor is said to be critical? Ans: K=1 (2) 7. 4 nuclei of an element fuse together to form a heavier nucleus .If the process is accompanied by release of energy, which of the two: the parent or the daughter nuclei would have higher binding energy per nucleon. Justify your answer. (2) 8. If 200MeV energy is released in the fission of single nucleus of 235 92𝑈, how much fission must occur to produce a power of 1 kW. (3)
VALUE BASED QUESTIONS 1. Medha’s grandfather was reading article is newspaper. He read that after so many years of atomic bombing is Hiroshima or Nagasaki, Japan National census indicated that children born even now are genetically deformed. His grandfather was not able to understand the reason behind it. He asked his Granddaughter Medha who is studying in class XII science. Medha sat with her grandfather and showed him pictures from some books and explained the harmful effects of radiations. (i) What are the values/ skills utilized by Kajal to make her grandfather understand the reason of genetically deformity? (ii) Name the nuclear reactions that occurred is atom bomb. 2. Muthuswami a resident of Kundakulam was all set to leave everything and shift to another place in view of the decision of Govt. to start nuclear thermal power plant at Kundakulam. His granddaughter Prachi, a science student, was really upset on the ignorant decision of her grandfather. She could finally convince 128
him not to shift, since adequate safety measures to avoid any nuclear mishap have already been taken by the Govt. before starting nuclear thermal plants. • What is the value displayed by Prachi in convincing her grandfather • What is the principle behind working of nuclear reactor • What are the main components of nuclear reactor
129
9. ELECTRONIC DEVICES GIST ENERGY BAND DIAGRAMS In metals, the conduction band and valence band partly overlap each other and there is no forbidden energy gap. In insulators, the conduction band is empty and valence band is completely filled and forbidden gap is quite large = 6 eV. No electron from valence band can cross over to conduction band at room temperature, even if electric field is applied. Hence there is no conductivity of the insulators. In semiconductors, the conduction band is empty and valence band is totally filled. But the forbidden gap between conduction band and valence band is quite small, which is about 1 eV. No electron from valence band can cross over to conduction band. Therefore, the semiconductor behaves as insulator. At room temperature, some electrons in the valence band acquire thermal energy, greater than energy gap of 1 eV and jump over to the conduction band where they are free to move under the influence of even a small electric field. Due to which, the semiconductor acquires small conductivity at room temperature
Metals
Insulators
Semiconductors
Differences Distinction between Intrinsic and Extrinsic Semiconductor Intrinsic Extrinsic 1 It is pure semiconducting 1 It is prepared by doping a small material and no impurity quantity of impurity atoms to the pure atoms are added to it semiconducting material. 2 Examples are crystalline 2 Examples are silicon and germanium forms of pure silicon and crystals with impurity atoms of arsenic, germanium. antimony, phosphorous etc. or indium, boron, aluminum etc. 3 The number of free electron 3 The number of free electrons and holes in conduction band and the is never equal. There is excess of number of holes in valence electrons in ntype semiconductors and 130
4 5
band is exactly equal and very excess of holes in ptype small indeed. semiconductors. Its electrical conductivity is 4 Its electrical conductivity is high. low Its electrical conductivity is a 5 Its electrical conductivity depends upon function of temperature the temperature as well as on the alone. quantity of impurity atoms doped in the structure.
Distinction between ntype and ptype semiconductors ntype semiconductors ptype semiconductors 1 It is an extrinsic 1 It is an intrinsic semiconductors which semiconductors which is is obtained by doping the impurity obtained by doping the atoms of III group of periodic table to impurity atoms of Vth group the pure germanium or silicon of periodic table to the pure semiconductor. germanium or silicon semiconductor. 2 The impurity atoms added, 2 The impurity atoms added, create provide extra electrons in the vacancies of electrons (i.e. holes) in the structure, and are called structure and are called acceptor donor atoms. atoms. 3 The electrons are majority 3 The holes are majority carriers and carriers and holes are electrons are minority carriers. minority carriers. 4 The electron density (ne) is 4 The hole density (ne) is much greater much greater than the hole than the electron density (nh)i.e. nh>> density (nh)i.e. ne>>(nh) ne 5 The donor energy level is 5 The acceptor energy level is close to close to the conduction band valence band and is far away from the and far away from valence conduction band. band. 6 The Fermi energy level lies in 6 The Fermi energy level lies in between between the donor energy the acceptor energy level and valence level and conduction band. band. Pn junction diode 131
Two important processes occur during the formation of pn junction diffusion and drift. The motion of majority charge carriers give rise to diffusion current. Due to the space charge on nside junction and negative space charge region on pside the electric field is set up and potential barrier develops at the junction Due to electric field e on pside moves to n and holes from nside to pside which is called drift current. In equilibrium state, there is no current across pn junction and potential barrier across pn junction has maximum value . The width of the depletion region and magnitude of barrier potential depends on the nature of semiconductor and doping concentration on two sides of pn junction. Forward Bias Pn junction is FB when ptype connected to the +ve of battery and ntype connected to –ve battery Potential barrier is reduced and width of depletion layer decreases. Reverse Bias Pn junction in RB ptype connected to the –ve battery and ntype connected to +ve Resistance of pn junction is high to the flow of current.
0 Rrectification
132
LED
PHOTODIODE
SOLARCELL
Forward biased
Reverse biased
No external baising,It generates emf when
133
Recombination of electrons and holes take place at the junction and emits e m radiations
Energy is supplied by light to take an electron from valence band to conduction band.
It is used in Burglar alarm, remote control
It is used in photo detectors in communication
solar radiation falls on it. Generation of emf by solar cells is due to three basic process generation of eh pair,separation and collection It is used in satellites,space vechicles calculators.
• There are two types of transistor – NPN & PNP
• Applications of transistor (1) Transistor as a switch (2) Transistor as an amplifier • Transistor as an oscillator Transistor Switch When a transistor is used in cut off or saturated state, it behaves as a switch.
134
TransistorAmplifier_ An amplifier is a device which is used for increasing the amplitude of variation of alternating voltage or current or power,thus it produces an enlarged version of the input signal. For Circuit diagram refer Ncert diagram
135
TransistorOscillator• In an oscillator, we get ac output without any external input signal. In other words, the output in an oscillator is self sustained. Oscillator converts D.C into A.C Digital Electronics –Logic Gates • The three basic Logic Gates are
(1) OR Gate OUTPUT Y= A + B (2) AND Gate OUTPUT Y=A.B (3) NOT GATE OUTPUT Y=Y’
COMBINATION OF GATES __ (1) NOR GATEOUT PUT Y = A+B __ (2) NAND GATEOUT PUT Y= A .B
136
CONCEPT MAP
Semiconductor and electronic devices
137
QUESTIONS SEMICONDUCTORS 1. What is the order of energy gap in an intrinsic semiconductor? (1) 2. How does the energy gap vary in a semiconductor when doped with penta valent element? (1) 3. How does the conductivity change with temperature in semiconductor?(1) 4. What type of semiconductor we get when: Ge is doped with Indium? Si is doped with Bismuth? (1) 13 3 5. In a semiconductor concentration of electron is 8 x 10 cm and holes 5 x 1012 cm2 : is it P or N type semiconductor? (1) 6. Draw energy gap diagram of a P Type semiconductor? (1) 7. What is Fermi energy level? (1) 8. Energy gap of a conductor, semiconductor, insulator are E1, E2, E3 respectively. Arrange them in increasing order. (1) 9. Name the factor that determines the element as a conductor or semiconductor? (1) 10. Why semiconductors are opaque to visible light but transparent to infrared radiations? (2) Ans: The photons of infrared radiation have smaller energies, so they fall to excite the electrons in the valence band. Hence infrared radiations pass through the semiconductors as such; i.e. a semiconductor is transparent to infrared radiation 11. The ratio of number of free electrons to holes ne/nh for two different materials A and B are 1 and <1 respectively. Name the type of semiconductor to which A and B belongs. (2) Ans: If ne/nh =1 . Hence A is intrinsic semiconductor. If ne/nh<1 , ne
PN JUNCTION DIODE 138
1. How does the width of depletion layer change, in reverse bias of a pn junction diode? (1) 2. Draw VI characteristic graph for a Zener diode? (1) 3. In a given diagram, is the diode reverse (or) forward biased? (1)
Ans: Reverse biased. 4. Why Photo diode usually operated at reverse bias? (2) 5. State the factor which controls wave length and intensity of light emitted by LED. (2) Ans: (i) Nature of semiconductor (ii) Forward Current 6. With the help of a diagram show the biasing of light emitting diode. Give two advantages over conventional incandescent Lamp. (2) Ans: Mono chromatic, Consume less power. 8. Draw a circuit diagram to show, how is a photo diode biased? (2) 16 9. Pure SI at 300K have equal electron and holes concentration 1.5 x 10 per m3. Doping by Indium increases hole concentration to 4.5 x 1022 per m3. Calculate new electron concentration. Ans: nenh = ni2 (2) 10. VI characteristics of SI diode is given. Calculate diode resistance for bias voltage 2V. (2)
Ans: R = V / I = 2/70 x 10 3 Ohms 11. What is an ideal diode? Draw its output wave form. 13. In the following diagram, identify the diodes which are in forward biased and which are in reversed biased. +10V
139
2
+5V
1
0V
3
12V
R 4
10V
0V 5V
*14. A semiconductor has equal electron and hole concentrations of 6x108/m3. On doping with a certain impurity, the electron concentration increases to 9x1012/ m3. (2) (i) Identify the new semiconductor obtained after doping. (ii) Calculate the new hole concentrations. Ans: (i) ntype semiconductor. (ii) nenh=ni 2 => nh=6x108 x6x108 = 4x104 perm2 *15. Determine the current through resistance “R” in each circuit. Diodes D1 and D2 are identical and ideal. 2
Ans: In circuit (i) Both D1 and D2 are forward biased hence both will conduct current and resistance of each diode is “0”.Therefore I = 3/15 = 0.2 A (i) Diode D1 is forward bias and D2 is reverse bias, therefore resistance of diode D1 is “0” and resistance of D2 is infinite. Hence D1 will conduct and D2 do not conduct. No current flows in the circuit. 140
16. From the given graph identify the knee voltage and breakdown voltage. Explain? (2)
*17. Germanium and silicon junction diodes are connected in parallel. A resistance R, a 12 V battery, a milli ammeter (mA) and Key(K) is closed, a current began to flow in the circuit. What will be the maximum reading of voltmeter connected across the resistance R? (2)
Ans: The potential barrier of germanium junction diode is 0.3v and silicon is 0.7V, both are forward biased. Therefore for conduction the minimum potential difference across junction diode is 0.3V.Max.reading of voltmeter connected across R=120.3=11.7V. 18.A Zener diode has a contact potential of .8Vin the absence of biasing .It undergoes breakdown for an electricfield of 10V/m at the depletion region of pn junction.If the width of the depletion region is 2.4µm?What should be the reverse biased potential for the Zener breakdown to occur? 2 *18. A germanium diode is preferred to a silicon one for rectifying small voltages. Explain why? (2) Ans: Because the energy gap for Ge (Eg = 0.7 ev) is smaller than the energy gap for Si (Eg = 1.1eV) or barrier potential for Ge
*1. A photodiode is fabricated from a semiconductor with a band gap of 2.8eV.can it Can it detect a wavelength of 600nm?Justify? (2) Ans: Energy corresponding to wavelength 600 nm is E=hc/ = 6.6x1034 x 3x108 joule = 0.2eV. 600x109 It cannot detect because E
Ans: In fig (i) emitter –base junction has no source of emf. Therefore Ic =0, bulb will not glow. In fig (ii) emitter – base junction is forward biased; therefore lamp “L” will glow. (iii) emitter – base junction is received biased so the bulb will not glow. *3. Why do we prefer NPN transistor to PNP for faster action? (2) Ans: For faster action NPN Transistor is used. In an NPN transistor, current conduction is mainly by free electron, whereas in PNP type transistor, it is mainly holes. Mobility of electrons is greater than that of holes. 4. In which mode, the cut off, active or saturation, the transistor is used as a switch? Why? (2) Ans: Cut off & saturation 5. In NPN transistor circuit, the collector current is 5mA. If 95% of the electrons emitted reach the collector region, what is the base current? (2) Here, Ic=95% of Ie = (95 / 100 ) Ie Ie = (100 / 95) × 5 mA = 5.26mA, Ie=Ic+ Ib 142
Ib = 0.25 mA 6. A student has to study the input and output characteristics of a npn silicon transistor in the common emitter configuration. What kind of a circuit arrangement should she use for this purpose? Draw the typical shape of input characteristics likely to be obtained by that student. (Ans: Fig 14.29, pg 493 & 494 NCERTPart2 physics 7. Which of input and output circuits of a transistor has a higher resistance and why? (3) Ans: The output circuit of a transistor has a higher resistance. Hint: The ratio of resistance of output circuit (r0) is 104 times that of input circuit ie ro =104ri; *8. In the circuit diagram given below, a volt meter is connected across a lamp. What changes would occur at lamp “L” and voltmeter “V”, when the resistor R is reduced? Give reason for your answer. (3)
Ans: In the given circuit, emitter –base junction of NPN transistor is forward biased. When “R” decreases, IE increases. Because IC = IE – I B. Therefore IC will also increase. Hence bulb will glow with more brightness and voltmeter reading will increase. 9. The base current of a transistor is 105 µA and collector current is 2.05 mA. (3) a) Determine the value of , Ie , and α b) A change of 27 µA in the base current produces a change of 0.65 mA in the collector current. Find a.c. Ic = 2.05 × 10 Ib = 105 × 10 6A 3A = Ic / Ib = 19.5 Also, Ie = Ib + Ic = 2.155 × 10 3 A α = Ic / Ie = 0.95 143
Ib = 27µA = 27 × 10 6 A ac = Ic / Ib = 24.1 10. Under what conditions an amplifier can be converted in to an oscillator? Draw a suitable diagram of an oscillator. (3) Hint: 1. when feedback is positive. 2. When feedback factor k is equal to l /Av.
11. Explain through a labeled circuit diagram, working of a transistor, as an amplifier in common emitter configuration. Obtain the expression for current gain, voltage gain and power gain. (3) 12. Draw a circuit diagram to study the input and output characteristic of an NPN transistor in common emitter configuration. Draw the graphs for input and output characteristics. (3) 13. Define trans conductance of a transistor. (2) Ans: gm = ∆IC/∆VB 14. How does the collector current change in junction transistor if the base region has larger width? Ans: Current decreases. (2) 15. The input of common emitter amplifier is 2KΏ. Current gain is 20. If the load resistances is 5KΏ. Calculate voltage gain trans conductance. (3) Ans: gm = β / RI, Av = β RL/RI 16. Define input, output resistance, current amplification factor, voltage amplification factor, for common emitter configuration of transistor. (3) 17. A change 0.2 mA in base current, causes a change of 5mA in collector current in a common emitter amplifier. (i) Find A.C current gain of Transistor. (ii) If input resistance 2KΏ and voltage gain is 75. Calculate load resistance used in circuit. β AC current gain = β ∆Ic / ∆ Ib (3) 144
19. In a transistor the base current is changed by 20μA. This results in a change of 0.02V in base emitter voltage and a change of 2mA in collector current. (3) (i) Find input resistance, (ii) Trans conductance. 20. With the help of circuit diagram explain the action of a transistor. (3) 21. Draw the circuit diagram to study the characteristic of NPN transistor in common emitter configuration. Sketch input – output characteristic for the configuration. Explain current gain, voltage gain. (3) 22. Draw the transfer characteristics of a transistor in common emitter configuration. Explain briefly the meaning of the term active region and cut off region in this characteristic. (3) 23. Explain with the help of a circuit diagram the working of NPN transistor as a common emitter amplifier. Draw input and output wave form. (3) 24. Draw a labeled circuit diagram of common emitter amplifier using PNP transistor. Define voltage gain and write expression. Explain how the input and output voltage are out of phase 180o for common emitter transistor amplifier.(3) 25. The output characteristic of transistor is shown. (i) Find current amplification (ii) Output Resistance
10mA 60μA 50μA
Ic (mA) 145
40μA 30μA 20μA
0.5
1.0 1.5
2.0
2.5
3.0
3.5
4.0 VCE (V)
LOGIC GATES *1. Modern technology use poly silicon instead of metal to form the gate. Why? (1) Ans: Poly silicon has high conductivity compared to metal. 2. Identify the logic gate; Give its truth table and output wave form? (1)
Ans: NAND GATE. *3. Draw the logic circuit and the output wave form for given output Y=0, 0, 1, 1 (2)
Ans: The output of the AND gate is Y = A.B consequently the input of the OR gate are A and A.B . Then the final Y = A + A.B Input for AND gate A
B
Output of AND gate Y= A.B
Input of output of OR gate OR gate A Y Y=A+Y
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1 146
1
*4. Construct the truth table for the Boolean equation Y=(A+B).C and represent by logic circuit.
(2) C A
Y
B Ans: The output of OR gate is A+B. Consequently, the inputs of AND gate are A+B & C Hence the Boolean equation for the given circuit is Y=(A+B).C
*5. Construct AND gate using NAND GATE and give its truth table? (2) Ans: AND Gate using NAND GATE:
A
B
Y= A.B
0
0
0
0
1
0
1
0
0
1
1
1
6. Identify which basic gate OR, AND and NOT is represented by the circuits in the dotted lines boxes 1,2 and 3. Give the truth table for the entire circuit for all possible values of A and B? (3) 147
Ans: The dotted line box 1 represents a NOT gate. The dotted line box 2 represents an OR gate. Here we use de Morgan’s theorem. The dotted line 3 represents AND gate. 7. Two input waveforms A and B shown in figure (a) and (b) are applied to an AND gate. Write the output (3) Time 1 2 3 4 5 6 interval Input A 0 1 1 0 0 1 Input B 0 0 1 1 0 0 Output 0 0 1 0 0 0 Y = A.B
Input waveform
148
8. A circuit symbol of a logic gate and two input wave forms A and B are shown. a) Name the logic gate b) Give the output wave form
A
B
a. Name the logic gate b. Give the output wave form (3) Ans: Current amplifier = ∆Ic / ∆ Ib = 9.5 – 2.5 / 50 x 10 6 1. Identify the Logic gate. A B Y = A B
2. Identify the Logic gate OR A (A+B) B AND A.B NAND 149
Ans: Y = (A+B) AB 3. Identify the gate: A B
A
Y B Ans: AND Gate
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VALUE BASED QUESTIONS 1. Ritu’s grandparents were planning to go for a long trip to Kashi from their home town Nagpur. Ritu’s father asked the grandparents to take one mobile phone with them. But the grandparents denied it telling that they were practiced to live without it. Now Ritu took much effort to convince the grandparents and finally they agreed. What are the values exhibited by ritu?The circuits in mobile phones essentially contain transistors. If two transistor amplifiers of voltage gain 20 and 5 are cascaded in series, find the voltage gain of the combination. 2. Ritu’s relatives planned to have DJ programme till midnight for her brother’s marriage. Hearing this Ritu opposes the plan and tells that latenight programme will disturb the sleep of neighbouring people. The relatives got convinced. Here what are the social values exhibited by her. The amplifier systems used in DJ programme uses transistor amplifier in common emitter configuration. Calculate the collector current and emitter current if the base current is 50 μA and current gain is 4. 3. Two students namely Ranjan and Praveen was asked to take up a project on efficient lighting for road ways, cycle paths and bus lanes. They found LED IS THE BEST source for the above said reasons. They collected the information from various sources and submitted the project about its working, advantages and its applications by presenting with a good working model. a) By seeing these two students, what kind of qualities you want adopt from them. b) Explain LED with neat diagram and draw its symbol. (ANS: a) Initiative, curiosity, punctuality, obedience & b) Refer NCERT text book)
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4.
I went out for shopping with my mother; during purchase of vegetables I
noticed that the Vendor used a digital weighing machine. On another shop, I noticed the vendor was using an ordinary weighing machine. So I used to go to the shop with digital machine. I remembered having studied about Logic Gates where, digital codes are used. a)
What do you mean by Logic Gate? Mention the basic universal gates.
b)
What is the value, in your opinion, that I created by the above incident.
(ANS: a) –Refer NCERT Text book; c)
concentration and observation in the class room, retaining capacity, co
relating of what was taught with the real life incident)
5.
Arun and Naveen studying in KENDRIYA VIDYALAYA watched the film
“Swadesh” together getting inspiration from the film,they realized the need of the hour for the conservation of energy. Together they decided to do something for the nation. With the help of their school teachers and principal they arranged an exhibition to depict the various renewable sources of energy and the applications of it. a)
What values must have highlighted so that the youngsters are motivated?
b)
Explain the working of a solar cell with a neat diagram.
(ANS: a) Need to conserve energy with the motto of sustainable development in fulfilling the needs of the present generation without compromising the need of the future generation, taking an initiative, bringing awareness among the students and the society. (b) Refer NCERT text book)
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10. COMMUNICATION SYSTEMS GIST 1. COMMUNICATION The sending and receiving of message from one place to another is called communication. Two important forms of communication systems are (i) Analog and (ii) digital. In analog communication the signal is continuous while in digital communication the signal is discrete. 2. THREE BASIC ELEMENTS OF COMMUNICATION (i) Transmitter (ii) Communication channel (iii) Receiver 3. MODULATION The superposition of (audio frequency) message signal (20 Hz20 kHz) over (high frequency) carrier wave (≈ 1MHz) is called modulation. 4. NEED FOR MODULATION: * Size of antenna h= λ/4 so, for high frequency. Height will be large which is impossible. * Effective power radiated by an antenna P α
1 2
* Mixing up of signals from different transmitters. 5. TYPES OF MODULATION There are two broad types of modulation: (i) Continuous wave modulation (ii) Pulse modulation. 1. Continuous wave modulation is of three types: (i) Amplitude modulation (AM): In amplitude modulation, the amplitude of carrier wave varies in accordance with instantaneous voltage of information (or message) signal. (ii) Frequency modulation (FM): In frequency modulation the frequency of carrier wave is varied in accordance with instantaneous voltage of information signal. (iii) Phase modulation (PM): In phase modulation, the phase of carrier wave is varied in accordance with the information signal.
153
6. Amplitude modulation
7. SPACE COMMUNICATION Space communication uses free space between transmitter and receiver. Space communication is via: (i) ground waves (ii) space waves (iii) sky waves
8. GROUND OR SURFACE WAVE PROPAGATION is a mode of wave propagation in which the ground has a strong influence on the propagation of signal wave from the transmitting antenna to receiving antenna .In this propagation ,the signal waves glides over the surface of earth, Ground waves are heavily absorbed by earth and not suitable for long range communication. Ground wave propagation can be sustained only at low frequencies (500 kHz1500 kHz). 9. SKY WAVE PROPAGATION is a mode of wave propagation in which the radiowave emitted from the transmitter antenna reach the receiving antenna after reflection by ionosphere. Sky wave propagation is possible because of reflection of carrier signals from ionosphere or satellite. 10. SPACE WAVE PROPAGATION higher than 30MHz is that mode of wave propagation in which the radiowaves emitted from the transmitter antenna reach the receiving antenna through space. These radiowaves are called space waves. It 154
is also called line of sight communication. Space wave is suitable for UHF/VHF regions. Band width of the signal Type of signal Band width Speech 2800 Hz Music 20 KHz Video 42 MHz Video & Audio 6.0 MHz (T.V) 11. COVERING RANGE OF T.V. TRANSMITTING TOWER is d=√2Reh, where h is height of tower and Re radius ofearth. T.V. waves are frequency modulated waves. VHF T.V. waves range from 47 to 230 MHz and UHF T.V. waves have range from 470 to 960 MHz. Maximum line of sight distance dm =√2RhT + √2RhR. 12. MAXIMUM USABLE FREQUENCY It is that highest frequency of radio waves which when sent at some angle towards the ionosphere, gets reflected from that and returns to the earth. 13. SATELLITE COMMUNICATION The communication satellite is used for reflecting sky waves without any disturbance. Its height is 35800 km above earth’s surface. To cover entire globe of earth simultaneously 3satellites are employed. II. IMPORTANT FORMULAE 1. Marconi antenna is grounded, and its length = λ/4, where λ is wavelength of the waves transmitted. It is called quarter wave antenna. 2. Hertz antenna is not grounded, and its length = λ/2. It is called half wave antenna. 3. Side band frequencies in AM wave are υSB = υc ± υmwhere υm is frequency of modulating (audio) signal. 4. Modulation index, ma = Em / Ec Modulation index, ma= Emax – Emin / Emax + Emin 6. Coverage range (d) for a given height (h) of antenna d = √2hR where R = radius of earth. d = √2Rhr + √2RhR,where hT , hR are the heights of transmitter and receiver antennas. 7. Population covered = population density x area covered. 155
8. Number of channels, N = Total band width of channels / Band width per channel III. Communication System – Block Diagrams 1)
2)
3) 4)
5)
156
CONCEPT MAP
EM Waves and Communication
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QUESTIONS ELEMENTS OF COMMUNICATION SYSTEMS 158
1. Mention the functions of the transponder? (1) Ans: A device fitted on the satellite which receives the signal and retransmits it after amplification. 2. What should be the length of dipole antenna for a carrier wave of 5 x 108 Hz? (1) 8 8 Ans: L = λ\2 = c\v x 2 = 3 x 10 / 5 x 10 x 2 = 0.3m. 3. *A device X can convert one form of energy into another. Another device Y can be regarded as a combination of a transmitter and a receiver. Name the devices X and Y. (1) (a) Transducer (b) Repeater 4. Name the two basic modes of communication. Which of these modes is used for telephonic communication? (2) HINT: Two basic modes of transmission are (i) Pointtopoint and (ii) broad cast mode. Pointtopoint mode is used for Telephonic communication. Differentiate an analog signal and a digital signal. How can an analog signal converted into a digital signal? (2)
(2) Hint: X= IF STAGE, Y = Amplifier 7.* Complete the following block diagram depicting the essential elements of a basic communication system. (3)
ANS:TRANSMITTER,MEDIUM AND RECIEVER 8.Calculate the length of a half wave dipole antenna at (a) 1 MHz (b) 100 MHz (c) 1000MHz What conclusion you draw from the results? Hint: Length of dipole antenna, L = λ/ 2 159
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(a) 150m (b) 1.5m (c) 15 cm II. PROPAGATION OF EM WAVES 1. Name the types of communication that uses carrier waves having frequencies in the range 1012 to 1016 Hz. Ans. Optical communication (1) 2. Write the expression for band width in FM. (1) Ans. width = 2 times frequency of modulating signal 3. What is attenuation? (1) 4. What is the role of band pass filter in modulation circuit? (1) Ans.If filters out low and high frequencies and only allow band of frequencies (wc – wm) to (wc+wm) 5. Distinguish between analog and digital communication. (1) 6. State the facts by which the range of transmission of signals by a TV tower can be increased? Ans. by increasing height of transmitting antenna (1) by increasing height of receiving antenna 7. What % of AM wave power is carried by side bands for m=1? (1) 8. Why moon cannot be used as a communicate satellite? (1) 9. Explain why medium waves are better parries of signals than radio waves?(1) Hint: Unidirectional propagation. 10. What is the requirement of transmitting microwaves from one to another on the earth? Ans: The transmitting and receiving antennas must be in line of sight. (1) 11. Name the type of radio waves propagation involved when TV signals broadcast by a tall antenna are intercepted directly by the receiver antenna.(1) 12. Why sky waves are not used for the transmission of TV signals? (1) 13. A TV tower has a height of 300m. What is the maximum distance upto which this TV transmission can be received? Ans: d = √2Rh = √ 2 x 6400 x 1000 x 300 = 62km (1) 14. How does the effective power radiated by an antenna vary with wavelength? (1) 15.*Why ground wave propagation is not suitable for high frequency? (OR)Why is ground wave propagation restricted to frequency up to 1500 kHz? (1) Hint: It is because radio waves having frequency greater than 1500MHz are strongly absorbed by the ground. 160
16.*Why are signals not significantly absorbed by ionosphere in satellite communication? Hint: It is because satellite communication employs HF carrier i.e. microwaves (1) 17. How many geostationary satellites are required to provide communication link over the entire globe and how should they be parked? (1) 18.* Why is the orbit of a remote sensing satellite called sun synchronous? (1) Hint: it is because when ever such a satellites passes over a particular area of the Earth, the position of the sun with respect to that area remains the same. 19.At a particular place at a distance of 10km from a transmission station a person can receive signals but not able to receive signals at 100km, suggest a method how he can receive signal at 11 km By using antenna. (1) 20. The tuned circuit of oscillator in a single AM transmitter employs 50 uH coil and 1nF capacitor. The oscillator output is modulated by audio frequency up to 10KHz. Determine the range of AM wave. (2) Hint: υc = 1/2π√LC ; USF = υc + υm ; LSF = υc – υm 21. The TV transmission tower at a particular station has a height of 160 m. What is the Coverage range? (2) 22. What is the population covered by the transmission, if the average Population density around the tower is 1200km2? (2) Hint: d = √2Rh=√2×6.4×103 ×160×103 =45km Range 2d=2×45=90km Population covered=area × population density=1200×6359= 763020 23. A transmitting antenna at the top of tower has a height of 36m and the height of the receiving antenna is 49m. What is the maximum distance between them, for the satisfactory communication in the LOS mode? (Radius of the earth =6400km). (2) Hint. Using d= √2Rht + √2Rhr we get =46.5km 24. Derive an expression for covering range of TV transmission tower (2) 25. * What is space wave propagation? Which two communication methods make use of this mode of propagation? If the sum of the heights of transmitting and receiving antennae in line of sight of communication is fixed at h, show that the range is maximum when the two antennae have a height h/2 each. (3) 161
Ans: Satellite communication and line of sight (LOS) communication make use of space waves. Here d1=√2Rh2 and d2= √2Rh2 For maximum range, Dm=√2Rh1 + √2Rh2 where dm =d1 + d2= d Given h1 + h2 = h Let h1 = x then h2 = hx Then dm = √2Rx + √2R(hx) , d dm /dx = √R/2x  √R/2(hx) = 0 i.e., 1/2x = 1/2(hx) i.e., x = h/2 => h1 = h2 = h/2. 26. * A ground receiver station is receiving signals at (i) 5 MHz and (ii) 100 MHz, transmitted from a ground transmitter at a height of 300 m located at a distance of 100km. Identify whether the signals are coming via space wave or sky wave propagation or satellite transponder. Radius of earth = 6400 km; Maximum electron density in ionosphere, Nmax = 1012m3 (3) Solution: Maximum coverage range of transmitting antenna, d = √2Reh Therefore d = √2 x 6400 x 103 x 300 = 6.2 x 104 The receiving station (situated at 100 km) is out of coverage range of transmitting antenna, so space wave communication is not possible, in both cases (i) and (ii) The critical frequency (or maximum frequency) of ionospheric propagation is fc = 9(Nmax)1/2 = 9 x √1012= 9 x 106 Hz = 9 MHz Signal (i) of 5MHz (< 9 MHz) is coming via ionosphere mode or sky wave propagation, while signal (ii) of 100MHz is coming via satellite mode. 27. * By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21%. ? (3) Solution: Transmission range of TV tower = d = √2hR If the height is increased by 21%, new height 162
h’ = h + 21\100h = 1.21h If d’ is the new average range, then d’/d =√h’ / √h = 1.1% increase in range Δd\ d x 100% = (d’ – d \ d) x 100% = (d’/ d 1) x100% = (1.1 – 1) x 100% = 10% MODULATION 1. What type of modulation is used for commercial broadcast of voice signal?(1) 2. *Over modulation result in distortion of the signal in amplitude modulation. Why?(1) Ans: When carrier wave is over modulated (i.e. ma>1), the modulated wave will be absent at negative peak of modulating signal. This results in distortion of the signal. 3.*An AM wave contains more power than the carrier wave. Why? (1) Ans: An AM wave contains three components, the carrier components and the two side band components (LSB and USB). It therefore contains more power than the carrier wave. 4.* Why is frequency modulation better than amplitude modulation? (1) 5.* What would be the modulation index for an amplitude modulated wave for which the maximum amplitude is ‘a’ while the minimum amplitude is ‘b’? (2) Ans. Modulation index, am = Em/Ec … (1) Maximum amplitude of modulated wave a=Ec + Em .....(2) Minimum amplitude of modulated wave b = Ec  Em …(3) From (2) and (3), Ec = a+b/2, Em = ab/2 From (1), modulation index, am = Em/Ec = (ab)/2 / (a+b)/2 = ab/ a+b
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6. A carrier wave of peak voltage 20 V is used to transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index of 80% ? (2) Hint: Modulation index, ma = Em / Ec Em =ma x Ec = 0.80 x 20 V = 16 V 7. A message signal of frequency 10 kHz and peak value of 8 volts is used to modulate a carrier of frequency 1MHz and peak voltage of 20 volts. Calculate: (i) Modulation index (ii) The side bands produced. (2) Solution: (i) Modulation index, ma = Em / Ec = 8/20 = 0.4 (ii) Side bands frequencies = fc ± fm Thus the side bands are at 1010KHz and 990 kHz. 8.An amplitude modulation diode detector, the output circuit consists of resistance R = 1kΩ and capacitance C = 10pf. It is desired to detect a carrier signal of 100 kHz by it. Explain whether it is a good detector or not? If not what value of capacitance would you suggest? (3) Solution: The satisfactory condition for demodulation is that reactance at carrier frequency must be much less than R. Reactance = 1 / ώC = 1 / 2πfCC = 1/ 2 x 3.14 x 100 x 103 x 10 x 1012 = 1.59 x 105 Ω = 159 kΩ This is much greater than the given resistance, so it is not a good detector. For detection, the condition is 1 / 2πfCC << R = C >> 1 / 1.59 x 109 fared or C >> 1.59 nF. Thus for proper detection the capacitance of output circuit must be much greater than 1.59 nF. The suitable capacitance is 1µF.
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VALUE BASED QUESTIONS 1. Sara & her mother went to purchase a colour TV set. Her mother got confused with so many features and functions of electronic appliances. Sara explained about the digital and analog signals to her. Then her mother asked about the flat screen. Sara told her that there are two main kinds of flat screen technology. She also told her mother that the cathode ray tubes used in olden days consume more electricity than a flat screen. Finally her mother purchased a colour TV with flat screen. a. What are the values we can find in Sara? b. A carrier wave of peak voltage 12V is used to transmit a message signal.What should be the peak value of the modulating signal in order to have a modulation index of 75%? 2. Vikas was interested to know about satellite videophone. Then he decided to meet his friend Samir.Then Samir explained to him that Satellite Videophone has a radio link ,not into the local telecom or cell phone network as used by mobile phones ,but direct to a satellite orbiting in space.The transmitterreceiver is situated in a laptop–sized case.A headset contains the camera to record the view ,the microphone for sound and a display screen and headphones ,either for what is being recorded,or to relay video and sound sent through the satellite link to the wearer. a.)What are the values noticed in samir? b.)A transmitting antenna at the top of a tower is 125 m high and the height of the receiving antenna is 20m .What is the maximum distance between them for satisfactory communication in the LOS mode? 3. Raj had no proper knowledge about pointtopoint and broadcast communication modes.His friend Sam explained to him the difference between these two types of communication.Sam convinced him with the examples of telephony for pointtopoint mode and radio & television for the broadcast mode. a.)What are the values displayed by Sam? b.)A message signal of frequency 10kHzand of peak voltage 10V is used to modulate a frequency of 1 MHz and of peak voltage 20V. Determine i.)modulation index ii.)Frequency of the side band produced?
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FREQUENTLY ASKED QUESTIONS UNIT I ELECTROSTATICS 2 MARKS 1) Force of attraction between two point charges placed at a distance of‘d’ is ‘F’. What distance apart they are kept in the same medium, so that, the force between them is ‘F/3’? 2) Define electric field intensity. Write its S I unit. Write the magnitude and direction of electric field intensity due electric dipole of length 2a at the midpoint of the line joining the two charges. 3) Define electric field intensity. Write its S.I unit. Write the magnitude and direction of electric field intensity due to an electric dipole of length2a at the midpoint of the line joining the two charges. 4) Sketch the electric lines of force due to point charges q > 0, q < 0 and for uniform field. 5) Define electric flux. Give its S.I unit and dimensional formula. 6) Two point charges 4μc and 2μc are separated by a distance of 1 m in air. At what point on the line joining the charges is the electric potential zero? 7) Depict the equipotential surfaces for a system of two identical positive point charges placed at distance d apart. 8) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from infinity to that points r1 and r2. 3 MARKS 9) Derive an expression for electric field intensity at a point on the axial line and on the equatorial line of an electric pole. 10) Derive an expression for torque acting on an electric dipole in a uniform electric filed. 11) Derive an expression for total work done in rotating an electric dipole through an angle ‘θ’ in uniform electric field. 12) A sphere ‘S1’ of radius ‘r1’ encloses a charge ‘Q’. If there is another concentric sphere S2 of the radius r2 (r2 > r1) and there be no additional 166
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charges between S1 and S2, find the ratio of electric flux through S1 and S2. State Gauss’s Theorem in electrostatics. Using this theorem, find the electric field strength due to an infinite plane sheet of charge. State Gauss' theorem. Apply this theorem to obtain the expression for the electric field intensity at a point due to an infinitely long, thin, uniformly charged straight wire. . Using Gauss’s theorem, show mathematically that for any point outside the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be zero according to this theorem? Deduce an expression for the electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric of a dipole at a point as compared to that due to single charge. Define dielectric constant in terms of the capacitance of a capacitor.
17) 5 MARKS 18) Give the principle and working of a Van de Graff generator. With the help of a labelled diagram, describe its construction and working. How is the leakage of charge minimised from the generator? 19) Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium. 20) Derive an expression for the energy stored in a parallel plate capacitor with air between the plates. How does the stored energy change if air is replaced by a medium of dielectric constant ‘K’? ; Also show that the energy density of a capacitor is. 21) A parallelplate capacitor is charged to a potential difference V by a dc source. The capacitor is then disconnected from the source. If the distance between the plates is doubled, state with reason how the following change (i) electric field between the plates (ii) capacitance, and (iii) energy stored in the capacitor 22) Explain the underlying principle of working of a parallel plate capacitor. If two similar plates, each of area ‘A’ having surface charge densities ‘+ σ’ & ‘σ’ are separated by a distance ‘d’ in air, write expressions for (i) the electric field at points between the two plates, (ii) the potential 167
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difference between the plates & (iii) the capacity of the capacitor so formed A parallel plate capacitor is charged by a battery and the battery remains connected, a dielectric slab is inserted in the space between the plates. Explain what changes if any , occur in the values of (I) potential difference between the plates (II) electric field between the plates (III) energy stored in the capacitor. UNIT II CURRENT ELECTRICITY
2 MARKS 1. Two wires ‘A’ & ‘B’ are of the same metal and of the same length. Their areas of crosssection are in the ratio of 2:1. if the same potential difference is applied across each wire in turn, what will be the ratio of the currents flowing in ‘A’ & ‘B’? 2. Explain, with the help of a graph, the variation of conductivity with temperature for a metallic conductor. 3. Draw VI graph for ohmic and nonohmic materials. Give one example for each. 4. Explain how does the resistivity of a conductor depend upon (i) number density ‘n’ of free electrons, & (ii) relaxation time‘t’. 5. Define the term ‘temperature coefficient of resistivity’. Write its SI unit. Plot a graph showing the variation of resistivity of copper with temperature. 6. A cell of emf (E) and internal resistance (r) is connected across a variable external resistance (R) Plot graphs to show variation of (i) E with R (ii) terminal p.d. of the cell (V) with R. 7. Explain how electron mobility changes from a good conductor (i) when temperature of the conductor is decreased at constant potential difference and (ii) applied potential difference is doubled at constant temperature. 8. Write the mathematical relation between mobility and drift velocity of charge carriers in a conductor. Name the mobile charge carriers responsible for conduction of electric current in: (i) an electrolyte, & (ii) an ionised gas. 9. Define drift velocity. Establish a relation between current & drift velocity. 10.Define the term current density of a metallic conductor. Deduce the relation connecting current density ‘J’ & the conductivity ‘σ’ of the conductor when an electric field ‘E’ is applied to it. 168
11.Why do we prefer potentiometer to compare the e.m.f of cells than the voltmeter. Why? 12.State Kirchhoff’s rules of current distribution in an electric network. 13.The variation of potential difference “V’ with length ‘l’ in the case of two potentiometers ‘X’ & ‘Y’ is as shown in figure. Which one of these two will you prefer for comparing ‘emf’s of two cells and why? X V Y l 3 MARKS 14.Draw a circuit diagram using a metre bridge and write the necessary mathematical relation used to determine the value of an unknown resistance. Why cannot such an arrangement be used for measuring very low resistance? 15.With the help of a circuit diagram, explain in brief the use of a potentiometer for comparison of ‘emf’s of two cells. 16.Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons. 17.A number of identical cells, n, each of emf E, internal resistance r connected in series are charged by a d.c. source of emf E′, using a resistor R. (i) Draw the circuit arrangement. (ii) Deduce the expressions for (a) the charging current and (b) the potential difference across the combination of the cells. 18.Derive the principle of wheatstone bridge using Kirchoff’s law. 19.State Kirchhoff’s rules of current distribution in an electrical network. Using these rules determine the value of the current I1 in the electric circuit given below.
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20.Write the mathematical relation for the resistivity of material in terms of relaxation time, number density and mass and charge of charge carriers in it.Explain, using this relation, why the resistivity of a metal increases and that of semiconductor decreases with rise in temperature. 21.Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0·2 A. What would be the potential difference between points A and B?
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UNIT III MAGNETIC EFFECTS OF CURRENT AND MAGNETISM 2 MARKS A circular coil of radius ‘R’ carries a current ‘I’. Write the expression for the magnetic field due to this coil at its centre. Find out the direction of the magnetic field. Write the expression for the force on the charge moving in a magnetic field. Use this expression to define the SI unit of magnetic field. Define magnetic susceptibility of a material. Name two elements, one having positive susceptibility and the other having negative susceptibility. What does negative susceptibility signify? Define the term magnetic dipole moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed around an orbit of radius in hydrogen atom.. Explain with the help of a diagram the term ‘magnetic declination’ at a given place. Define the term ‘angle of dip’. What is the value of the angle of dip at the magnetic equator? What does it mean? 170
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Two wires of equal lengths are bend in the form of two loops. One of the loop is square shaped where as the other loop is circular. These are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience greater torque? Give reasons. Explain why steel is preferred for making permanent magnets while soft iron is preferred for making electromagnets. Draw diagram to show behavior of magnetic field lines near a bar of 1)copper2)aluminum and3)mercury cooled at a very low temperature(4.2K) How will the magnetic field intensity at the centre of the circular coil carrying current will change, if the current through the coil is doubled and radius of the coil is halved? What do you mean by current sensitivity of a moving coil galvanometer? On what factors does it depend? Derive an expression for the force experienced by a current carrying straight conductor placed in a magnetic field. Under what condition is this force maximum? 3 MARKS Obtain the force per unit length experienced by two parallel conductors of infinite length carrying current in the same direction. Hence define one ampere. A) If Ҳ stands for the magnetic susceptibility of a given material, identify the class of materials for which (a) 1 ≥ Ҳ < 0, and (b) 0 < Ҳ < έ [έ is a small positive number]. Write the range of relative magnetic permeability of these materials. B) Draw the pattern of the magnetic field lines when these materials are placed on a strong magnetic field. Derive an expression for the force acting on a current carrying conductor in a magnetic field. Under what conditions this force is maximum and minimum? Define the term magnetic moment of current loop. Derive the expression for the magnetic moment when an electron revolves at a speed ‘v’ around an orbit of radius r in hydrogen atom.Also calculate the value of Bohr’smagnetic moment. With the help of diagram explain how a galvanometer can be converted into an ammeter and a voltmeter.
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To increase the current sensitivity of a moving coil galvanometer by 50%, its resistance is increased so that the new resistance becomes twice its initial resistance. By what factor does its voltage sensitivity change?
5 MARKS 19. Write an expression for force experienced by a charged particle moving in a uniform magnetic field? With the help of labeled diagram, explain principle and working of a cyclotron. Show that cyclotron frequency does not depend upon the speed of particles. Write its two limitations. 20. State Ampere’s Circuital Law. Derive an expression for the magnetic field at a point due to straight current carrying conductor. 21. Derive an expression for the magnetic field at a point along the axis of an air cored solenoid using a Ampere’s circuital law.. 22. Derive an expression for torque acting on a rectangular current carrying loop kept in a uniform magnetic field B. Indicate the direction of torque acting on the loop. 23. With neat diagram, describe the principle, construction and working of a moving coil galvanometer. Explain the importance of radial field. 24. State Biot Savart Law. Use this law to obtain a formula for magnetic field at the centre of a circular loop of radius R ,number of turns N carrying current I. Sketch the magnetic field lines for a current loop clearly indicating the direction of the field. 25. Distinguish the magnetic properties of dia, para and ferromagnetic substances interms of (i) susceptibility, (ii) magnetic permeability and (iii) coercivity. Give one example of each of these materials.Draw the field lines due to an external magnetic field near a (i) diamagnetic,(ii) paramagnetic substance. UNIT IV ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENT 2 MARKS 1. How does the selfinductance of an air core coil change, when (i) the number of turns in the coils is decreased & (ii) an iron rod is introduced in the coil. 2. What is the effect on the mutual inductance between the pair of coil when (i) the distance between the coils is increased?(ii) the number of turns in each coil is decreased? Justify your answer in each case. 172
3. State Lenz’s law. Show that it is in accordance with the law of conservation of energy. 4. The closed loop PQRS is moving into a uniform magnetic field acting at right angles to the plane of the paper as shown. State the direction of the induced current in the loop. x x x x x P
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x x x x x 5. Define mutual inductance and give its S.I. unit.Write two factors on which the mutualinductance between a pair of coil depends. 6. What is the power dissipated in an ac circuit in which voltage & current are given by V = 230 sin (ωt + π/2) and I = 10 sin ωt? 7. The instantaneous current & voltage of an ac circuit are given by: i = 10 sin 314t ampere, & V = 50 sin 314t volt. What is the power dissipation in the circuit? 8. The coils in certain galvanometers have fixed core made of a nonmagnetic material. Why does the oscillating coil come to rest so quickly in such a core? 9. What are eddy currents. How are these produced? in what sense are eddy currents considered undesirable in a transformer and how are these reduced in such a device? 10. Prove that average power consumed over a complete cycle of ac through an ideal inductor is zero. 11. Prove that an ideal capacitor in an ac circuit does not dissipate power. 12.Distinguish resistance,reactance and impedance. 13.What is an induced emf? Write Faraday’s law of electromagnetic induction Express it mathematically. 173
14.Two identical loops, one of copper and the other of aluminum, are rotated with the same angular speed in the same magnetic field. Compare (i) the induced emf and (ii) the current produced in the two coils. Justify your answer. 3 MARKS 15.Derive an expression for: (i) induced emf & (ii) induced current when, a conductor of length is moved into a uniform velocity v normal to a uniform magnetic field B. Assume resistance of conductor to be R. 16.Derive an expression for average power consumed over a complete cycle of ac through an LCR circuit. 17.Define mutual inductance and give its SI unit. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound over the other. 18.. Define selfinductance and give its S. I. Unit. Derive an expression for selfinductance of a long, aircored solenoid of length l, radius r, and having N number of turns 5 MARKS 19.Explain the term 'capacitive reactance'. Show graphically the variation of capacitive reactance with frequency of the applied alternating voltage.An a.c. voltage E=E0sinωt is applied across a pure capacitor of capacitance C. Show mathematically that the current flowing through it leads the applied voltage by a phase angle of π/2. . 20.Explain the term 'inductive reactance'. Show graphically the variation of inductive reactance with frequency of the applied alternating voltage. An a.c. voltage E=E0 sinωt is applied across a pure inductor of inductance L. Show mathematically that the current flowing through it lags behind theapplied voltage by a phase angle of π/2. 21.An AC source of voltage V = Vm sin ωt is applied across a series LCR circuit. Draw the phasor diagrams for this circuit, when: a) Capacitive impedance exceeds the inductive impedance AND b) Inductive impedance exceeds capacitive impedance. 22.A coil of inductance ‘L’, a capacitor of capacitance ‘C’, & a resistor of resistance ‘R’ are all put in series with an alternating source of emf E = E0 sin ωt. Write expressions for a) total impedance of circuit, and (b) frequency of source emf for which circuit will show resonance. 23.A circular coil of Nturns & radius ‘R’ is kept normal to a magnetic field, given by: B = B0 cos ωt. Deduce an expression for the emf induced in this coil. State the rule which helps to detect the direction of induced current. 174
24.Discuss a series resonant circuit. Derive an expression for resonant frequency and show a graphical variation between current and angular frequency of applied ac. Define quality factor and derive an expression for it. 25.Explain with help of a labelled diagram the principle, construction and working of a transformer. Mention the various energy losses in a transformer? Explain the role of transformer in long distance transmission of power ? 26.With the help of a neat diagram, explain the principle construction and working of an a.c generator. UNIT V ELECTROMAGNETIC WAVES 2 MARKS 1. A plane monochromatic light wave lies in the visible region. It is represented by sinusoidal variation with time by the following components of electric field: EX = 0, EY = 4 sin [2π/λ (x – vt)], Ez = 0 Where, v = 5 x 1014 Hz and λ is the wave length of light. (i) What is the direction of propagation of the wave? (ii) What is its amplitude? And (iii) Compute the components of magnetic field. 2. Give two characteristics of electromagnetic waves. Write the expression for the velocity of electromagnetic waves in terms of permittivity and magnetic permeability of free space. 3. Find wavelength of electromagnetic waves of frequency 5 x 1019 Hz in free space. Give its two applications. 4. Name the characteristics of e. m. waves that: (i) increases, & (ii) remains constant in e. m. spectrum as one moves from radiowave region towards ultraviolet region. 3 MARKS 5. Which constituent radiation of electromagnetic spectrum is used: (i) in radar? (ii) To photograph internal parts of human body? & (iii) for taking photographs of the sky during night and foggy condition? Give one reason for your answer in each case. 6. Write any four characteristics of e. m. waves. Give two uses of: (i) Radio waves & (ii) Microwaves. 175
7. Name the following constituent radiations of e. m. spectrum which, (i) produce intense heating effect? (ii) is absorbed by the ozone layer, &(iii) is used for studying crystal structure. 8. Experimental observations have shown: (i) that Xrays travel in vacuum with a speed of 3 x 108 m s1, & (ii) the phenomenon of diffraction and can be polarized. What conclusion is drawn about the nature of Xrays from each of these observations? 9. Why are infrared radiations referred to as heat waves? Name the radiations which are next to these radiations in e. m. spectrum having: (i) shorter wavelength, & (ii) longer wavelength. 10.The oscillating magnetic field in a plane electromagnetic wave is given by: By = 8 x 106 sin [2 x 1011 t + 300 π x] T (i) Calculate the wavelength of the electromagnetic wave & (ii) Write down the expression for oscillating electric filed. 11.Identify the following electromagnetic radiation as per the wavelengths given below: (a) 103nm, & (b)103m,&(c)1nm; Write one application of each. 12. Name the constituent radiation of electromagnetic spectrum which (a) is used in satellite communication. (b) is used for studying crystal structure. (c) is similar to the radiations emitted during decay of radioactive nuclei. (d) has its wavelength range between 390 nm and 770 nm. (e) is absorbed from sunlight by ozone layer. (f) produces intense heating effect. 13.What is meant by the transverse nature of electromagnetic waves? Drawdiagram showing the propagation of the an electromagnetic wave along X direction, indicating clearly the directions of oscillating electric and magnetic fields associated with it.
UNIT VI OPTICS 2 MARKS 1. What is the geometrical shape of the wavefront when a plane wave passes through a convex lens? 176
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What is total internal reflection? Under what condition does it take place. A convex lens made up of a material of refractive index n1, is immersed in a medium of refractive index n2. Trace the path of a parallel beam of light passing through the lens when: (i) (i) n1> n2, (ii) n1 = n2, & (iii) n1< n2..Explain your answer. A concave lens made of material of refractive index n1 is kept in a medium of refractive index n2. A parallel beam of light is incident on the lens. Complete the path of rays of light emerging from the concave lens if: (i) n1> n2, (ii) n1 = n2, & (iii) n1< n2. Draw a ray diagram to show how an image is formed by a compound microscope. ? A microscope is foucssed on a dot at the bottom of a beaker. Some oil is poured into the beaker to a height of ‘y’ cm & it is found necessary to raise microscope through a vertical distance of ‘x’ cm to bring the dot again into focus. Express refractive index of oil in terms of ‘x’ & ‘y’. How does the (i) magnifying power & (ii) resolving power of a telescope change on increasing the diameter of its objective? Give reasons for your answer. How will magnifying power of a “refracting type astronomical telescope” be affecting on increasing for its eye piece: (i) the focal length, & (ii) the aperture. Justify your answer. Draw a labelled ray diagram showing the formation of image of a distant object using an astronomical telescope in the ‘normal adjustment position’ Draw a labelled ray diagram showing the formation of image of a distant object using an astronomical telescope in the near point adjustment. Draw a ray diagram to illustrate image formation by a Cassegrain type reflecting telescope. Explain with reason, how the resolving power of an astronomical telescope will change when (i) frequency of the incident light on objective lens is increased (ii) the focal length of the objective lens is increased & (iii) aperture of the objective lens is halved. Draw a graph to show variation of angle of deviation ‘D’ with that of angle of incidence ‘i’ for a monochromatic ray of light passing through a glass prism of reflecting angle ‘A’.
3 MARKS 14. Derive lens/mirror formula in case of a convex/concave mirror. 177
15. 16.
17. 18.
19.
20.
21.
22.
23.
Stating the assumptions and sign conventions, derive expression for lens maker’s formula. A rightangled crown glass prism with critical angle 41○ is placed before an object, ‘PQ’ in two positions as shown in the figures (i) & (ii). Trace the paths of the rays from ‘P’ & ‘Q’ passing through the prisms in the two cases.
(a) Draw a labelled ray diagram to show the formation of an image by a compound microscope. Write the expression for its magnifying power. (b) Define resolving power of a compound microscope. How does the resolving power of a compound microscope change, when (i) refractive index of the medium between the object and the objective lens increases and (ii) Wavelength of the radiation used is increased? Define the term wave front? Using Huygen’s construction draw a figure showing the propagation of a plane wave reflecting at the interface of the two media. Show that the angle of incidence is equal to the angle of reflection. Define the term ‘wavefront’. Draw the wavefront and corresponding rays in the case of a (i) diverging spherical wave (ii) plane wave. Using Huygen’s construction of a wavefront, explain the refraction of a plane wavefront at a plane surface and hence deduce Snell’s law. What is meant by ‘interference of light’? Write any two conditions necessary for obtaining welldefined and sustained interference pattern of light. What is the effect on the interference fringes in a Young’s double slit experiment due to each of the following operations? Give reason for your answer: (i) Separation between two slits is increased & (ii) monochromatic source is replaced by a source of white light. Draw the curve depicting variation of intensity in the interference pattern in Young’s double slit experiment. State conditions for obtaining sustained interference pattern of light. 178
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27. 28.
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In a single slit diffraction pattern, how is angular width of central bright maximum changed when (i) the slit width is decreased, (ii) the distance between the slit and the screen is increased, & (iii) light of smaller wavelength is used? Justify your answers. Why is diffraction of sound waves easier to observe than diffraction of light waves? What two main changes in diffraction pattern of a single slit will you observe when the monochromatic source of light is replaced by a source of white light? In a single slit diffraction experiment, if the width of the slit is doubled, how does the (i) intensity of light and (ii) width of the central maximum change? Give reason for your answer. What is wavefront? What is the geometrical shape of a wavefront emerging from a convex lens when point source is placed at the focus? What is wavefront? Distinguish between a plane wavefront and a spherical wavefront. Explain with the help of a diagram, the refraction of a plane wavefront at a plane surface using Huygens’s construction. Using Huygens’s principle show that for parallel beam incident on a reflecting surface the angle of reflection is equal to the angle of incidence. Distinguish between unpolarised and plane polarised light. An unpolarised light is incident on the boundary between two transparent media. State the condition when the reflected wave is totally plane polarised. Find out the expression for the angle of incidence in this case. The following data was recorded for values of object distance and the corresponding values of image distance in the experiment on study of real image formation by a convex lens of power +5D. One of the observations is incorrect. Identify the observation and give reason for your choice. S. No. 1 2 3 4 5 6 Object distance (cm) 25 30 35 45 50 55 Image distance (cm) 97 6 37 35 32 30
5 MARKS 32. (i) Derive the mirror formula which gives the relation between f, v and u. What is the corresponding formula for a thin lens? (ii) Calculate the distance d, so that a real image of an object at O, 15cm in front of a convex lens of focal length 10cm be formed at the same point O. The radius of curvature of the mirror is 20cm. Will the image be inverted or erect? 179
33.
A spherical surface of radius of curvature ‘R’ separates a rarer and a denser medium as shown in the figure.
Complete the path of the incident ray of light, showing the formation of real image. Hence derive the relation connecting object distance ‘u’, image distance ‘v’ radius of curvature ‘R’ and the refractive indices ‘n1’ & ‘n2’ of the media. Briefly explain how the focal length of a convex lens changes with Increase in wavelength of incident light. 34. State the assumptions and sign conventions in deriving the Lens maker’s formula and also derive an expression for it. 35. Derive an expression for thin lens formula. 36. (a) In Young’s double slit experiment, deduce the conditions for: (i) constructive and (ii) destructive interference at a point on the screen. Draw a graph showing variation of the resultant intensity in the interference pattern against position ‘x’ on the screen. (b) Compare and contrast the pattern which is seen with two coherently illuminated narrow slits in Young’s experiment with that seen for a coherently illuminated single slit producing diffraction. 37. State Huygens principle. Using the geometrical construction of secondary wavelets, explain the refraction of a plane wavefront incident at a plane surface. Hence verify Snell’s law of refraction. Illustrate with the help of diagrams the action of: (i) convex lens and (ii) concave mirror on a plane wavefront incident on it. 38. What is interference of light? Write two essential conditions for sustained interference pattern to be produced on the screen. Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits are opened and (b) 180
39.
40.
41.
42.
one of the slit is closed. What is the effect on the interference pattern in Young’s double slit experiment when: (i) Screen is moved closer to the plane of slits? (ii)Separation between two slits is increased. Explain your answer in each case. What are coherent sources of light? Two slits in Young’s double slit experiment are illuminated by two different sodium lamps emitting light of the same wavelength. Why is no interference pattern observed? (b) Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence write the expression for the fringe width. (c) If S is the size of the source and its distance from the plane of the two slits, what should be the criterion for the interference fringes to be seen? What do we understand by ‘polarization of wave’? How does this phenomenon help us to decide whether a given wave is transverse or longitudinal in nature? Light from an ordinary source (say, a sodium lamp) is passed through a Polaroid sheet ‘P1’. The transmitted light is then made to pass through a second Polaroid sheet P2 which can be rotated so that the angle θ between the two Polaroid sheets varies from 0●to 90●. Show graphically the variation of intensity of light, transmitted by P1& P2 as a function of the angle θ. Take the incident beam intensity a I0. Why does the light from a clear blue portion of the sky, show a rise and fall of intensity when viewed through a Polaroid which is rotated? (a) Draw a ray diagram to show the refraction of light through a glass prism. Hence obtain the relation for the angle of deviation in terms of the angle of incidence, angle of emergence and the angle of the prism. (b) A right angled isosceles glass prism is made from glass of refractive index When a monochromatic yellow coloured light beam is incident on a given photosensitive surface, photoelectrons are not ejected, while the same surface gives photoelectrons when exposed to green coloured monochromatic beam. What will happen if the surface is exposed to: (i) red coloured, monochromatic beam of light? Justify your answer. UNIT VII DUAL NATURE OF MATTER
2 MARKS 1. When a monochromatic yellow coloured light beam is incident on a given photosensitive surface, photoelectrons are not ejected, while the same surface gives photoelectrons when exposed to green coloured 181
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3. 4.
5. 6. 7. 8.
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monochromatic beam. What will happen if the surface is exposed to: (i) red coloured, monochromatic beam of light? Justify your answer. What is meant by work function of a metal? How does the value of work function influence the kinetic energy of electrons liberated during photoelectric emission? Define the terms: (i) work function, (ii) threshold frequency & (iii) stopping potential with reference of photoelectric effect. The work function of lithium is 2.3 eV. What does it mean? What is the relation between the work function ‘ωo’ and threshold wavelength ‘λo’ of a metal? Red light, however bright, cannot cause emission of electrons from a clean zinc surface. But, even weak ultraviolet radiations can do so. Why? An electron and a proton have same kinetic energy. Which of the two has a greater wavelength? Explain. Define the term threshold frequency & work function in relation to photoelectric effect. An electron and a proton are moving in the same direction and possess same kinetic energy. Find the ratio of deBroglie wavelengths associated with these particles. In the photoelectric effect experiment, the graph between the stopping potential ‘V’ and frequency ‘v’ of the incident radiation on two different metal plates P and Q are shown in the figure. (i) Which of the two metal plates, P & Q has greater value of work function? & (ii) What does the slope of the line depict?
3 MARKS 10.What is photoelectric effect? Write Einstein’s photoelectric equation and use it to explain: (i) independence of maximum energy of emitted photoelectrons from the intensity of incident light. (ii) Existence of a threshold frequency for the emission of photoelectrons. 11.Draw the variation of maximum kinetic energy of emitted electrons with frequency of the incident radiation on a photosensitive surface. On the 182
graph drawn, what do the following indicate: (i) slope of the graph & (ii) intercept on the energy axis. 12.Obtain Einstein’s photoelectric equation. Explain how it enables us to understand the (i) linear dependence of the maximum kinetic energy of the emitted electrons, on the frequency of the incident radiation & (ii) existence of a threshold frequency for a given photo emitter. 13.Given below is the graph between frequency (v) of the incident light and maximum kinetic energy (E) of emitted photoelectrons. Find the values of: (i) threshold frequency and (ii) work function from the graph.
14.Sketch a graph between frequency of incident radiations and stopping potential for a given photosensitive materials. What information can be obtained from the value of intercept on the potential axis? A source of light of frequency greater that the threshold frequency is replaced at a distance of 1 m from the cathode of a photo cell. The stopping potential is found to be V. If the distance of the light source from the cathode is reduced, explain giving reason, what change you will observe in the (I0 photoelectric current & (ii) stopping potential. 15.Explain the laws of photoelectric emission on the basis of Einstein’s photoelectric equation. Write one feature of the photoelectric effect which cannot be explained on the basis of wave theory of light. 16.Draw graphs showing the variation of photoelectric current with anode potential of a photocell for (i) the same frequency but different intensities I1> I2> I3 of incident radiation, & (ii) the same intensity but different frequencies v1> v2> v3 of incident radiation. Explain why the saturation current is independent of the anode potential? UNIT VIII ATOMS & NUCLEI 2 MARKS 183
1. Define disintegration constant and mean life of a radioactive substance. Give the unit of each. 2. What is impact parameter? What is the value of impact parameter for a head on collision? The sequence of the stepwise decays of radioactive nucleus is: α
β α α D D1 D2 D3 D4. If the nucleon number and atomic number for D2 are respectively 176 & 71, what are the corresponding values for D and D4 nuclei? Justify your answer. 3. Draw a diagram to show the variation of binding energy per nucleon with mass number for different nuclei. Explain with the help of this plot the release of energy in the processes of nuclear fission and fusion? 4. The value of ground state energy of hydrogen atom is: 13.6 eV; (i) What does the negative sign signify? & (ii) How much energy is required to take an electron in this atom from the ground state to the first excited state? 5. Give one point of difference between ‘nuclear fission’ & ‘nuclear fusion’. Will neutron to proto ratio increase or decrease in a nucleus when: (i) an electron, (ii) a positron is emitted? 6. Sketch the graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Write three characteristic properties of nuclear force which distinguish it from the electrostatic force. 7. State two characteristics of nuclear force. Why does the binding energy per nucleon decrease with increase in mass number for heavy nuclei like 235U? 8. State the condition for controlled chain reaction to occur in a nuclear reactor. Heavy water is often used as a moderator in thermal nuclear reactors. Give reason. 9. Define activity of a substance. State its S.I unit. Derive an expression for activity of a substance. 10.Define average or mean value of a radioactive substance, and derive an expression for it. 3 MARKS 11.State the basic postulates of Bohr’s atomic model & derive an expression for the energy of an electron in any orbit of hydrogen atom. 12.Derive an expression for the radius of stationary orbit. Prove that the various stationary orbits are not equally spaced. 184
13.Derive mathematical expressions for: (i) kinetic energy, & (ii) potential energy of an electron revolving in an orbit of radius ‘r’; how does the potential energy change with increase in principal quantum number (n) for the electron and why? 14.Define the decay constant for a radioactive sample. Which of the following radiations α, β, & λ rays are: (i) similar to Xrays? (ii) easily absorbed by matter? & (iii) similar in nature to cathode rays? 15. Define the terms: half life period and decay constant of a radioactive sample. Derive the relation between these terms. 16.In Rutherford’s scattering experiment, mention two important conclusions which can be drawn by studying the scattering of α particles by an atom. Draw the schematic arrangement of Geiger and Marsden experiment showing the scattering of α particle by a thin foil of gold. How does one get the information regarding the size of the nucleus in this experiment? 17.Sketch the energy level diagram for hydrogen atom. Mark the transitions corresponding to Lyman and Balmer series. 18.Prove that the instantaneous rate of change of the activity of a radioactive substance is inversely proportional to the square of its half life. (3) UNIT IX ELECTRONIC DEVICES 2 MARKS 1. How is a ptype semiconductor formed? Name the majority carriers in it. Draw the energy band diagram of a ptype semiconductor. 2. How is an ntype semiconductor formed? Name the majority carriers in it. Draw the energy band diagram of a ntype semiconductor. 3. With the help of a diagram, show the biasing of a light emitting diode (LED). Give its two advantages over conventional incandescent lamps. 4. Draw a circuit diagram to show how a photodiode is biased. Draw its characteristic curves for two different illumination intensities. 5. Give the logic symbol for an AND gate. Draw the output wave form for input wave forms for this gate. 3 MARKS 6. What is rectification? How can a diode valve be used as half wave rectifier and full wave rectifier? 7. Explain how the depletion layer and the barrier potential are formed in a pn junction diode. 185
8. Draw a circuit diagram for use of NPN transistor as an amplifier in common emitter configuration. The input resistance of a transistor is On changing its base current by , the collector current increases by 2 m A. If a load resistance of is used in the circuit, calculate (i) the current gain & (ii) voltage gain of the amplifier 9. The output of an AND gate is connected to both the inputs of a NAND gate. Draw the logic circuit of this combination of gates and write its truth table. 10.What is a Zener diode? How it is symbolically represented? With the help of a circuit diagram, explain the use of Zener diode as a voltage stabilizer. 11.With the help of a suitable diagram, explain the formation of depletion region in a pn junction. How does its width change when the junction is: (i) forward biased? & (ii) reverse biased? 5 MARKS 12. With the help of a circuit diagram explain the working of a transistor as an oscillator. 13.Explain briefly with the help of a circuit diagram how VI characteristics of a pn junction diode are obtained in: (i) forward bias & (ii) reverse bias. 14. Explain the function of base region of a transistor. Why this region is made thin and lightly doped? Draw a circuit diagram to study the input and the output characteristics of npn transistor in a common emitter (CE) configuration. Show these characteristics graphically. Explain how current amplification factor of the transistor is calculated using output characteristics. 15.Draw the energy bands of ptype and ntype semiconductors. Explain with a circuit diagram the working of a full wave rectifier. 16.Explain with the help of a circuit diagram the use of an npn transistor as an amplifier in common emitter configuration. Draw the input and output wave forms of the signal. Write the expression for its voltage gain. 17.What is an npn transistor? How does it differ from pnp transistor? Give their symbols. Explain transistor action. 18.Explain the working of transistor as a switch. Draw transfer characteristic curve by showing 1) Cutoff region 2) Active region and 3) Saturation region. 186
UNIT X COMMUNICATION SYSTEMS 2MARKS 1. Draw a block diagram of communication system. 2. Distinguish between point to point and broadcast communication modes. Give one example of each. 3. Explain the following terms. a) Ground waves b) Space waves and c) sky waves. 4. What does the term LOS communication mean? Name the types of waves that are used for this communication. Give typical examples, with the help of a suitable figure, of communication systems that use space wave mode propagation. 5. Write the function of 1) Transducer and 2) repeater in the context of communication system. 6. What is modulation? Explain the need of modulating a low frequency information signal. 7. We do not choose to transmit an audio signal by just directly converting it to an E.M wave of the same frequency. Give two reasons for the same. 8. Explain briefly with the help of diagrams the terms (i) amplitude modulation and (ii) Frequency modulation. Which of these (i) gives better quality transmission? (ii) Has a larger coverage 9. Why is short wave bands used for long distance transmission of signals? 10. Optical and radio telescope are built on the ground but xray astronomy is possible only from satellite? 11.Draw a block diagram for a transmitter and a receiver of AM wave. 3 MARKS 12.Define the term modulation index for an AM wave. What would be the modulation index for an AM wave for which the maximum amplitude is ‘a’ and the minimum amplitude is b’ 13.A TV tower has a height ‘h’. Derive an expression for maximum distance up to which the signal can be received from the earth. 14.What is meant by the term modulation? Explain with the help of a block diagram, how the process of modulation is carried out in AM broadcasts? 15. What is meant by ‘production’ of a modulated carrier wave? Describe briefly the essential steps with block diagram production. 16.What is meant by ‘detection’ of a modulated carrier wave? Describe briefly the essential steps with block diagram detection. 187
MARKING SCHEME FOR CLASS XII (PHYSICS) 201516 CLASS XII (201516) (THEORY) Time: 3 hrs.
Max Marks: 70 No. of Periods
UnitI
Electrostatics
Marks
22
Chapter1: Electric Charges and Fields Chapter2: Electrostatic Potential and Capacitance UnitII
Current Electricity
15 20
Chapter3: Current Electricity UnitIII
Magnetic Effects of Current and Magnetism
22
Chapter4: Moving Charges and Magnetism Chapter5: Magnetism and Matter UnitIV
16
Electromagnetic Induction and Alternating Currents
20
Chapter6: Electromagnetic Induction Chapter7: Alternating Current UnitV
Electromagnetic Waves
04
Chapter8: Electromagnetic Waves UnitVI
Optics
25
17
Chapter9: Ray Optics and Optical Instruments Chapter10: Wave Optics UnitVII
Dual Nature of Radiation and Matter
08
Chapter11: Dual Nature of Radiation and Matter UnitVIII
Atoms and Nuclei
14
10
Chapter12: Atoms Chapter13: Nuclei UnitIX
Electronic Devices Chapter14: Semiconductor Devices and Simple Circuits
UnitX
15 Electronics:
Materials,
12
Communication Systems
10
188
Chapter15: Communication Systems Total
Unit I:
70
160
Electrostatics
22 Periods
Chapter1: Electric Charges and Fields Electric Charges; Conservation of charge, Coulomb's lawforce between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric fleld. Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Chapter2: Electrostatic Potential and Capacitance Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.
Unit II:
Current Electricity
20 Periods
Chapter3: Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm's law, electrical resistance, VI characteristics (linear and nonlinear), electrical energy and power, electrical resistivity and conductivity, Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff's laws and simple applications, Wheatstone bridge, metre bridge. Potentiometer  principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell.
Unit III:
Magnetic Effects of Current and Magnetism
22 Periods
Chapter4: Moving Charges and Magetism Concept of magnetic field, Oersted's experiment. Biot  Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields, Cyclotron. Force on a currentcarrying conductor in a uniform magnetic field, force between two parallel currentcarrying conductorsdefinition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometerits current sensitivity and conversion to ammeter and
189
voltmeter.
Chapter5: Magnetism and Matter Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic elements. Para, dia and ferro  magnetic substances, with examples. Electromagnets and factors affecting their strengths, permanent magnets.
Unit IV:
Electromagnetic Induction and Alternating Currents
20 Periods
Chapter6: Electromagnetic Induction Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz's Law, Eddy currents. Self and mutual induction. Chapter7: Alternating Current Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer.
Unit V:
Electromagnetic waves
04 Periods
Chapter8: Electromagnetic Waves Basic idea of displacement current, Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, Xrays, gamma rays) including elementary facts about their uses.
Unit VI:
Optics
25 Periods
Chapter9: Ray Optics and Optical Instruments Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker's formula, magnification, power of a lens, combination of thin lenses in contact, combination of a lens and a mirror, refraction and dispersion of light through a prism. Scattering of light  blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Chapter10: Wave Optics Wave optics: Wave front and Huygen's principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light, diffraction due to a single slit, width of central maximum, resolving
190
power of microscope and astronomical telescope, polarisation, plane polarised light, Brewster's law, uses of plane polarised light and Polaroids.
Unit VII:
Dual Nature of Radiation and Matter
08 Periods
Chapter11: Dual Nature of Radiation and Matter Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equationparticle nature of light. Matter waveswave nature of particles, deBroglie relation, DavissonGermer experiment (experimental details should be omitted; only conclusion should be explained).
Unit VIII: Atoms and Nuclei
14 Periods
Chapter12: Atoms Alphaparticle scattering experiment; Rutherford's model of atom; Bohr model, energy levels, hydrogen spectrum. Chapter13: Nuclei Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Massenergy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion.
Unit IX:
Electronic Devices
15 Periods
Chapter14: Semiconductor Electronics: Materials, Devices and Simple Circuits Energy bands in conductors, semiconductors and insulators (qualitative ideas only) Semiconductor diode  IV characteristics in forward and reverse bias, diode as a rectifier; Special purpose pn junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics, zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration), basic idea of analog and digital signals, Logic gates (OR, AND, NOT, NAND and NOR).
Unit X:
Communication Systems
10 Periods
Chapter15: Communication Systems Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation, satellite communication. Need for modulation, amplitude modulation and frequency modulation, advantages of frequency modulation over amplitude modulation. Basic ideas about internet, mobile telephony and global positioning system (GPS)
PRACTICALS
(Total Periods 60)
The record to be submitted by the students at the time of their annual examination has to include: Record of at least 15 Experiments [with a minimum of 6 from each section], to be performed by the
191
students. Record of at least 5 Activities [with a minimum of 2 each from section A and section B], to be demonstrated by the teachers. The Report of the project to be carried out by the students.
Evaluation Scheme Time Allowed: Three hours
Max. Marks: 30
Two experiments one from each section
8+8 Marks
Practical record [experiments and activities]
6 Marks 3
Investigatory Project
Marks 5
Viva on experiments, activities and project
Marks Total
30 marks
SECTIONA Experiments 1.
To determine resistance per cm of a given wire by plotting a graph for potential difference versus current.
2.
To find resistance of a given wire using metre bridge and hence determine the resistivity (specific resistance) of its material.
3.
To verify the laws of combination (series) of resistances using a metre bridge.
4.
To verify the laws of combination (parallel) of resistances using a metre bridge.To
5.
compare the EMF of two given primary cells using potentiometer.
6.
To determine the internal resistance of given primary cell using potentiometer.
7.
To determine resistance of a galvanometer by halfdeflection method and to find its figure of merit.
8.
To convert the given galvanometer (of known resistance and figure of merit) into a voltmeter of desired range and to verify the same.
9.
To convert the given galvanometer (of known resistance and figure of merit) into an ammeter of desired range and to verify the same.
10. To find the frequency of AC mains with a sonometer. Activities (For the purpose of demonstration only) 1.
6.
2.
3. 4. 5.
192
T
the resistance and impedance of an inductor with or without iron core.
o
To measure resistance, voltage (AC/DC), current (AC) and check continuity of a given circuit using multimeter.
m
To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse and a power source.
e a s u r
To assemble the components of a given electrical circuit. To study the variation in potential drop with length of a wire for a steady current. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key, ammeter and voltmeter. Mark the components that are not connected in proper order and correct the circuit and also the circuit diagram.
e
SECTIONB
Experiments 1.
To find the value of v for different values of u in case of a concave mirror and to find the focal length.
193
2.
To find the focal length of a convex mirror, using a convex lens.
3.
To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and 1/v.To find
4.
the focal length of a concave lens, using a convex lens.
5.
To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and angle of deviation.
6.
To determine refractive index of a glass slab using a travelling microscope.To find
7.
refractive index of a liquid by using convex lens and plane mirror.
8.
To draw the IV characteristic curve for a pn junction in forward bias and reverse bias.
9.
To draw the characteristic curve of a zener diode and to determine its reverse break down voltage.
10. To study the characteristic of a common  emitternpn or pnp transistor and to find out the values of current and voltage gains. Activities (For the purpose of demonstration only) 1.
To identify a diode, an LED, a transistor, an IC, a resistor and a capacitor from a mixed collection of such items.
2.
Use of multimeter to (i) identify base of transistor, (ii) distinguish between npn and pnp type transistors, (iii) see the unidirectional flow of current in case of a diode and an LED, (iv) check whether a given electronic component (e.g., diode, transistor or IC) is in working order.
3.
To study effect of intensity of light (by varying distance of the source) on an LDR.
4.
To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab. To
5.
observe polarization of light using two Polaroids.To observe diffraction of light due to a thin slit.
6.
To study the nature and size of the image formed by a (i) convex lens, (ii) concave mirror, on a screen
7.
by using a candle and a screen (for different distances of the candle from the lens/mirror). To obtain a lens combination with the specified focal length by using two lenses from the given set of
8.
lenses.
Suggested Investigatory Projects 1.
To study various factors on which the internal resistance/EMF of a cell depends.
2.
To study the variations in current flowing in a circuit containing an LDR because of a variation in (a) the power of the incandescent lamp, used to 'illuminate' the LDR (keeping all the lamps at a fixed distance). (b) the distance of a incandescent lamp (of fixed power) used to 'illuminate' the LDR.
3.
To find the refractive indices of (a) water (b) oil (transparent) using a plane mirror, an equi convex lens (made from a glass of known refractive index) and an adjustable object needle.
4.
To design an appropriate logic gate combination for a given truth table.
5.
To investigate the relation between the ratio of (i) output and input voltage and (ii) number of turns in the secondary coil and primary coil of a self designed transformer.
6.
To investigate the dependence of the angle of deviation on the angle of incidence using a hollow prism filled one by one, with different transparent fluids.
194
To estimate the charge induced on each one of the two identical styrofoam (or pith) balls suspended in a vertical plane by making use of Coulomb's law. To set up a common base transistor circuit and to study its input and output characteristic and to 7.
calculate its current gain. To study the factor on which the self inductance of a coil depends by observing the effect of this coil,
8.
when put in series with a resistor/(bulb) in a circuit fed up by an A.C. source of adjustable frequency.
9. 10. To construct a switch using a transistor and to draw the graph between the input and output voltage and mark the cutoff, saturation and active regions. 11. To study the earth's magnetic field using a tangent galvanometer.
Practical Examination for Visually Impaired Students of Classes XI and XII Evaluation Scheme Time Allowed: Two hours
Max. Marks: 30
Identification/Familiarity with the apparatus
5 marks
Written test (based on given/prescribed practicals)
10 marks
Practical Record
5 marks
Viva
10 marks Total
30 marks
General Guidelines The practical examination will be of two hour duration. A separate list of ten experiments is included here. The written examination in practicals for these students will be conducted at the time of practical examination of all other students. The written test will be of 30 minutes duration. The question paper given to the students should be legibly typed. It should contain a total of 15 practical skill based very short answer type questions. A student would be required to answer any 10 questions. A writer may be allowed to such students as per CBSE examination rules. All questions included in the question papers should be related to the listed practicals. Every question should require about two minutes to be answered. These students are also required to maintain a practical file. A student is expected to record at least five of the listed experiments as per the specific instructions for each subject. These practicals should be duly checked and signed by the internal examiner. The format of writing any experiment in the practical file should include aim, apparatus required, simple theory, procedure, related practical skills, precautions etc. Questions may be generated jointly by the external/internal examiners and used for assessment. The viva questions may include questions based on basic theory/principle/concept, apparatus/ materials/chemicals required, procedure, precautions, sources of error etc.
195
Class XII A. Items for Identification/ familiarity with the apparatus for assessment in practicals (All experiments) Meter scale, general shape of the voltmeter/ammeter, battery/power supply, connecting wires, standard resistances, connecting wires, voltmeter/ammeter, meter bridge, screw gauge, jockey Galvanometer, Resistance Box, standard Resistance, connecting wires, Potentiometer, jockey, Galvanometer, Lechlanche cell, Daniell cell (simple distinction between the two visàvis their outer (glass and copper) containers, rheostat connecting wires, Galvanometer, resistance box, Plugin and tapping keys, connecting wires battery/power supply, Diode, Transistor, IC, Resistor (Wirewound or carbon ones with two wires connected to two ends), capacitors (one or two types), Inductors, Simple electric/electronic bell, battery/power supply, Plugin and tapping keys, Convex lens, concave lens, convex mirror, concave mirror, Core/hollow wooden cylinder, insulated wire, ferromagnetic rod, Transformer core, insulated wire. B. List of Practicals 1.
To determine the resistance per cm of a given wire by plotting a graph between voltage and current.
2.
To verify the laws of combination (series/parallel combination) of resistances by ohm's law.
3.
To find the resistance of a given wire using a meter bridge and hence determine the specific resistance (resistivity) of its material.
4.
To compare the e.m.f of two given primary cells using a potentiometer.
5.
To determine the resistance of a galvanometer by half deflection method.
6.
To identify a
7.
(i)
diode, transistor and IC
(ii)
resistor, capacitor and inductor, from a mixed collection of such items.
To understand the principle of (i) a NOT gate (ii) an OR gate (iii)an AND gate and to make their equivalent circuits using a bell and cells/battery and keys /switches.
8.
To observe the difference between (i) a convex lens and a concave lens (ii) a convex mirror and a concave mirror and to estimate the likely difference between the power of two given convex /concave lenses.
9.
To design an inductor coil and to know the effect of (i) change in the number of turns (ii) introduction of ferromagnetic material as its core material on the inductance of the coil.
196
10. To design a (i) step up (ii) step down transformer on a given core and know the relation between its input and output voltages. Note: The above practicals may be carried out in an experiential manner rather than recording observations. Prescribed Books: 1.
Physics, Class XI, Part I and II, Published by NCERT. 2. Physics, Class XII, Part I and II, Published by NCERT.
3.
The list of other related books and manuals brought out by NCERT (consider multimedia also).
PHYSICS (Code No. 042) QUESTION PAPER DESIGN CLASS  XII (201516) Time 3 Hours
Max. Marks: 70
S. No.
Typology of Questions
1.
2
3
4
Very Short Answer (VSA) (1 mark)
Short AnswerI (SAI) (2 marks)
Remembering  (Knowledge based Simple recall questions, to know specific facts, terms, concepts, principles, or theories, Identify, define, or recite, information)
2
1
1

Understanding (Comprehension to be familiar with meaning and to understand conceptually, interpret, compare, contrast, explain, paraphrase information)

2
4
Application  (Use abstract information in concrete situation, to apply knowledge to new situations, Use given content to interpret a situation, provide an example, or solve a problem)

2
2

High Order Thinking Skills (Analysis & SynthesisClassify, compare, contrast, or differentiate between different pieces of information, Organize and/or integrate unique pieces of information from a
197
Short Value Long Answer II based Answer (SAII) (3 question (LA) marks) (4 marks) (5 marks)
Total Marks
% Weightage

7
10%

1
21
30%
4

1
21
30%
1

1
10
14%
variety of sources) 5
Evaluation  (Appraise, judge, and/or justify the value or worth of a decision or outcome, or to predict outcomes based on values) TOTAL
1

2
1

11
16%
5x1=5
5x2=10
12x3=36
1x4=4
3x5=15
70(26)
100%
QUESTION WISE BREAK UP Type of Question
Mark per Question
Total No. of Questions
Total Marks
VSA
1
5
05
SAI
2
5
10
SAII
3
12
36
VBQ
4
1
04
LA
5
3
15
26
70
Total
198
SAMPLE QUESTION PAPER –I (2016) . CLASSXII SUBPHYSICS(THEORY) Time allowed:3 hours
MaximumMarks:70
General Instructions: 1.All questions are compulsory. 2.There are 30 questions in total. Questions 1 to 5 carry 1 mark each, questions 6 to 10 carry 2 marks each, questions 11 to 22 carry 3 marks each, question 23 carries 4 marks and questions 24 to 26 carry 5 marks each. 3.There is no overall choice .However ,an internal choice has been provided in one question of two marks,one question of three marks and all questions of five marks each. 4.Use of calculators is not permitted. 5.Use the following values of constants wherever necessary. c=3×108 m/s h=6.626×1034 Js e=1.602×1019C 0=4×107TmA1 1/40=9×109Nm2C2 1.Represent the variation of electric field E due to a point charge with 1/r2 graphically.
1
2.How does the rise of temperature affect the conductivity of semiconductors and metals? 1 3.What is the resistance of ideal (i)ammeter(ii)voltmeter?
1
4.Two identical loops, one of copper and the other of aluminium ,are rotated with the same angular speed in the same magnetic field. In which coil will more current be produced?
1
5.Draw the symbol of NAND gate and write its truth table.
1
6.Two point charges 4Q and Q are separated by 1m in air. At what point on the line joining the charges is the electric field intensity zero?
2 199
7. Using Ampere's circuital law obtain an expression for magnetic field of a current carrying solenoid.
2 OR
Using Ampere's circuital law obtain an expression for magnetic field of a current carrying torroid.
2
8. I1 and I2 flow in the same direction in two parallel straight conductors.At what distance from the current I2 between the conductors is the magnetic field equal to zero?
2
9. An a.c .source is connected to an inductor.Find the expression for the current flowing through it.Plot a graph of voltage versus current to show that lags behind the voltage by/2.
2
10. A circuit contains a series combination of an 80mH inductor and a 50 F capacitor in series to a 200 V ac source with angular frequency 100 rad/s.The resistance of the circuit is negligible.Obtain the impedance of the circuit and r.m.s.value of current.
2
11.A copper wire of resistivity c and an iron wire of resistivity i have the same length and potential difference applied to them. a)What must be the ratio of their radii if the same current is to flow between them? b)If the wires with equal radius and length are joined in series ,what is equivalent resistivity? 3 12.Derive the condition of balance of a Wheatstone bridge using Kirchoff's laws.
3
OR State the principle of potentiometer.Explain with diagram how the e.m.f.of two primary cells can be compared using a potentiometer.
3
13.With the help of a circuit show how a moving coil galvanometer can be converted into a voltmeter of a given range.Write the necessary mathematical formula.
3
14.With the help of a suitable diagram explain the working of an AC Generater. Also, derive an expression for alternating voltage produced by this device. 15.a) Identify the following e.m. wave and write one application of each (i) Over exposure to these waves may cause skin cancer . (ii) these waves are produced by bombarding a high atomic number metal target using 200
ast moving electrons.
201
b). A certain part of e.m. spectrum is used for cooking. Name the part. What special frequency of these waves is most suitable?
3
16.State Huygen's principle. With the help of this principle, verify the laws of reflection of light.
3
17.What is the difference between unpolarized and plane polarised light?State the condition when the reflected wave is totally plane polarized.Find the expression for refractive index of the transparent medium in this case. 18.Derive the lens maker's formula for a double convex lens.
3
19. Draw the graph showing variation of binding energy per nucleon. Explain using the graph why light nuclei can undergo fusion and heavy nuclei can undergo fission.
3
20. Using the law radio activity , deduce the formula N= N0 et . Hence, find the expression for half life . ( the symbols have their usual meaning) .
3
21.What is meant by amplitude modulated carrier wave? Draw a block diagram to describe the steps for its detection.
3
22.Explain why high frequency carrier waves are needed for effective transmission of signals?
3
23.Ramesh while explaining photoelectric effect to his friend, who was not able to understand the phenomenon before the exams, told him that the graph between stopping potential and frequency of incident light is found to be a straight line. (i)State the general equation represented by the straight line in the graph with slope 4.12×1018Vs. (ii)How can the value of Planck's constant be determined from the equation? (iii)What value is shown by Ramesh?
4
24.What are coherent sources of light? Find the expression for fringe width of interference fringes in Young's double slit experiment. Draw a graph showing the variation of intensity with position of fringes for interference pattern .
5
202
OR Define diffraction . Plot a graph showing the variation of intensity with angular position of fringes due to a single slit .Explain the formation of central bright fringe, first secondary maxima and first minima.
5
25. a) With the help of a proper circuit diagram explain the working of a full wave rectifier. Draw the input and output waveforms. b) How does a Zener diode act as a voltage regulator? Explain.
OR Draw a labelled circuit diagram of a common emitter amplifier using a npn transistor. Define voltage gain and write its expression. Explain how is the input and output voltage out of phase by 1800.
5
26.a) What is an equipotential surface?Draw schematically equipotential surface corresponding to a field that uniformly increases in magnitude but remains constant in the zdirection. b)Using Gauss theorem deduce an expression for the electric field at a point near an infinitely long straight uniformly charged wire.
5
OR An electric dipole of dipole moment p is held in a uniform electric field E. i)Prove that no translatory force acts on the dipole. ii)Find the torque acting on the dipole iii)How much work is required in turning the electric dipole from the position of most stable equilibrium to the position of most unstable equilibrium.

203
5
SAMPLE QUESTION PAPER –II CLASSXII SUBPHYSICS(THEORY) Time allowed:3 hours
MaximumMarks:70
General Instructions: 1.All questions are compulsory. 2.There are 30 questions in total. Questions 1 to 5 carry 1 mark each, questions 6 to 10 carry 2 marks each, questions 11 to 22 carry 3 marks each, question 23 carries 4 marks and questions 24 to 26 carry 5 marks each. 3.There is no overall choice .However ,an internal choice has been provided in one question of two marks,one question of three marks and all questions of five marks each. 4.Use of calculators is not permitted. 5.Use the following values of constants wherever necessary. c=3×108 m/s h=6.626×1034 Js e=1.602×1019C 0=4×107TmA1 1/40=9×109Nm2C2 1.Represent the variation of electric field E due to a point charge with 1/r2 graphically.
1
2.How does the rise of temperature affect the conductivity of semiconductors and metals?
13.What is the
resistance of ideal (i)ammeter(ii)voltmeter?
1
4.Two identical loops, one of copper and the other of aluminium ,are rotated with the same angular speed in the same magnetic field. In which coil will more current be produced?
1
5.Draw the symbol of NAND gate and write its truth table.
1
6.Two point charges 4Q and Q are separated by 1m in air. At what point on the line joining the charges is the electric field intensity zero?
2
7. Using Ampere's circuital law obtain an expression for magnetic field of a current carrying solenoid.
2 204
OR Using Ampere's circuital law obtain an expression for magnetic field of a current carrying torroid. 2 8. I1 and I2 flow in the same direction in two parallel straight conductors.At what distance from the current I2 between the conductors is the magnetic field equal to zero?
2
9. An a.c .source is connected to an inductor.Find the expression for the current flowing through it.Plot a graph of voltage versus current to show that lags behind the voltage by/2.
2
10. A circuit contains a series combination of an 80mH inductor and a 50 F capacitor in series to a 200 V ac source with angular frequency 100 rad/s.The resistance of the circuit is negligible.Obtain the impedance of the circuit and r.m.s.value of current.
2
11.A copper wire of resistivity c and an iron wire of resistivity i have the same length and potential difference applied to them. a)What must be the ratio of their radii if the same current is to flow between them? b)If the wires with equal radius and length are joined in series ,what is equivalent resistivity?
312.Derive the
condition of balance of a Wheatstone bridge using Kirchoff's laws.
3
OR State the principle of potentiometer.Explain with diagram how the e.m.f.of two primary cells can be compared using a potentiometer.
3
13.With the help of a circuit show how a moving coil galvanometer can be converted into a voltmeter of a given range.Write the necessary mathematical formula.
3
14.With the help of a suitable diagram explain the working of an AC Generater. Also, derive an expression for alternating voltage produced by this device. 15.a) Identify the following e.m. wave and write one application of each (i) Over exposure to these waves may cause skin cancer . (ii) these waves are produced by bombarding a high atomic number metal target using fast moving electrons.
b). A certain part of e.m. spectrum is used for cooking. Name the part. What special frequency of these waves is most suitable?
3 205
16.State Huygen's principle. With the help of this principle, verify the laws of reflection of light.
3
17.What is the difference between unpolarized and plane polarised light?State the condition when the reflected wave is totally plane polarized.Find the expression for refractive index of the transparent medium in this case. 18.Derive the lens maker's formula for a double convex lens.
3
19. Draw the graph showing variation of binding energy per nucleon. Explain using the graph why light nuclei can undergo fusion and heavy nuclei can undergo fission.
3
20. Using the law radio activity , deduce the formula N= N0 et . Hence, find the expression for half life . ( the symbols have their usual meaning) .
3
21.What is meant by amplitude modulated carrier wave? Draw a block diagram to describe the steps for its detection.
3
22.Explain why high frequency carrier waves are needed for effective transmission of signals?
3
23.Ramesh while explaining photoelectric effect to his friend, who was not able to understand the phenomenon before the exams, told him that the graph between stopping potential and frequency of incident light is found to be a straight line. (i)State the general equation represented by the straight line in the graph with slope 4.12×1018Vs. (ii)How can the value of Planck's constant be determined from the equation? (iii)What value is shown by Ramesh?
4
24.What are coherent sources of light? Find the expression for fringe width of interference fringes in Young's double slit experiment. Draw a graph showing the variation of intensity with position of fringes for interference pattern .
5
OR Define diffraction . Plot a graph showing the variation of intensity with angular position of fringes due to a single slit .Explain the formation of central bright fringe, first secondary 206
maxima and first minima.
5
25. a) With the help of a proper circuit diagram explain the working of a full wave rectifier. Draw the input and output waveforms. b) How does a Zener diode act as a voltage regulator? Explain.
OR Draw a labelled circuit diagram of a common emitter amplifier using a npn transistor. Define voltage gain and write its expression. Explain how is the input and output voltage out of phase by 1800.
5
26.a) What is an equipotential surface?Draw schematically equipotential surface corresponding to a field that uniformly increases in magnitude but remains constant in the zdirection. b)Using Gauss theorem deduce an expression for the electric field at a point near an infinitely long straight uniformly charged wire.
5
OR An electric dipole of dipole moment p is held in a uniform electric field E. i)Prove that no translatory force acts on the dipole. ii)Find the torque acting on the dipole iii)How much work is required in turning the electric dipole from the position of most stable equilibrium to the position of most unstable equilibrium.

207
5
MODEL QUESTION PAPER1 MAX.MARKS 70
TIME 3 HOURS
General Instructions : (i) (ii) (iii) (iv) (v) (vi) (vii) (viii)
All questions are compulsory. Question numbers 1 to 8 are very short answer type questions, carrying one mark each. Question numbers 9 to 16 are short answer type questions , carrying two marks each. Question numbers 17 to 25 are also short answer type questions, carrying three marks each. Question number 26 is value based question , carrying 4 marks. Question numbers 27 to 29 are long answer type questions, carrying five marks each. Use of calculators is not permitted. However, you may use log tables, if necessary. You may use the following values of physical constants wherever necessary c = 3 x 108 m/s
h = 6.6 x 1034Js e = 1.6 x 1019 C μo = 4π x 107 Tm/A Mass of neutron mn = 1.6 x 1027 kg Boltzmann,s constant k = 1.38 x 1023 J/K Avagadro’s number NA = 6.023 x 1023/mole 1) Draw the graph between electric field strength and distance from the centre of the hollow conducting charged sphere.
208
2) The electric current passing through a wire in the direction from Q to P is decreasing. What is the direction of induced current in the metallic loop kept above the wire as shown in the figure?
3) Which among Xrays, sound waves and radio waves can be polarized? 4) What is photodiode? Draw its symbol. 5) In a photoelectric effect experiment, the following graphs were obtained between the photoelectric current and the applied voltage . Name the characteristic of the incident radiation that was kept constant in this experiment.
6) A proton and electron have the same kinetic energy. Which of the two have higher wavelength? 209
7) The amplitude of carrier wave is 10V. Find the amplitude of modulating signal if modulation index is 80%. 8) The transmission signals using sky waves are restricted to 30MHz. Why? 9) Two capacitors of capacitances 3μF and 6μF are charged to potentials of 2V and 5V respectively. These two charged capacitors are connected in series. Find the potential across each of the two capacitors now? 10) Length of a given conductor is increased to 3 times by stretching it. What is its effect on drift velocity and resistivity? (Assume potential difference across the conductor is kept constant). 11) What is potential gradient? Write its unit also. Write its expression in terms of specific resistance of the wire. (OR) Draw the graphs showing variation of resistivity with temperature for metals and silicon. 12) State Biot –Savart’s law. Using it, write the expression for the magnetic field at the centre of the circular current carrying coil of radius ‘a’. 13) A circular copper disc, 10cm in radius rotates at 20π rad/s about an axis through its centre and perpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the plane of the disc. (i) Calculate the potential difference developed between the axis of the disc and the rim. (ii) What is the induced current if the resistance of the disc is 2 ohm. 14) Derive an expression for the energy stored in an inductor of inductance L. 15) Discuss the ground wave propagation of waves. What are the limitations for it. 16) Define polarization of light and write Malus’ law of polarization.
210
17) The threshold frequency for a certain metal is 3.3 x 1014 Hz. If light of frequency 8.2 x 1014 Hz is incident on the surface of the metal. Find (i) work function (ii) maximum K.E of photoelectron ejected. 18) If the base region of a transistor is made large as compared to the usual transistor, how does it affect (a) collector current (b) current gain? 19) A set of 4 cells each of emf 2V and internal resistance 1 ohm are connected across an external load of 10 ohms with 2 rows, 2 cells in each branch. Calculate the current in each branch and the potential difference across 10 ohms. 20) What is the force on a wire of length 2 cm placed inside a solenoid near its centre (a) making an angle of 60o with the axis (b) parallel to the axis(c) perpendicular to the axis? The wire carries a current of 1A and the magnetic field inside the solenoid is 0.4T. 21) Compare the properties of ferro, para and dia magnetic substances. 22) A 100V,50Hz source is connected to a series combination of an inductance of 100mH and resistance 20 ohms. Calculate the magnitude and phase of current. (Or) A 25μF capacitor,0.1H inductor and 25 ohms resistor are connected in series with an ac source whose emf is given by E = 310 Sin (314t) Calculate (a) frequency of the ac power supply? (b) Impedance. (c)Peak current in the circuit. 23) Explain various series of spectral lines Hydrogen atom and draw energy level diagram. 24) Using the data given below, state which of the two given lenses will you prefer to construct the best possible (i) Telescope (ii) Microscope. Also indicate which of the selected lenses is to be used as objective and as 211
eyepiece in each case. Lens
Power(P)
L1
6D
Aparture(A) 1 cm
L2
3D
8 cm
L3
10 D
1 cm
25)A star converts all its hydrogen to helium achieving 100% helium composition. It then converts helium to carbon via the reaction 4 4 2He + 2He
+ 2He4 → 6C12 + 7.27 MeV
The mass of the star is 5 x 1012 kg and it generates energy at the rate of 5 x1030 W. How long will it take to convert all the helium to carbon at this rate. 26) In the famous conversation, Rakesh Sharma, the first Indian Astronaut in space, was asked by the then Prime Minister Indira Gandhi as to how India looked from space. To which he replied ‘Sare Jahan Se Achcha’ (better than the whole world).Answer the following questions based on above passage: a. Which scientific mode of communication enabled The Prime Minister to speak to theAstronaut? b. Name the scientific values displayed in this anecdote. c. Which values are being reflected in the reply given by the astronaut? 27) Writethe principle, construction and working of VandeGraff generator. How is the leakage of charge minimized from the generator? (Or) a) State Gauss’s theorem in electrostatics. b) Obtain expression for electric field at a point which is at a perpendicular distance ‘r’ from a plane infinite sheet of charge with uniform charge density. 28) a)State Huygen’s principle. b)Describe the single slit diffraction experiment and obtain the expression for fringe width. (Or)
212
a) Derive the relation between the focal length of a convex lens in terms of the radii of curvature of the two surfaces and refractive index of its material. Write the sign conventions and two assumptions used in the derivation of the relation. b) A convex lens of focal length 40 cm and a concave lens of focal length 25 cm are kept in contact with each other. What is the value of power of this combination? 29) a) With the help of a labeled diagram, explain how npn transistor is used as an amplifier in CE configuration. Explain how the input and output in this case are out of phase. b)A transistor operated in CE configuration at Vc=2V such that change in base current from 100μA to 200 μA produces change in the collector current from 9mA to 16.5mA.Calculate the current gain. OR a) Explain the working of npn transistor as an oscillator with the help of a labeled diagram. b) Sketch the output waveform for the following inputs A and B obtained from NAND gate.
213
MARKING SCHEME QUESTION EXPECTED ANSWER / VALUE POINTS NO. 1
MARKS
2 3 4 5 6 7 8
1 ½ +½ ½ +½ 1 1 1 1
9
10 11
12 13
Anticlockwise Xrays , radio waves Definition , symbol Frequency of incident ray Wavelength=0.0347 nm I t determines the strength and quality of the signal Above 1500 kHz, the absorption of signals from earth’s surface increases Charge in Q1 = 6µC and on Q2 = 30 µC Total charge = 24 µC In series the charge on each capacitor is same. So, the charge on each capacitor = 24 µC Potential difference on C1 = 8/3 V and on C2 = 8/3 V Drift velocity became 1/27 time the initial drift velocity No change in the resisstivity Definition , V/m Expression OR Graph for metals Graph for Silicon Statement Expression B=µo I/2a Emf = ½ Bl2 = 6.29 x 102 V 214
1
½ ½ ½ ½ 1 1 1 1 1 1 1 1 1
14 15 16 17
18 19
Current = 3.15 x 102A Energy stores in the inductor = ½ LI2 Explanation Limitation Definition I = I0 Cos2 Work function = 1.36 eV Energy of incident photon = 3.38 eV Kinetic energy of photoelectrons = 2.02 eV A thin transistor base will have less majority carrier and this gives more current in the collector circuit , explanation Say n is the number of cells in reverse order, emf of each cell = Then total emf = (12 – 2n) Current 3 = [(12 – 2n ) + 2]/ R 2 = [(12 – 2n ) – 2] / R Solving these equations we get n = 1
20
21 22
23
B1 = µ0 I (sin 1 + sin 2) / 4 R R = OD = BD/tan60 B = 4.6 x 104 T Any three differences
1 2 1 1 1 1 1 ½ ½ 2
½ 1 1 1/2 3
3
V=100V f=50Hz L=100mH R=20 Z = 37.24 ohm I = Vrms / Z = 2.68 A = tan 1(L/R) = 57.5o OR Frequency = 50 Hz Impedance Z = (R2 + (XL – Xc))1/2 = 98.1 ohm Peak current=310/98.1 =3.1A Explanation of spectral series 215
1 1 1 1 1 1 2
24 25
26
27
28
29
Energy level diagram For telescope, objective lens = L2 and eye lens = L3, reason For microscope, objective lens = L1 and eye lens = L2, Reason Total No of nuclear reaction Total energy released Time = total energy / power Space wave communication Values in the anecdote Values in the reply Principle of van de Graff Generator Construction and diagram Working Minimisation of leakage OR Gauss theorem statement Diagram of plane sheet Derivation of expression
1 1½ 1½ 1½ 1 ½ 1 1½ 1½ 1 2 1 1
Huygene Principle Single slit diffraction diagram Derivation of Expression for fring width β = λ D/a OR Diagram Derivation 1/f = (µ  1) (1/R1 – 1/R2) P = P1 + P2 P = 2.5 – 4 = 1.5D
1 1 3
Circuit diagram CE amplifier Working In put and out put waveform Current gain = 75 OR Circuit diagram of oscillator Working of oscillator Out put wave form
1 2 1 1
1 1 3
1 2 2
1 2 2
216
Tips for scoring well in the exam(FOR STUDENTS) Objectives: Create a positive attitude. You may ask "how does creating a good attitude supposed to boost up my mark?" Well, if you create a good attitude in studying and think positive things about studying, it's likely that you will start liking a subject that you were really not fond of before. You may also get marks for having a good attitude and for not disrupting a class. Attend your classes regularly. If you attend classes daily instead of skipping them, you will be there to listen to all the lessons the teachers are teaching and won't miss important days. It's likely that you will remember or learn more if you are in class when the teacher is teaching than if you skipped class and then take notes later on. Set goals for yourself. Set goals like 'get good marks in math, science etc' for yourself and then try your hardest to achieve those goals. If you fail once, don't give up, keep trying. Do your homework daily. When you get homework, do it, don't leave it. If you're tempted to watch your favourite TV show instead of do homework, think about it this way: Is your favourite TV show going to help you get to a good university and possibly help you achieve the job of your dreams? If the answer is yes, then by all means watch the show. Homework is important because it gives you practice on the subject that you are learning. Always do your homework.
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Ask for help when you need it. If you have a question on something, ask for help, don't just leave it behind. You can ask anybody who has knowledge on the subject that you need help with like your parents, teacher, brother or sister. It will most definitely help you in tests and quizzes. Manage your time effectively. It will help you reduce anxiety and focus on studying. If you have a test next week, start studying now. Try not to study at the last minute and cram the night before. Try studying 1 or 2 hours daily and leave a half hour for homework. If you study before you do homework, it will help you do your homework faster and help you understand the subject better. Always review. After school, review what you learned that day Develop test smarts. This will really help and increase your confidence when taking exams if you're familiar with the typical exam format, common errors to avoid, and know how the concepts in a subject area usually tested. Know your personal learning style. It will help you maximize your learning by using effective study techniques, developing meaningful notes, and making the most efficient use of your study time. •
Linguistic learner: learns best by saying, hearing and seeing words; is good at memorizing formulae
and its uses in various formats. •
Logical/mathematical learner: learns best by categorizing, classifying and working with abstract
relationships; is good at logic, problem solving and reasoning. •
Interpersonal learner: learns best by sharing, comparing, relating, cooperating; is good at organizing,
communicating, leading, and understanding others. •
Intrapersonal learner: learns best by working alone, individualized assignments, and selfpaced
instruction. Action plan for 100% quality result( FOR TEACHERS) Strategies for Slow learners: 218
1. Identify the slow learners at the beginning of the year. Set achievable targets and motivate themthroughout the year so that they will not be depressed and discouraged. 2. Question papers of last five years (both main and supplementary examinations) are to be collectedand the list out all repeated, important concepts/problems. The slow learners are to be givensufficient practice in these areas/concepts. 3. The Latest Blue Print prepared by the CBSE to be given to each child especially to the slow learnersin the beginning of the session.(From 20142015 onwards , pattern is changed) 4. The strengths and weaknesses are to be diagnosed in these areas. Thorough revision in these concepts is to be given by conducting frequent slip tests and reteaching. 5. Preparation of Questionwise analysis of each examination including slip tests to be done to locatethe weak areas and thorough revision is to be conducted. 6. Collect the drilling problems of a particular concept, and solve two or three problems in the class.Then allow the slow learners to solve the remaining problems as per their capacity to attain a goodcommand and confidence over that particular method/type (Drilling Exercises). 7. Three model papers based on the Sample Papers issued by CBSE (SET I, II, III) along with markingscheme should be prepared by the teacher. Copies of these papers are to be issued to all the slowlearners. This will help the child to know the type of questions/methods important for board exams.They will get more confidence to face the board exam. 8. Concept wise, specially designed home assignments are to be given to students daily. The assignments are to be corrected by giving proper suggestions in front of students. 9. After the completion of each concept/topic allow the low achiever to solve the problem pertaining tothat method. If possible every day at least one low achiever should come on to the board to solve aproblem.
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10. Whenever possible, teach Mathematics by using PP Presentations in an effective way. 11. Weekly test pertaining to these formulae has to be conducted regularly. 12. The students have to be asked to read the entire text book thoroughly. 13. The students are to be made aware about the chapter wise distribution of marks or marking scheme. 14. Sufficient tips should be given for time management. 15. Few easy topics are to be identified from examination point of view and are to be assigned to theslow learners. The slow learners are to be prepared for reduced, identified syllabus. Strategies for bright and Gifted Students: 1) Bright Children are the back bones to improve the overall Performance Index of the Vidyalaya. So they should be encouraged by providing concepts wise HOTS questions. They should beencouraged to solve more challenging questions which have more concepts and challenging tasks. 2) More thought provoking questions are tobe collected and a question bank is to be given to gifted students to develop their analyzing and reasoning capabilities. 3) Instead of preparing the PP presentation by the teacher, better to handover all the necessary content to the students and ask the bright students, to prepare one PPT each. After submission of completed PP Presentation, check the PPT and the same can be used effectively in the teaching learning process. 4) On completion of syllabus topic wise revision plan is to be framed for both slow learners and gifted students. 5) The students have to be asked to read the entire text book thoroughly. 6) The students are to be made aware about the chapter wise distribution of marks or marking scheme. 7) Sufficient tips should be given for time management. 8) Revision Plan: a. After completion of coverage of syllabus, proper revision plan is to be prepared 9) Conceptwise (questions for slow learners/gifted students), HOTS questions/optional exercises (for gifted students) is to be prepared and given to the students. 220
10) Minimum learning programme for slow learners is to be prepared and identified/reduced syllabus is to assigned to slow learners. 11) CBSE papers to be solved: a. CBSE Board pattern question papers (at least 10 papers should be solved) b. CBSE Board papers 2015 (3 sets) c. CBSE Board Compartment Paper 2015 (1 set) d. CBSE Board papers 2011, 2012, 2013, 2014 (3 sets) e. Common Preboard Board Examination 2014, 2015
Remedial teaching for slow learners
Remedial teaching is identifying slow learners and giving them the necessary guidance to help them overcome their problems, after identifying their areas of difficulty. Contrary to what is said, remedial teaching is done perfunctorily without identifying their areas of difficulty and underlying cause for lagging behind. Some students are unsympathetically branded as `block heads' without an earnest attempt to know the real cause of their slow learning. Low achievers Who is a low achiever? In the present system of education, students are identified as slow learners purely on the basis of their poor performance in the examination, which, in most cases deviates from what is taught. Consequently even talented students are sometimes misconstrued as dullards. So, a slow learner is 221
one whose performance is very dismal in the examination. He is neither mentally retarded nor is on the lower rungs of intelligence scale. The reasons for some students learning slowly are innumerable. One of the main reasons is the `no detention system' at the primary and upper primary level. Students are promoted to higher classes on the basis of attendance, even if they score low marks. The heterogeneous composition (mental age & physical age) of overcrowded classes in all government run schools and private schools also produces slow learners. So the incapacity of the teacher to pay individual attention to a student over a long period makes a student a slow learner. A slow learner is thus a product of negligence of school at different stages of learning, inspite of his innate capacity to learn. There are some problems very specific to the individual. Ill health, lack of concentration, less exposure to the subject taught and parental background are some causative factors for slow learning. Talents differ. A child’s capacity to learn different subjects varies from student to student. For instance, learning mathematics is a knack. All students do not do well in mathematics just as they do in other subjects. While other subjects can be learnt at any stage, it is very difficult for students to learn mathematics without the basics. Students show interest in the subjects they like and neglect other subjects if not taken care of. An urban child learns languages like English well while a rural child cannot, however well the teacher tries to explain.
Remedial measures Learning takes place from simple to complex. If for some reason the student has not learnt the basics, it is futile to teach him the advanced topics. Remedial teaching is not revising the topics taught repeatedly. Careful analysis of the students' performance in the examination and diagnosing the areas of difficulty are key aspects in remedial teaching. Once the difficult areas are identified, the next task is to plan the learning experiences to teach the basics to understand the given topic. Teachers often feel that what has not been learnt at the primary level, cannot be taught simultaneously with the prescribed topics at the secondary level as they are busy completing the syllabus. Experience shows that 222
once the basics are taught, the learning process is accelerated and the slow learners comprehend and grasp the given topics of the class, since they have already attained the mental age. In government run residential schools in Andhra Pradesh and JawaharNavodaya Vidyalayas nation wide, the students are admitted in class VI based on a selection test consisting of a variety of questions to test intelligence and aptitude of the students. It has been observed that many students thus selected do not possess the basics which they are supposed to learn at the primary level. But these schools have produced excellent results over the years by introducing bridge courses in their academic planning. Subjects like physics pose difficulty for students when compared to biology. In biological sciences, students can see and find meaning in what they study. Whereas physics is somewhat intricate and difficult for students without good knowledge of mathematics. Poor performance in physics can be remedied by first teaching the required basic mathematical operations. Sometimes language becomes a barrier for students to understand the vast areas in subjects like geography. The innumerable new words used to describe various phenomena baffle the students. Students do not find these words in English language textbooks although they learn English language to pursue others subjects in an inter disciplinary approach. The teacher has to explain all the words and their usage related to his subject before he teaches the concept. The new words used in questions could confuse students and elicit wrong answers from them. Students should be exposed to a variety of questions with antonyms and synonyms  all the words used to frame a question to test the topic taught. Merely tagging the slow learners with bright students or segregating them into separate sections will not help the slow learners. Slow learners harbour themselves unobtrusively in the group of bright students. Students learn a lot from the peer group. Unconscious learning does not take place if students are segregated. Keeping the slow learners in the peer group of bright students and paying individual attention to them by the teacher will enable them to overcome their difficulties.
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Student is central in the learning process. The learning experiences should be activityoriented and the teaching should motivate and create interest in the student to learn on his own. When group discussions are held in the classroom, the slow learners are benefited much. Suitably tailored lesson plan by the teacher and careful monitoring by the school administration will help slow learners have a better grasp of all lessons in schools.
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LEARNING STYLE OF STUDENTS Every student has a different learning style and a preferred way of learning. Try to understand your own learning style.
If you can learn by reading or hearing, books or lectures will be very useful. If you learn by discussing, working with fellow students will be helpful to you. If solving problems is difficult for you, spend more time learning how to solve problems. Remember, it is necessary as well as important to understand and develop good study habits. Ask the following question from yourself: Am I comfortable with basic concepts of the subject learnt in lower classes? If not, spend sometime in understanding these concepts. Do not hesitate asking your teachers or friends. Am I familiar with fundamental mathematical concepts from arithmetic, algebra, geometry and trigonometry? If not, learn these concepts and formulae through practice. Do I understand the subject better if I read the book before the lecture ? One may learn better by skimming the textbook in advance, going to the class and then studying the learning material in detail. Do I study every day and regularly and devote adequate time for studying Physics ? If not, make it a habit to devote adequate time for selflearning and revision. Am I an active learner ? Do I ask questions and participate in class discussions? Remaining mentally active and alert in the class helps in great deal. 225
The following actions on your part may help you understand and enjoy learning of Physics : Try to interact with your fellow students and friends. Do not hesitate to raise and clarify your doubts. You can have more fun in learning physics through discussions with friends. Take your class notes in outline form and fill in the details later. Listening to the teacher attentively in the classroom and understanding the content of the lecture is more important. Taking notes blindly does not help much. Do not miss lectures. If for some reasons you do, ask a member of your study group to provide you with notes so that you remain in touch with the flow and development of the topic. Solve as many numerical problems of different variety as possible. This will immensely help to understand concepts and their applications. Supplement your classroom learning by reading additional books. The additional learning material has to be carefully identified. Attend your practical classes regularly. It will give you handson experience of the concepts learnt in theory classes. Try learning the technique of translating mathematical expressions and graphs intoword interpretations and viceversa. This would surely help to improve your grasp of the subject and your ability to feel thrilled and excited by the finer details and intricacies of the subject. The Internet has certainly openedup a host of possibilities and opportunities for extended learning. Try visiting various sites suggested here and elsewhere to develop a passion and taste for the subject. This would not only widen your horizon but provide you a higher level ofbuiltin confidence about the subject. Perhaps, the most important favour you can do for yourself is to set aside adequate, regularly scheduled, studytime in a distractionfree environment.
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List of reference books and websites Physics Study Material Reference Books 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Conceptual Physics : Paul G Hewitt Principles of Modern Physics : Arthur Beiser University Physics : Young, Freedman : AddisonWeslyLongman,Inc The Feynman Lectures on Physics: Feynman, Leighton& Sands : Narora Publishing House, New Delhi. Physics Vol I & II : Robert Resnick, David Halliday & Kenreth S Krane : Wiley India Problems in General Physics : I E Irodov : Global Publications Principles of Physics : Brij Lal & Subbramanyam : Eurasia Publication company (Pvt.) Ltd, New Delhi Schaum’s Solved Problems Series : Alvin Hulpern : McGraw hill Book Company, New Delhi Conceptual Physics : Paul G Hewitt : Addison – Wesley Publishing Company, California IIT Physics – Tata McGraw Hill
Websites 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
www.plustwophysics.com http://www.sciencedaily.com/ www.askphysics.com www.physicsclassroom.com http://www.physicstoday.org/ http://realworldphysicsproblems.com http://opensourcephysics.org www.antonineeducation.co.uk www.mcwdn.org www.phys.hawaii.edu www.aacg.bham.ac.uk www.imagine.gsfc.nasa.gov www.atoptics.co.uk http://www.physice.ccsu.edu/LEMAIRE/genphys/virtualphysicslabs.htm http://zebu.uoregon.edu. http://www.myphysicslab.com/index.html
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