QUESTION BANKPHYSICS

Gujarat Secondary and HigherSecondary Education Board,

Gandhinagar

Price : ` 95.00Published by :

SecretaryGujarat Secondary and Higher Secondary Education Board,

Gandhinagar

I

Copyright of this book is reserved by Gujarat Secondary and Higher Secondary EducationBoard, Gandhinagar. No reproduction of this book in whole or in part, or in any form ispermitted without written permission of the Secretary, Gujarat Secondary and Higher

Secondary Education Board, Gandhinagar.

Contribution

1 Dr. Hasmukh Adhiya (IAS) Principal Secretary , Education Department Gandhinagar

2 Shri R. R. Varsani (IAS) Chairman , G.S&H.S.E. Bord, Gandhinagar

3 Shri H. K. Patel (G.A.S) Dy. Chairman, G.S&H.S.E. Bord, Gandhinagar

4 Shri M. I. Joshi (G.E.S) Secretary , G.S&H.S.E. Bord, Gandhinagar

Coordination

1 Shri B. K. Patel O.S.D., G.S&H.S.E. Bord, Gandhinagar

2 Shri D. A.Vankar Assistant Secretary (Retd.), G.S&H.S.E. Bord, Gandhinagar

5 Shri G. M. Rupareliya Assistant Secretary, G.S&H.S.E. Bord, Gandhinagar

Expert Teachers

1. Shri J. M. Patel Shree J. M. Chaudhary Sarvajanik Vidhyalaya, Mehsana

2. Shri K. D. Patel J. N. Balika Vidhyalaya, Saraspur

3. Shri Mayur M. Raval P. J. Vakharia High School, Kalol

4. Shri S. G. Patel Sarkari Schook, Sector-12, Gandhinagar

5. Shri J. P. Joshi Diwan Ballubhai High School, Ahmedabad

6. Shri Vasudev B. Raval Vidhya Mandir High School, Palanpur

7. Shri Surendrabhai M. Rajkutir Convent of Jesus And Merry

8. Shri Sureshchandra H. Patel Alambic Vidhyalaya, Vadodara

9. Shri C. D. Patel Lalbahadur Shastri Vidhyalaya, Vadodara

10. Shri Mukesh N. Gandhi New English School, Nadiad

11. Shri Dineshbhai V. Suthar Retired Teacher

12. Shri S. S. Patel J. M. Chaudhary Sarvajanik Vidhyalaya, Mehsana

13. Shri Jayesh M. Purohit Ankur Vidhyalaya, Ahmedabad

14. Smt. Asha M. Patel Shree M.B. Vamdot Sarvajanik High School, Bardoli

15. Shri Maheshbhai Dhandhla Bhavnagar

16. Shri Mukesh M. Bhatt Bhavnagar

17. Shri Anilkumar Trivedi Anand

18. Shri Anand Thakkar Navchetan High School, Ahmedbad

19. Shri Sudhirkumar G. Patel Nutan High School, Visnagar

20. Smt. Anita Pillai Surat

II

P R E FA C E

Uptil now , the Students had to appear in various entrance examinations forengineering and medical courses after std-12. The burden of examinations on the side of thestudents was increasing day-by-day. For alleviating this difficulty faced by the students,from the current year, the Ministry of Human Resource Development , Government of India,has Introduced a system of examination covering whole country. For entrance to engineeringcolleges, JEE(Main) and JEE(Advanced) examinations will be held by the CBSE. TheGovernment of Gujarat has except the new system and has decided to follow the examinationsto be held by the CBSE.

Necessary information pertaining to the proposed JEE (Main) andJEE(Advanced) examination is available on CBSE website www.cbse.nic.in and it is requestedthat the parents and students may visit this website and obtain latest information guidanceand prepare for the proposed examination accordingly. The detailed information about thesyllabus of the proposed examination, method of entrances in the examination /centers/places/cities of the examinations etc. is available on the said website. You are requested togo through the same carefully. The information booklet in Gujarati for JEE( Main) examinationbooklet has been brought out by the Board for Students and the beneficieries and a copy ofthis has been already sent to all the schools of the state. You are requested to take fulladvantage of the same also However, it is very essential to visit the above CBSE websitefrom time to time for the latest information guidance . An humble effort has been made bythe Gujarat secondary and Higher Secondary Education Boards, Gandhinagar for JEE andNEET examinations considering the demands of the students and parents , a question bankhas been prepared by the expert teachers of the science stream in the state. The MCQ typeObjective questions in this Question Bank will provide best guidance to the students and wehope that it will be helpful for the JEE and NEET examinations.

It may please be noted that this Question Bank is only for the guidance of theStudents and it is not a necessary to believe that questions given in it will be asked in theexaminations. This Question Bank is only for the guidance and practice of the Students. Wehope that this Question Bank will be useful and guiding for the Students appearing in JEE andNEET entrance examinations. We have taken all the care to make this Question Bank errorfree, however, if any error or omission is found, you are requested to refer to the text books.

M.I. Joshi R.R. Varsani (IAS)Date: 02/ 01/ 2013 Secretary Chairman

III

INDEX

IV

Unit Unit Name GSEB NEET JEE PageNo. No.

PART - II

11 Electrostatics Y Y Y 1

12 Current Electricity Y Y Y 53

13 Magnetic Effects of Currentand Magnetism Y Y Y 107

14 Electromagnetic Induction andAlternating Currents Y Y Y 173

15 Electromagnetic Waves Y Y Y 197

16 Optics Y Y Y 211

17 Dual Nature of Matter andRadiation Y Y Y 235

18 Atoms and Nuclii Y Y Y 285

19 Electronic Devices Y Y Y 321

20 Communication Systems Y Y Y 347

21 Experimental Skills (1 to 21) Y Y Y 359

1UNIT - 11ELECTROSTATICS

2SUMMARY1. Electric Charge : Just as masses of two particles are responsible for the gravitational force,

charges are responsible for the electric force. Electric charge is an intrinsic property of a particle.Charges are of two types : (1) Positive charges (2) Nagative charges.The force acting between two like charges is repulsive and two unlike charges it is attractivebetween .

2. Quantization of Electric Charge : The magnitude of all charges found in nature are an integralmultiple of a fundamental charge. ,neQ where e is the fundamental unit of charge.

3. Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sumof electric charges in an electrically isolated system always remains constant.

4. Coulomb's Law : The electric force between two stationary point charges is directly propor-tional to the product of their charges and inversely proportional to the square of the distancebetween them.

221

02

21

rqq

41

rqqkF

If 0qq 21 then there is a repulsion between the two charges and for 0qq 22 , there is a attrac-tion between the charges.

5. Equation for Force using Columbs Law, when two charges are placed in a medium havingdielectric constant k.

(1) The electric force F experienced by a test charge (q0) due to a source charge (q) whenboth are placed in a medium having dielectric constant k and separated by a dis-tance r, is given by :

rkr

qq4

1F 221

0

Fr

P

O (q)

(qo)

Here r is the unit vector directed from q to q0.

(2) The equation of coulomb's force may be written as follows : rrkqq

41F

221

0

(3) If the source charge and test charge are separated by a number of medium of thickness

1 2 3d , d , d ........ having dielectric constants ........k,k,k 321 respectively, then theelectric force on charge q0 due to a charge q is given by

0

2 2 20 1 1 2 2 3 3

qq1 F r4 k d k d k d

0

20 i i

qq1 F r4 k d

OR

In this equation ki is dielectric constant of medium which spreads through the distance dialong the line joining q and q0.

3For example, see the figure below :

Here, the space between the charges q and q0 is filled with medium (1, 2, 3). The thickness ofmedium 1 is d1 and its dielectric consant is k1 Similarly the thickness of medium 2 and 3 is d2 andd3 of medium 3 and their dielectric constants are k2 and k3 respectively.

6. Conditions for Equilibrium in Various Cases :Suppose three charges q1, q2 and q are situated on a straight line as shown below :

If q1 and q2 are like charges and q is of unlike charge then,

(1) Force on q1

2

12

21

1

0

11 r

qrr

q4

qF

(2) Force on q2

2

22

21

1

0

22 r

qrr

q4qF

(3) Force on q =

2

2

22

1

1

0 rq

rq

41F

Now, from above equations, it is clear that various equilibrium conditions can be as follows :

(a) Condition for 1F to be zero is, 221

21

221

22

1 rrr

qq

rrq

rq

(b) Condition for 2F to be zero is, 221

22

12

21

12

2 rrr

qq

rrq

rq

(c) Condition for F to be zero is, 22

22

1

1

rq

rq

22

21

2

1

rr

rq

If 21 q,q and q are of same type charges in nature, then,(1) Charge q will be in equilibrium, if

0rq

rq

4qF 2

2

22

1

1

0

21 2 1 12 2 2

1 2 2 2

q q q rr r q r

(2) Charges q1 and q2 will not be in equilibrium.

47. Electric Field Intensity : The electric force acting on a unit positive charges at a given point inan electric field of a system of charges is called the electric field or the intensity of electric field

E at that point.

qFE

The SI unit of E is CN

or 1Vm .

If n21 r...,.........r,r are the position vectors of the charges n21 q.,.........q,q respectively, then the

resultant electric field at a point of position vector r is,

jn1j

3

j

j rrrr

qkE

8. Electric Dipole : A system of two equal and opposite charge, separated by a finite distance iscalled electric dipole.

Electric dipole moment a2qp The direction of p is from the negative electric charge to the positive electric charge.

9. Electric field of a dipole on the axis of the dipole at point z = z

^32kpE z p for z az

Electric field of a dipole on the equator of the dipole at point y = y

^3kpE y p for y ay

10. The torque acting on the dipole place in an uniform the electric field at an angle ,

sinEp||,Ep

11. Electric Flux : Electric flux associated with surface of area A , placed in the uniform electricfield.

cosEAAE where, is the angle between AandE ,

Its SI unit is 2Nm

C or V.m.

12. Gauss's Law : The total electric flux associated with the closed surface,

0S

qE d a

where, q is the net charge enclosed by the surface.

513. Electric field due to an infinitely long straight charged wire,

,rr1

2E

0

where, r is the perpendicular distance from the charged wire.

14. Electric field due to bending of charged rod,

15. Electric field due to uniformly charged thin spherical shell,

(1) Electric field inside the shell 0E (2) Electric field at a distance r from the centre outside the shell,

2

2

02 r

RrqkE

where, R = radius of spherical shell.

16. Electric field due to a uniformly charged density sphere of radius R,

(1) Electric field inside the region of the sphere, 30 0

Q r rE4 R 3

6(2) Electric field outside the sphere, 0

2

3

20 r3

Rrr

4QrE

where, Q is the total charge inside the sphere.17. The information about the work done to take an electric charge from one point to the other in a

given electric field, obtained from the quantities called electric potential and electric potentialenergy.

18. B

A

drE is the line-integral of electric field between point A and B and it shows the work done by

the electric field in taking a unit positive charge from A and B. Moreover, it does not depend on

the path and 0drE .19. "The work required to be done against the electric field to bring a unit positive charge from

infinite distance to the given point in the electric field, is called the electric potential (V) at thatpoint".

Electric potential at point P is

P

p drEV

It unit is .voltcoulombJoule

Symbolically CJV

Its dimensional formula is 1321 ATLM

Absolute value of electric potential has no importance but only the change in it is important.20. "The work required to be done against the electric field to bring a given change (q) from infinite

distance to the given point in the electric field is called the electric potential energy of thatelectric charge at that point."

p

P

p qVdrEqU

The absolute value of electric potential energy has no importance, only the change in it is impor-tant.

21. Electric potential at point P, lying at a distance r from a point charge q is r

kqVp

22. The electric potential at a point at distance r from an electric dipole is

,rp

41rv 2

0 ( For r > > 2a)

Potential on its axis is ,rp

41V 2

0 Potential on its equator is 0V

23. Electric potential at a point r due to a system of point charge n21 q,.........q,q situated at position

at position n21 r,.........r,r is

n

1i i

i

rrkqV

7The electric potential at point r , due to a continuous charge distribution is

04

1rV

volume irr

'dr

The electric potential due to a spherical shell is

0

1 qV For r R4 r

and 0

1 qV For r R4 R

24. A surface on which electric potential is equal at all points is called an equipotential surface. Thedirection of electric field is normal to the equipotential surface.

25.dVEdl

gives the magnitude of electric field in the direction of dl

.

To find E from V, in general, we can use the equation

V V V E i j kx y z

The direction of electric field is that in which the rate of decrease of electric potential with

distance dVdl

is maximum, and this direction is always normal to the equipotential surface.

26. The electrostatic potential energy of a system of point charges n21 q.,.........q,q situated at positions

n21 r,.......r,r is

ni j

i 1 iji j

kq qU

r

where ijij rrr

27. The electrostatic potential energy of an electric dipole in an external electric field E, is

U E p Ep cos

28. When a metallic conductor is placed in an external electric field,(i) A stationary charge distribution is induced on the surface of the conductor.(ii) The resultant electric field inside the conductor is zero.(ii) The net electric charge inside the conductor is zero.(iv) The electric field at every point on the outer surface of conductor is locally normal to thesurface.(v) The electric potential inside the region of conductor is the same every where.(vi) If there is a cavity in the conductor then, even when the conductor is placed in an external

electric field, the resultant electric field inside the conductor and also inside the cavity isalways zero.This fact is called the electrostatic shielding.

8When electric charge is placed on the metallic conductor :(i) The electric field inside the conductor is zero everywhere.(ii) The charge is distributed only on the outer surface of the conductor.

(iii) The electric field on the surface is locally normal, and is equal to nE0

.

(iv) If a charge is placed inside the cavity in the conductor, the electric field in the conductorremains zero.

29. "A device formed by two conductors seprated from each other is called a capacitor." Its capaci-

tance is VQC constant. The unit of C is volt

coulomb which is also called farad.

F10pF.F10F1 126

30. The effective capacitance in series connection is C then,

..........C1

C1

C1

C1

321

The effective capacitance in parallel connection is C then,

.........CCCC 321

31. The capacitance of the parallel plate capacitor is dAC 0 .

32. The energy stored in the capacitor is 2

VQ2

CVC2

QU22

and the energy density = energy

stored per unit volume ,E21 2

0 where E electric field.

33. When a dielectric is placed in an external electric field 0E , polarisation of dielectric occurs dueto electrical induction. The electric field produced by these induced charges is in the oppositedirection to the direction of external electric field. Hence the resultant electric field E, inside thedielectric is less than the external electric field 0E .

The dipole moment produced per uint volume is called the intensity of polarisation or in shortpolarisation

.nP b

Since EP , P E0 e ex x is called the electric susceptibility of the dielectric medium.

1 0 ex is called the permittivitty of the dielectric medium. 0

is called the relative

permittivity of that medium and it is also called the dielectric constant K.

9i.e. K

r0

EK 1 , E .K

0ex Thus in the dielectric the electric field reduces to the thK part.

PED 0 is called the electric displacement. Gauss Law in the presence of dielectric is

written as qdsD , where q is only the net free charge.34. when there is air (or vacuum) between the plates of a parallel plate capacitor, the capacitance is

dAC 0 . On placing a medium of dielectric constant K, the capacitance is .CK'C Thus the

capacitance becomes K times, due to the presence of the dielectric.

35. With the help of Van-De-Graf generator a potential differance of a few nillion volt can beestablished.

10

CO

NC

EPT

MA

P

11

MCQFor the answer of the following questions choose the correct alternative from among thegiven ones.1. When a Piece of Polythene is rubbed with wool, a charge of 72 10 is developed on

polythene. The mass transferred to polythene is ..... kg.

(A) 1911.38 10 (B) 195.69 10 (C) 192.25 10 (D) 199.63 102. The protonic charge in 100 gm of water is .......... c

(A) 54.8 10 (B) 65.4 10 (C) 43.6 10 (D) 64.9 10

3. A copper sphere of mass 2 gm contains about 222 10 atoms. The charge on the nucleus ofeach atom is 29e. The fraction of electrons removed.

(A) 102 10 (B) 121.19 10 (C) 111.25 10 (D) 112.16 104. The rate of alpha partical falls on neutral spheare is 1012 per second. The time in which

sphere gets charged by 2c is ......... sec.

(A) 2.25 (B) 3.15 (C) 6.25 (D) 1.665. A charge Q is divided into two parts and then they are placed at a fixed distance. The force

between the two charges is always maximum when the charges are .........

(A) Q Q,3 3

(B) Q Q,2 2

(C) Q 3Q,4 4

(D) Q 4Q,5 5

6. Two point charges repel each other with a force of 100 N. One of the charges is increasedby 10% and other is reduced by 10%. The new force of repulsion at the same distance wouldbe ........ N.(A) 121 (B) 100 (C) 99 (D) 89

7. Given that q1 + q2 = q if the between q1 and q2 is maximum,1q

q ...............

(A) 1 (B) 0.75 (C) 0.25 (D) 0.5

8. Two small conducting sphere of equal radius have charges +1c and 2c respectively andplaced at a distance d from each other experience force F1. If they are brought in contact andseparated to the same distance, they experience force F2. The ratio of F1 to F2 is ..........(A) 8 : 1 (B) 1 : 2 (C) 1 : 8 (D) 2 : 1

9. Three charges, each of value Q, are placed at the vertex of an equilateral triangle. A fourthcharge q is placed at the centre of the triangle. If the charges remains stationery then,q = ...............

(A) Q2 (B)

Q3 (C)

Q2 (D)

Q3

12

10. Tw o small charged spheres repal each other w i th a force 32 10 N . The charge on one sphereis twice that of the other. When these two spheares displaced 10 cm further apart the forceis 45 10 N , then the charges on both the spheres are ........

(A) 19 191.6 10 C, 3.2 10 C (B) 19 193.4 10 C,11.56 10 C

(C) 19 1933.33 10 C, 66.66 10 C (D) 19 192.1 10 C, 4.41 10 C

11. Three charges q1, + q2 and q3 are placedas shown in figure. The x component ofthe force on q1 is proportional to .........

(A) 322 2qq sin

b a(B) 322 2

qq cosb a

(C) 322 2qq + sin

b a(D) 322 2

qq + cosb a

12. Two equal negative charges q are fixed at points (o, a) and (o, a). A positive charge Q isreleased from rest at the point (2a, o) on the X - axis. The charge Q will ..........(A) move to the origin and remain at rest there(B) execute simple harmonic motion about the origin(C) move to infinity(D) execute oscillations but not simple harmonic motion

13. Four charges, each equal to Q, are placed at the corners of a square and a charge +q isplaced at its centre. If the system is in equilibrium, the value of q is .........

(A) Q 1 2 24 (B) Q 1 2 24

(C) Q 1 2 22 (D) Q 1 2 22

14. For the system shown in figure, if the

resultant force on q is zero, then

Q = ...............

(A) 2 2Q (B) 2 2Q

(C) 2 3Q (D) 3 2Q

1q1 +q2

X

Y

ba

q3

Q qFA

FAa

q(0, a) Q

a

13

15. Two point positive charges q each are placed at (a, o) and (a, o). A third positive charge qo isplaced at (o, y). For which value of y the force at qo is maximum .........

(A) a (B) 2a (C) a2 (D)

a3

16. Two identical charged spheres suspended from a common point by two massless strings oflength l are initially a distance d (d

14

22. Point charges 4c and 2c are placed at the vertices P and Q of a right angle triangle PQR

respectively. Q is the right angle, 2PR = 2 10 m and 2QR = 10 m . The magnitude anddirection of the resultant electric field at c is .........

(A) 9 1 04.2810 NC , 45 (B) 8 1 02.3810 NC , 40.9

(C) 4 1 01.7310 NC , 34.7 (D) 10 1 04.9 10 NC , 34.7

23. An inclined plane making an angle of 30o with the horizontal is placed in an uniformelectric field E = 100 Vm1. A particle of mass 1 kg and charge 0.01 c is allowed to slidedown from rest from a height of 1m. If the coefficient of friction is 0.2 the time taken bythe particle to reach the bottom is .......... sec.(A) 2.337 (B) 4.337 (C) 5 (D) 1.337

24. A small sphere whose mass is 0.1 gm carries a charge of 103 10 C and is tieup to one endof a silk fibre 5 cm long. The other end of the fibre is attached to a large vertical conductingplate which has a surface charge of 6 225 10 Cm , on each side. When system is freelyhanging the angle fibre makes with vertical is ...............(A) 41.80 (B) 450 (C) 40.80 (D) 45.80

25. A Semicircular rod is charged uniformly with a total charge Q coulomb. The electric fieldintensity at the centre of curvature is .......

(A) 22KQr

(B) 23KQr

(C) 2KQr

(D) 24KQr

26. The electron is projected from a distance d and withinitial velocity 0 parallel to a uniformly charged flatconducting plate as shown in figure. It strikes the plateafter travelling a distance l along the direction. The sur-face charge density of conducting plate is equal to

(A) 0 02d m

e

l (B) 2

00d me

l

(C) 0 0d m

e

l (D) 2

002

2d me

l

27. Two point masses m each carrying charge q and +q are attached to the ends of a masslessrigid non-conducting rod of length l. The arrangement is placed in a uniform electric fieldE such that the rod makes a small angle 50 with the field direction. The minimum timeneeded by the rod to align itself along the field is ........

(A) 2mt = 3qE

l(B)

mt =2 2qE

l(C)

mt =qE

l(D)

mt = 2E

l

v0p

X

Y

----l-----

15

28. Two uniformaly charged spherical conductors A and B having radius 1mm and 2mm areseparated by a distance of 5 cm. If the spheres are connected by a conducting wire then inequilibrium condition, the ratio of the magnitude of the electric fields at the surfaces ofspheres A and B is .........(A) 4 : 1 (B) 1 : 2 (C) 2 : 1 (D) 1 : 4

29. Let 4QP(r) = rR

be the charge density distribution for a solid sphere of radius R and total

charge Q. For a point P inside the sphere at distance r1 from the centre of the sphere themagnitude of electric field is

(A) 20 1

Q4 r (B)

21

40

Qr4 R (C)

21

40

Qr3 R (D) 0

30. Two point charges 1q 2c and 2q 1c are placed atdistance b = 1cm and a = 2 cm from the origin on the yand x axes as shown in figure. The electric field vectorat point P (a, b) will subtend an angle with the X - axisgiven by,(A) tan 4 (B) tan 1

(C) tan 3 (D) tan 231. A simple pendulum consists of a small sphere of mass m suspended by a thread of length

l. The sphere carries a positive charge q. The pendulum is placed in a uniform electricfield of strength E directed Vertically upwards. If the electrostatic force acting on thesphere is less than gravitational force the period of pendulum is

(A)

12

qEm

T = 2g

l

(B) 12

T = 2 lg

(C)

12

T = 2 qEm

lg +

(D) 12mlT = 2

qE

32. Consider a system of three charges q/3, q/3 and 2a/3placed at points A, B and C respectively as shown in thefigure. It the radius of the circle is R and 0CAB = 60then the electric field at centre 0 is ........

(A) 20

q8 R (B)

2

20

q54 R

(C) 20

q6 R (D) 0

O

B

C

A

600

X

Y

q1

b

a q2

P(a, b)

16

33. In Millikans oil drop experiment an oil drop carrying a charge Q is held stationary by a p.d.2400 v between the plates. To keep a drop of half the radius stationary the potential differ-ence had to be made 600 v. What is the charge on the second drop ?

(A) 3Q2 (B)

Q4 (C) Q (D)

Q2

34. Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a.The magnitude of electric field at the point c is .........

(A) 2Kqa (B) 2

3Kqa

(C) 22Kqa

(D) 20q

2 t a

35. An electric dipole is placed along the x-axis at the origin o. A point P is at a distance of 20

cm from this origin such that OP makes an angle 3 with the x-axis. If the electric field at

P makes an angle with the x-axis, the value of would be ...........

(A) 1 3tan3 2

(B)

3 (C)

23

(D) 13tan

2

36. A particle having a charge of 191.6 10 C enters between the plates of a parallel platecapaciter. The initial velocity of the particle is parallel to the plates. A potential differenceof 300v is applied to the capacitor plates. If the length of the capacitor plates is 10cm andthey are separated by 2cm, Calculate the greatest initial velocity for which the particlewill not be able to come out of the plates. The mass of the particle is 2412 10 kg .

(A) 4m10s (B)

2 m10s (C)

1 m10s (D)

3 m10s

37. A charged particle of mass 1 kg and charge 2c is thrown from a horizontal ground at anangle o = 45 with speed 20m/s. In space a horizontal electric field 7E = 2 10 V/m exist.The range on horizontal ground of the projectile thrown is ............... .(A) 100 m (B) 50 m (C) 200 m (D) 0 m

38. If electron in ground state of H-atom is assumed in rest then dipole moment of electronproton system of H-atom is ............... .

Orbit radius of H atom in ground state is 0

0.56 A .

(A) 290.25310 cm (B) 290.84810 cm (C) 290.305 10 cm (D) 281.20510 cm

39. At what angle a point P must be located from dipole axis so that the electric fieldintensity at the point is perpendicular to the dipole axis ?(A) 530 to 540 (B) 500 to 510 (C) 450 to 460 (D) 520 to 530

17

40. A n electric dipole is placed at an angle of 60o with an electric field of intensity 105 NC1.It experiences a torque equal to 8 3Nm . If the dipole length is 2cm then the charge on thedipole is ........... c.

(A) 38 10 (B) 48.54 10 (C) 38 10 (D) 60.85 10

41. An electric dipole coincides on z axis and its mid point is on origin of the cartesianco-ordinate system. The electric field at an axial point at a distance z from origin is E(z)

and electric field at an equatorial point at a distance y from origin is (y)E

(z)

(y)

EE

(y = z > > a) = ...............

(A) 1 (B) 2 (C) 4 (D) 342. An oil drop of 12 excess electrons is held stationary under a constant electric field of

4 12.5510 Vm . If the density of the oil is 1.26 gm/cm3 then the radius of the drop is.......... m.

(A) 79.81 10 (B) 79.29 10 (C) 89.38 10 (D) 89.34 10

43. A Charge q is placed at the centre of the open end of cylindrical vessel. The flux of theelectric field through the surface of the vessel is ...........

(A) 0

q (B) 0

q2 (C) 0

2q (D) Zero

44. The inward and outward electric flux for a closed surface in units of Nm2/C are respec-tively 38 10 and 34 10 . Then the total charge inside the surface is ........... c.

(A) 3

0

4 10

(B) 34 10 (C) 34 10 (D) 3 04 10

45. A sphere of radius R has a uniform distribution of electric charge in its volume. At adistance x from its centre, (for x < R), the electric field is directly proportional to ..........(A) x (B) x1 (C) x2 (D) x2

46. The electric flux for gaussian surface A that enclose the chrged particles in free space is.............(given q1 = 14nc, q2 = 78.85 nc, q3 = 56nc)

(A) 104 Nm2/C (B) 103 Nm2/C (C) 3 26.2 10 Nm /C (D) 4 26.310 Nm /C

18

47. A hollow cylinder has a charge q coulomb within it. If is the electric flux in units of volt-meter associated with the curved surface B, the flux linked with the plane surface A in unitsof volt-meter will be .............

(A) 0

1 q 2

(B) 0

q2

(C) 3

(D) 0

q

48. An infinitly long thin straight wire has uniform linear charge density of 1 c/m3 . Then, the

magnitude of the electric intiensity at a point 18 cm away is .......... NC1.

(A) 110.66 10 (B) 111.32 10 (C) 110.33 10 (D) 113 1049. Two points are at distances a and b (a < b) from a long string of charge per unit length .

The potential difference between the points in proportional to .............

(A) blna

(B)

2

2

blna (C) 02

blna (D) 02

blna

50. A long string with a charge of per unit length passes through an imaginary cube of edgel. The maximum possible flux of the electric field through the cube will be ...........

(A) 0

l3 (B) 0

l (C) 0

l2 (D)

2

0

6 l

51. Two Points P and Q are maintained at the Potentials of 10 v and 4 v, respectively. Thework done in moving 100 electrons from P to Q is ..............

(A) 162.24 10 J (B) 179.60 10 J (C) 162.24 10 J (D) 179.60 10 J

52. The electric Potential V at any Point o (x, y, z all in metres) in space is given by V = 4x2volt. The electric field at the point (1m, 0.2m) in volt/metre is ......(A) 8, along negative x - axis (B) 8, along positives x - axis(C) 16, along negative x - axis (D) 16, along positives x - axis

53. Charges of 910+ 10 C3 are placed at each of the four corners of a square of side 8cm. The

potential at the intersection of the diagonals is ....

(A) 150 2 Volt (B) 900 2 Volt (C) 1500 2 Volt (D) 900 2 2 Volt

C

AB

19

54. Three charges 2q, q, q are located at the vertices of an equilateral triangle. At the centreof the triangle. (A) The Field is Zero but Potential is non - zero(B) The Field is non - Zero but Potential is zero(C) Both field and Potential are Zero(D) Both field and Potential are non- Zero

55. In the electric field of a point charge q, acertain charge is carried from point A to B, C,D and E. Then the work done ....(A) Is least along the Path AB(B) Is least along the Path AD(C) Is Zero along all the Path AB, AC, and(D) Is least along AE

56. Three concentric spherical shells have radii a, b and c (a < b < c) and have surface chargedensities , and respectively. If VVA, VVB and VVC denote the Potentials of the threeshells, then for c = a + b, we have

(A) VC = VB = VA (B) c B AV = V V (C) c B AV V V (D) c A BV V V

57. The electric Potential at a point P (x, y, z) is given by V = x2y xz3 + 4 The electric field

E at that point is ..........

(A) 3 2 2i (2 + ) + j + k3 xy z x xz (B) 2 2 2i 2 + j ( + ) + k (3 ) xy x y xy y

(C) 3 2i + j + k z xyz z (D) 3 2 2i (2 ) + j + k3 xy z xy z x

58. Three particles, each having a charge of 10c are placed at the corners of an equilateraltriangle of side 10 cm. The electrostatic potential energy of the system is

9 2 2

o

1Given = 9 10 N.m /c4

.

(A) 100 J (B) 27 J (C) Zero (D) Infinite59. Four equal charges Q are placed at the four corners of a square of each side is a. Work

done in removing a charge - Q from its centre to infinity is ...

(A) 0 (B) 2

0

2Q a (C)

2

0

2Q4 a (D)

2

0

Q2 a

BC D

E

A

+q

20

60. Two charged spheres of radii R1 and R2 having equal surface charge density. The ratio oftheir potential is ...

(A) 21

RR (B)

2

2

1

RR

(C) 2

1

2

RR

(D) 12

RR

61. Two equal charges q are placed at a distance of 2a and a third charge -2q is placed at themidpoint. The potential energy of the system is ....

(A) 2

0

9q8 a (B)

2

0

q8 a (C)

2

0

7q8 a (D)

2

0

6q8 a

62. Two point charges 100c and 5c are placed at points A and B respectively with AB = 40cm. The work done by external force in displacing the charge 5c from B to C where BC

= 30 cm, angle ABC = 2 and

9 2 2

0

1 9 10 Nm /c4

.

(A) 9 J (B) 9 J25 (C)

81 J20 (D)

9 J4

63. The electric potential V is given as a function of distance x (metre) by V = (5x2 + 10x 9)volt. Value of electric field at x = 1 is .....

(A) v20m (B)

v6m (C)

v11m (D)

v23m

64. A sphere of radius 1cm has potential of 8000 v, then energy density near its surfacewill be ...

(A) 5 3J64 10

m (B) 3J2.83

m (C) 3

3

J810m (D) 3

J32m

65. If a charged spherical conductor of radius 10cm has potential v at a point distant 5 cmfrom its centre, then the potential at a point distant 15cm from the centre will be .....

(A) 1 V3 (B)

3 V2 (C) 3V (D)

2 V3

66. Electric charges of +10c, 5c, 3c and 8c are placed at the corners of a square of side

2m the potential at the centre of the square is ......

(A) 1.8 V (B) 51.8 10 V (C) 61.8 10 V (D) 41.8 10 V

67. Two positive point charges of 12c and 8c are 10 cm apart each other. The work done inbringing them 4cm closer is .....(A) 5.8 J (B) 13eV (C) 5.8eV (D) 13 J

21

68. The displacement of a charge Q in the electric field 1 2 3E = e i + e j + e k is r = ai + b j

.The work done is .....

(A) 2 21 2Q e + e a + b (B) 2 21 2Q e + e a + b

(C) 1 2Q ae + be (D) 2 2

1 2Q ae + be

69. If an electron moves from rest from a point at which potential is 50 volt to another pointat which potential is 70 volt, then its kinetic energy in the final state will be .....

(A) 1 N (B) 183.2 10 J (C) 103.2 10 J (D) 1 dyne

70. Three charges Q, + q and + q are placed at the verticlesof a right-angled triangle as shown. The net electrostaticenergy of the configuration is zero if Q is equal to .....

(A) 2q (B) q

1 + 2

(C) + q (D) 2q

2 + 271. Two electric charges 12c and 6c are placed 20cm apart in air. There will be a point P

on the line joining these charges and outside the region between them, at which the elec-tric potential is zero. The distance of P from 6c charge is ........

(A) 0.20 m (B) 0.10 m (C) 0.25 m (D) 0.15 m72. In the rectangle, shown below, the two corners have

charges 1q = 5c and 2q = +2.0c . The work done inmoving a charge 3c from B to A is

10 2 2

0

1take = 10 Nm /c4

.

(A) 5.5 J (B) 2.8 J (C) 3.5 J (D) 4.5 J73. 4 Points charges each +q is placed on the circumference of a circle of diameter 2d in such

a way that they form a square. The potential at the centre is ......

(A) 0 (B) 4dq (C)

q4d (D)

4qd

74. Three identical charges each of 2c are placed at the vertices of a triangle ABC as shownin the figure. If AB + AC = 12 cm and AB . AC = 32cm2, the potential energy of the chargeat A is .....(A) 1.53 J (B) 5.31 J (C) 1.35 J (D) 3.15 J

+q+q

Q

a

A

q2

q1

B------ 15 cm -------

22

75. A ball of mass 1 gm and charge 108 c moves from a point A, where the potential is 600 voltto the point B where the potential is zero. Velocity of the ball of the point B is 20cm/s. Thevelocity of the ball at the point A will be .....

(A) m16.8s (B)

cm22.8s (C)

cm228s (D)

m168s

76. Three charges Q, +q and +q are placed at the vertices of anequilateral triangle of side l as shown in the figure. It thenet electrostatic energy of the system is zero, then Q is equal(A) q (B) +q

(C) Zero (D) q2

77. Electric potential at any point is V = 5x + 3y + 15z , then the magnitude of the electricfield is ..... N/C.

(A) 3 2 (B) 4 2 (C) 7 (D) 5 278. A small conducting sphere of radius r is lying concentrically inside a bigger hollow con-

ducting sphere of radius R. The bigger and smaller sphere are charged with Q and q (Q >q) and are insulated from each other. The potential difference between the sphers will be......

(A) 0

1 q Q4 r R

(B) 0

1 q q4 r R

(C) 0

1 Q q+4 R r

(D) 0

1 q Q4 R r

79. If 3 charges are placed at the vertices of equilateral triangle of charge q each. What is thenet potential energy, if the side of equilateral triangle is l cm.

(A) 2

0

1 3q4 l (B)

2

0

1 2q4 l (C)

2

0

1 q4 l (D)

2

0

1 4q4 l

80. If identical charges (q) are placed at each corner of a cube of side b, then electric poten-tial energy of charge (+q) which is placed at centre of the cube will be .....

(A) 2

0

4q3 b (B)

2

0

8 2q4 b (C)

2

0

8 2q b (D)

2

0

4 2q4 b

81. A simple pendulum of period T has a metal bob which is negatively charged. If it isallowed to ascillate above a positively charged metal plate, its period will ........(A) Remains equal to T (B) Less than T(C) Infinite (D) Greater than T

+q +q

Q

l l

l

23

82. A charged particale of mass m and charge q is released from rest in a uniform electric fieldE. Neglecting the effect of gravity, the kinetic energy of the charged particale after tsecond is ......

(A) 2

2

Eq m2t

(B) 2 2 2E q t2m

(C) 2 22E t

qm (D) Eqm

t

83. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at

the centre of the shell. The electrostatic potential at a point p a distance R2 from the centre

of the shell is .....

(A) 0

(q + Q) 24 R (B) 0 0

2Q 2q4 R 4 R (C) 0 0

2Q q4 R 4 R

(D) 0

2Q4 R

84. Two point charges q and +q are located at points (o, o, a) and (o, o, a) respectively. Thepotential at a point (o, o, z) where z > a is ......

(A) 2 202qa

4 z a (B) 0

q4 a (C) 20

qa4 z (D) 2 20

2qa4 z a

85. Point charges 1q = 2c and 2q = 1c are kept at points x = 0 and x = 6 respectively..Electrical potential will be zero at points .....(A) x = 2, x = 2 (B) x = 1, x = 5 (C) x = 4, x = 12 (D) x = 2, x = 9

86. Two thin wire rings each having a radius R are placed at a distance d apart with their axescoinciding. The charges on the two rings are +q and q. The potential difference betweenthe centres of the two rings is ....

(A) 0 (B) 2 20

Q 1 12 R R + d

(C) 2 2

0

Q 1 14 R R + d

(D) 2

0

QR4 d

87. Tw o charges q1 and q2 are placed 30cm apart, as shownin the figure. A third charge q3 is moved along the arc ofa circle of radius 40 cm from C to D. The change in the

potential energy of the system is 30

q K4 , where k is .....

(A) 8q2 (B) 8q1 (C) 6q2 (D) 6q1

q3

q2 BDAq1

40 c

m

30 cm

C

24

88. Figure shows a triangular array of three pointcharges. The electric potencial v of thesesource charges at the midpoint P of the base

of the triangle is 9 2 20

1 9 10 Nm /c4

(A) 55 KV (B) 63 KV(C) 49 KV (D) 45 KV.

89. Charges +q and q are placed at point A and Brespectively which are a distance 2L apart, C is themidpoint between A and B. The work done inmoving a charge +Q along the semicircle CRDis .......

(A) 0

qQ2 L (B) 0

qQ6 L (C) 0

qQ6 L (D) 0

qQ4 L

90. N identical drops of mercury are charged simultaneously to 10 volt. when combined toform one large drop, the potential is found to be 40 volt, the value of N is ......(A)4 (B)6 (C) 8 (D) 10

91. Tw o paral lel plate ai r capaci tors have thei r plate areas 100 and 500 cm2 respectively. Ifthey have the same charge and potential and the distance between the plates of the firstcapacitor is 9.5 mm, what is the distance between the plates of the second capacitor ?(A) 0.25 cm (B) 0.50 cm (C) 0.75 cm (D) 1 cm

92. The effective capacitances of two capacitors are 3F and 16F , when they are connectedin series and parallel respectively. The capacitance of each capacitor is

(A) 2F,14F (B) 4F,12F (C) 6F, 8F (D) 10F, 6F

93. An electrical technician requires a capacitance of 2F in a circuit across a potential dif-ference of 1KV. A large number of 1F capacitors are available to him, each of which canwithstand a potential difference of not than 400 V. suggest a possible arrangement thatrequires a minimum number of capacitors.(A) 2 rows with 2 capacitors (B) 4 rows with 2 capacitors(C) 3 rows with 4 capacitors (D) 6 rows with 3 capacitors

94. Two spherical conductors of radii r1 and r2 are at potentials V1 and V2 respectively, thenwhat will be the common potential when the conductors are brought in contant ?

(A) 1 1 2 21 2

r v + r vr + r

(B) 1 1 2 21 2

r v + r vr r

(C) 1 1 2 21 2

r v r vr + r

(D) None of these

q = 3 10 C3 -6

l l

| 0.2 m | | 0.2 m | q = -2 10 C2 -6q = 1 10 C1

-6

0.3m

A C B D

R

25

95. A 5F capacitor is charged by a 220 V supply. It is then disconnected from the supply and is

connected to another uncharged 2.5F capacitor. How much electrostatic energy of thefirst capacitor is lost in the form of heat and electromagnetic radiation ?

(A) 0.02 J (B) 0.121 J (C) 0.04 J (D) 0.081 J

96. Find the equivalent capacitance of thesystem across the terminals A and B. Allthe capacitors have equal capacitances.

(A) 2C (B) 4C(C) 3C (D) 5C

97. Capacitance of a parallel plate capacitor becomes 43 times its original value if a dielectric

slab of thickness t = d/2 is inserted between the plates (d is the separation between theplates). The dielectric constant of the slab is(A) 8 (B) 4 (C) 6 (D) 2

98. The plates of a parallel capacitor are charged up to 100 V. If 2 mm thick plate is insertedbetween the plates, then to maintain the same potential difference, the distance betweenthe capacitor plates is increased by 1.6mm the dielectric constant of the plate is(A) 5 (B) 4 (C) 1.25 (D) 2.5

99. A parallel plate air capacitor has a capacitance 18F . If the distance between the plates is

tripled and a dielectric medium is introduced, the capacitance becomes 72F . The dielec-tric constant of the medium is(A) 4 (B) 12 (C) 9 (D) 2

100. Taking earth to be a metallic spheres, its capacity will approximately be

(A) 66.4 10 F (B) 700 F (C) 711 F (D) 700 pF

101. A parallel plate capacitor has the space between its plates filled by two slabs of thickness

d2 each and dialectric constant K1 and K2. If d is the plate separation of the capacitor, then

capacity of the capacitor is ...............

(A) 0 1 21 2

2d K + KA K K

(B) 0 1 21 2

2A K Kd K + K

(C) 0 1 21 2

2A K + Kd K K

(D) 0 1 22A K + K

d

A

B

C

C C

C CC

26

102. For the circuit shown in figure the charge on4F capacitor is

(A) 20c (B) 40c(C) 30c (D) 54c

103. The capacitors of capacitance 4F, 6F and 12F are connected first in series and then inparallel. What is the ratio of equivalent capacitance in the two cases ?(A) 2 : 3 (B) 11 : 1 (C) 1 : 11 (D) 1 : 3

104. Large number of capactors of rating 10F/200V V are available. The minimum number ofcapacitors required to design a 10F/700V capacitor is

(A) 16 (B) 8 (C) 4 (D)7105. A variable condenser is permanently connected to a 100 V battery. If capacitor is changed

from 2F to 10F . then energy changes is equal to

(A) 22 10 J (B) 22.5 10 J (C) 26.510 J (D) 24 10 J

106. Two positive point charges of 12c and 8c are placed 10 cm apart in air. The work doneto bring them 4 cm closer is(A) Zero (B) 4.8 J (C) 3.5 J (D) 5.8 J

107. 1000 similar electrified rain drops merge together into one drop so that their total chargeremains unchanged. How is the electric energy affected ?(A) 100 times (B) 200 times (C) 400 times (D) 102 times

108. There are 10 condensers each of capacity 5F . The ratio between maximum and mini-mum capacities obtained from these condensers will be(A) 40 : 1 (B) 25 : 5 (C) 60 : 3 (D) 100 : 1

109. A parallel plate capacitor is made by stocking n equally spaced plates connected alter-nately. If the capacitance between any two plates is x, then the total capacitance is,

(A) nx (B) nx2 (C) nx (D) (n 1)x

110. For the circuit shown figure, which ofthe following statements is true ?

(A) With S1closed V1 = 15V, V2 = 20V

(B) With S3 closedV1 = V2 = 20V

(C) With S1 and S3 closed V1 = V2 = 0

(D) With S1and S3closed V1 = 30V, V2 = 20V

1 F

5 F

4 F

3 F

10V

+

S1 S3 S2v1=30v v2=20v

C1=2pf C2=3pf

27

111. Two identical metal plates are given positive charges Q1 and Q2 (< Q1) respectively. If theyare now brought close to gether to form a parallel plate capacitor with capacitance C, thepotential difference between them is

(A) 1 2(Q Q )2c (B) 1 2(Q Q )

c (C) 1 2(Q Q )

2c(D) 1 2(Q Q )

c

112. In the circuit arrangement shown in figure, the valueof C1 = C2 = C3 = 30 pF and C4 = 120 pF. If thecombination of capacitors is charged with 140VDC supply, the potencial differences across the fourcapacitors will be respectively

(A) 80, 40, 40 and 20V (B) 20, 40, 40 and 80V

(C) 35, 35, 35 and 35V (D) 80, 20, 20 and 20V

113. In the arrangement of capacitors shownin figure, each capacitor is of 9F , then

the equivalent capacitance between thepoints A and B is

(A) 18F (B) 9F

(C) 15F (D) 4.5F

114. The electric potencial V at any point x, y, z (all in metre) in space is given by V = 4x2 volt.The electric field at the point (1m, 0, 2m) in Vm1 is

(A) + 8i (B) 8i (C) 16i (D) +16i

115. Two air capacitors A = 1 F , B = 4 F are connected in series with 35 V source. When a

medium of dielectric constant K = 3 is introduced between the plates of A, change on thecapacitor changes by

(A) 16 c (B) 32 c (C) 28 c (D) 60 c

116. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. Theseparation between its plates is d. The space between the plates is now filled with twodielectrics. One of the dielectric constant K1 = 3 and thickness d/3 while the other one hasdielectric constant K2 = 6 and thickness 2d/3. Capacitance of the capacitor is now

(A) 1.8 pF (B) 20.25 pF (C) 40.5 pF (D) 45 pF

C1

140V

+

C4

C3

C2

C1

C2 C3

C4

A

B

28

117. A thin spherical shell of radius R has change Q spread uniformly over its surface. Which ofthe following graphs, figure most closely represents the electric field E (r) produced by theshell in the range 0 r < , where r is the distance from the centre of the shell.

(A) (B)

(C) (D)

118. A parallel plate condenser with dielectric of constant K between the plates has a capacity Cand is charged to potential V volt. The dielectric slab is slowly removed from between theplates and reinserted. The network done by the system in this process is

(A) Zero (B) 21 (K 1)cv2 (C) (K 1)cv

2 (D) 2(K 1)cv

K

119. Charges are placed on the vertices of a square as shown. Let E be the electric field and V

the potential at the centre. If the charges on A and B are interchanged with those on D andC respectively then

(A) EChange V remains unchanged

(B) E remains unchanged , V changes

(C) Both E

and V change

(D) E

and V remain unchanged

120. The potencial at a point x (measured in m ) due to some charges situated on the x-axis is

given by 220V( ) = Volt 4

xx . The electric field at = 5mx is given by

(A) 53 Vm1 and in positive x - direction

(B) 109 VVm1 and in positive x - direction

(C) 109 VVm1 and in positive x - direction

(D) 53 VVm1 and in positive x - direction

E

r R

E

r R

E

r R

E

r R

A B

C D

q q

-q -q

29

121. A battery is used to charge a parallel plate capacitor till the potential difference between theplates becomes equal to the electromotive force of the battery. The ratio of the energystored in the capacitor and work done by the battery will be

(A) 12 (B)

21 (C) 1 (D)

14

122. Two spherical conductors A and B of radii 1mm and 2mm are separated by a distance of5mm and are uniformly charged. If the spheres are connected by a conducting wire thenin equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces ofsphere of A and B is(A) 1 : 2 (B) 2 : 1 (C) 4 : 1 (D) 1 : 4

123. The following arrangement consists of fiveidentical metal plates marked 1, 2, 3, 4 and 5parallel to each other. Area of each plate is Aand separation between the successive platesis d. The capacitance between P and Q is

(A) 0A5

d

(B) 0A7

3 d

(C) 0A5

3 d

(D) 0A4

3 d

124. A parrallel plate capacitor of capacitance 5F and plate separation 6 cm is connected to a1 V battery and charged. A dielectric of dielectric constant 4 and thickness 4 cm is intro-duced between the plates of the capacitor. The additional charge that flows into the ca-pacitor from the battery is(A) 2c (B) 5c (C) 3c (D) 10c

125. For circuit the equivalent capacitance betweenpoints P and Q is(A) 6 C (B) 4 C

(C) 3 C2 (D)

6 C11

126. Four identical capacitors are connected in series with a 10 V battery as shown in thefigure. Potentials at A and B are(A) 10 V, 0 V (B) 5 V, 5V (C) 7.5 V, 2.5 V (D) 7.5 V, 2.5 V

127. 64 identical drops of mercury are charged simultaneously to the same potential of 10 volt.Assuming the drops to be spherical, if all the charged drops are made to combine to formone large drop, then its potential will be(A) 100 V (B) 320 V (C) 640 V (D) 160 V

128. Two metal plate form a parallel plate capacitor. The distance between the plates is d. Ametal sheet of thickness d/2 and of the same area is introduced between the plates. Whatis the ratio of the capacitance in the two cases ?(A) 4 : 1 (B) 3 : 1 (C) 2 : 1 (D) 5 : 1

12345

p

q

P Q

30

129. The circular plates A and B of a parrallel plate air capacitor have a diameter of 0.1 m and are32 10 m apart. The plates C and D of a similar capacitor have a diameter of 0.12 m and

are 33 10 m apart. Plate A is earthed. Plates B and D are connected together. Plate C isconnected to the positive pole of a 120 V battery whose negative is earthed, The energystored in the system is

(A) 0.1224J (B) 0.2224J (C) 0.4224J (D) 0.3224J

130. Two parallel conducting plates of area A = 2.5m2 eachare placed 6 mm apart and are both earthed. A thirdplate, identical with the first two, is placed at a dis-tance of 2 mm from one of the earthed plates and isgiven a charged of 1 C. The potencial of the centralplate is

(A) 76 10 V (B) 7310 V (C) 72 10 V (D) 74 10 V

131. What is the energy stored in the capacitor between terminals Aand B of the network shown in the figure ? (Capacitance of eachcapacitor C = 1 F )

(A)Zero (B) 50 J(C) 12.5 J (D) 25 J

132. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure.Capacitor 2 contains a dielectric slab of constant K. Q1 and Q2 are the charges stored in 1and 2. Now, the dielectric slab is removed and the corresponding charges are Q1 and Q2.Then

(A) 1

1

1

Q K + 1=Q K

(B) 1

11

1

Q K=Q 2

(C) 1

2

2

Q K +1=Q 2K

(D) 1

2

2

Q K +1=Q K

133. A parallel plate capacitor has plate of area A and separation d. It is charged to a potentialdifference Vo. The charging battery is disconnected and the plates are pulled apart to threetimes the initial separation. The work required to separate the plates is

(A) 2

0 0A Vd

(B) 2

0 0A V2d (C)

20 0A V

3d (D)

20 0A V

4d

134. Two identical capacitors have the same capacitance C. one of them is charged to a potentialV1 and the other to V2. The negative ends of the capacitors are connected together. Whenthe positive ends are also connected, the decrease in energy of the combined system is

(A) 2 21 21 c v v4 (B) 2 2

1 21 c v + v4 (C)

21 2

1 c v v4 (D)

21 2

1 c v + v4

10v+

C

C

C

C

C

C

1 2

k

E+

1

2

3

2mm

4mm

31

135. A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric ofdielectric constant 5, the percentage increase in the capacitance will be(A) 200 % (B) 33.3 % (C) 400 % (D) 66.6 %

136. A network of six identical capacitors, each of value C is made as shown in figure. Equiva-lent capacitance between points A and B is

(A) C4 (B)

3C4

(C) 4C3 (D) 3 C

137. The capacities of three capacitors are in the ratio 1 : 2 : 3. Their equivalent capacity when

connected in parallel is 60 F11 more then that when they are connected in series. The

individual capacitors are of capacities in F

(A) 4, 6, 7 (B) 1, 2, 3 (C) 1, 3, 6 (D) 2, 3, 4138. In the given arrangement of capacitors equivalent

capacitance between points M and N is

(A) 5 c4 (B)

4 c5

(C) 4 c3 (D)

3 c4

139. An electric circuit requires a total capacitance of 2F across a potencial of 1000 V. Largenumber of 1F capacitances are available each of which would breakdown if the poten-tial is more then 350 V. How many capacitances are required to make the circuit ?(A) 24 (B) 12 (C) 20 (D) 18

140. Read the assertion and reason carefully to mark the correct option out of the options givenbelow :(a) If both assertion and reason are true and the reason is the correct explanation of the

assertion.(b) If both assertion and reason are true but reason is not the correct explanation of the

assertion.(c) If assertion is true but reason is false.(d) If the assertion and reason both are false.(e) If assertion is false but reason is true.

A

B

C

C

C

C

C

C

CC

C

CC

CM N

32

1. Assertion : The coulomb force is the dominating force in the universe.Reason : The coulomb force is weaker than the gravitational force.

2. Assertion : If three capacitors of capacitance C1 < C2 < C3 are connected in parallel thentheir equivalent capacitance Cp > C3

Reason :p 1 2 3

1 1 1 1C C C C

3. Assertion : A metalic shield in form of a hollow shell may be built to block an electricfield.

Reason : In a hollow shherical shield, the electric field inside it is zero at every point.4. Assertion : Electrons move away from a low potential to high potential region.

Reason : Because electrons have negative charge5. Assertion : If the distance between parallel plates of a capacitor is halved and dielectric

constant is made three times, then the capacitance becomes 6 times.Reason : Capacity of the capacitor does not depend upon the nature of the material.

6. Assertion : A parallel plate capacitor is connected across battery through a key. A di-electric slab of constant K is introduced between the plates. The energy whichis stored becomes K times.

Reason : The surface density of charge on the plate remains constant or unchanged.7. Assertion : Electric lines of force cross each other.

Reason : Electric field at a point superimpose to give one resultant electric field.8. Assertion : If a proton and an electron are placed in the same uniform electric field.

They experience different acceleration.Reason : Electric force on a test charge is independent of its mass.

9. Assertion : Dielectric breakdown occrus under the influence of an intense light beam.Reason : Electromagnetic radiations exert pressure.

10. Assertion : When charges are shared between any two bodies, no charge is really lost,but some loss of energy does occur.

Reason : Some energy disappeares in the form of heat, sparking etc.

33

1(A) 17(C) 33(D) 49(D) 65(D) 81(B) 97(D) 113(C) 129(A)

2(B) 18(A) 34(C) 50(A) 66(B) 82(B) 98(A) 114(B) 130(A)

3(D) 19(D) 35(A) 51(A) 67(D) 83(C) 99(B) 115(C) 131(C)

4(C) 20(B) 36(A) 52(A) 68(C) 84(D) 100(B) 116(C) 132(C)

5(B) 21(A) 37(C) 53(C) 69(B) 85(C) 101(B) 117(B) 133(A)

6(C) 22(B) 38(B) 54(B) 70(D) 86(B) 102(B) 118(A) 134(C)

7(D) 23(D) 39(D) 55(C) 71(A) 87(A) 103(C) 119(A) 135(D)

8(A) 24(C) 40(C) 56(D) 72(B) 88(D) 104(A) 120(B) 136(C)

9(B) 25(A) 41(B) 57(A) 73(D) 89(B) 105(D) 121(A) 137(B)

10(C) 26(D) 42(A) 58(B) 74(C) 90(C) 106(D) 122(B) 138(A)

11(C) 27(B) 43(D) 59(B) 75(B) 91(A) 107(A) 123(C) 139(D)

12(D) 28(C) 44(D) 60(D) 76(D) 92(C) 108(D) 124(B)

13(B) 29(B) 45(A) 61(C) 77(C) 93(D) 109(D) 125(D)

14(A) 30(D) 46(B) 62(D) 78(B) 94(A) 110(D) 126(C)

15(C) 31(A) 47(A) 63(A) 79(A) 95(C) 111(D) 127(D)

16(B) 32(C) 48(C) 64(B) 80(A) 96(A) 112(A) 128(C)

KEY NOTES

1(D) 2(C) 3(A) 4(A) 5(B)

6(C) 7(E) 8(B) 9(B) 10(B) 140 :

35

(9) Distance OA = 23

a sin 60c h

= 23

32

. .a

= a 3

The force on the Charge at A due to those at B and C have magnitude F = 2

2

Qka

The Resultant of theses force isF F1 2 30 cos

F1 = 2

2

322

kQa

F KQq2

2

23

The force on the charge Q at A due to Charge q at o is, F2 = 2

3KQqa

Now for equilibrium of the Charges, F1 2 F Now Calculate q.(10) Let q and 2q be the Charges and r the distance between them.

Then 2 10 232

2 kq

r and 5 10

20 1

42

2 kq

r( . )

So, 205

= rr 0 1 2

2

.b g

2 = r

r 0 1

2.

r m 0 1. .

Now, Substitating the Value of r So obtained

2 10 3 = 9 109 2

2

2(0.1)

q

q21410

9

q 10

3

7

Now find out q and 2q.

(11) Force on -q1 due to q2 is F12 = kq q

b1 22 along axis

Force on -q1 due to q3 is Fkq q

a131 32 at negative direction of yaxis.

x component of force on -q, is Fx = F F12 13 sin

= Fqqb

qa1

22

32

LNM

OQPsin

i.e = sin32x 2 2qqF

b a

C

Oq

F2

Q

QB

AF

F1F

a

36

(12) Force exerted by charges -q at A and B onCharge Q are F1 amd F2 which are equal and

have a magnitude 2

KQqFr

The resultant of these equal forces equallyinclined with the X-axis is along the -X di-rection to wards the origin.so, ' cos2 2 2 2F F F 2F = 2 12F ( cos )

since F rF 12

1, is also Proportional to 12r ,

Hence charge Q will move towards the origin and because of its inertia it willovershoot the origin o. Thus charge Q will oscillate about o but its motion is notsimple harmonic.

(13) aOA OC r2

F F KQa1 2

2

2 FKQ

a32

22 4 2

2KQqFa

The resultant of F F1 2& is F FKQa

2 312

2

F and F3 act along AP So, F F F1 3 find.Now for equilibrium F F1 4 .From this find out q.

(14) Net attraction force on q due to Q = repulsion force due to q2 1F FA from find out q.

(15) 0 0

1 22 2 2 2

kq q kq qF Fa y a y

F F1 2By symmetry, the x components of force willcancel each other while along y axis will add up The resultant force on +q is

F F 2 1 cos .0

2 2 2 2

2kqq ya y a y

Now, Force on charge q0 will be maximum, when dFdy = 0

32

32

0 2 2 52 22

y (2y)1 2( y )( y )

kq qaa

1 3

52

02 2

32

2

2 2a y

ya yc h c h

Now find out y.

37

(16) Tcos = mg and Tsin = F

tan Fmg

=

2

22

x q

x q x2 3

q x23

2

12dq 3 dxx

dt 2 dt

12V x

Constantdqdt

(17) F RAB

14

94

2

2 (along

BA )

FRAC

1

49

4

2

2 (along

CA )

F F FAB AC

F F F F1 2 2 22 60cosNow find out F1 .

(18) Force on q is Fkq

a xkq

a x

2

2

2

2( ) ( )

ma = F kq a x a x

LNM

OQP

22 2

1 1( ) ( )

2

3q xama

Now compare with a = 2x and find out frequenly.(19) Suppose the balls having charges Q1 and Q2 respectively..

Initially,....... F = 2

1 2kQ Qr

It is given that F F1 4 5 .

K Q Qr

1 22

2

b g = 4.5 1 22Q QrQ Q1 2

2b g = 4.5 Q Q1 2 Now solve it, and find Q Q1 2 .

38

(20) Consider a small element of the rod of length dx, at a distance x from the pointcharge q.The force between q and charge element will be,

dF =kqdQ

x2 But dQ = QL

dx ,

dF kqQL

dxx2

L + L

r r

2r r

kqQ 1F dF dxL x

Now solve it.

(21)k q

xkqx

.( . )

12

220 08

then find x

(22) pE NC( )p 1

2

kqPQ

QE NC( )Q 1

2

kqQR

in PQR, QRPR

cos 12

= 60

0 cos 60 and2 2p Q p QE E 2E E

Q sin tan cos p QE

find out E and .(23) From the fig, Net force F acting

along the inclined plance ...(i)F = mgsin - qEcos - fma = mg sin - q E cosSo, ma = mg sin qE cos

- (mg cos + q E sin)from this, find out a.

Now, 2o1d v t at2

use this equation and calculate t.

(24) From the fig sino

ET qE

cos T mg cos q T

mg

Now calculate .

39

(25) Let be the charge Per unit length so, charge on Portion PQ ...

= Intensity at o is dE = k rd

r

k ddEr

Total intensity E = 0

dE

and

total cahrge on the rod, Q = r

Now find out E.

(26) Here E = and / ot l v

Along y axis vo = 0, a = FM

eE M /

So, 2o1d v t at2

Now Put the values(27) qE l sin

qEl The moment of inertia of the rod is

I m l m l ml FHGIKJ

FHG

IKJ 2 2 2

2 2 2

Now, = I =I

Calculate and compale with 2 then qEml

So, 2T =

and rod will become Paralled to E in a time Tt =4

Now calculate.

(28) After Connection V V1 2 , 1 2 1 21 2 2 1

KQ KQ Q r=r r Q r

The ratio of electric fields

12 2

1 1 1 22

22 1 222

KQE r Q r= = KQE r Q

r

Now Calculate

40

(29) Consider a Spherical Shell of thickness dx and radius x.The area of this Spherical shell = 4 2x dx

QxR

x dx QR

x dx

42

434 4LNM

OQP

The Charge enclosed in a Sphere of

radius r1 is 1rr 4

3 414 4 4

0 0

4Q 4Q Q= d = = rR R 4 R

xx x

= 1

44 1

4

12

.

QR

r

r

L

N

MMM

O

Q

PPPNow find out E.

(30) 11 2KqE =a

and 22 2KqEb

Now, 2

2 22

1 1

E qtan =E q b

a Now, Put the values.

(31) Net acceleration g ggEm

1

So, '

lTg

Now Put the Value of 'g .

(32) Net electric field due to both charges q3

will get cancelled.

So. electric field of O is

2

q

ER

= 2

2q

6 R(33) In balance condition

3V 4QE mg Q r gd 3

Q rV

3

Now find out Q2

(34) Use equation, E E E EB A 22 2 60cos

(35)

3

,tan tan 12 3

tan 1 3 2

So,

3

32

1tan

41

(36) 21d at2

2

1 qE x2 m v

2

2 x0

qEV2md

Now find out vo.

(37) Time of flight is tvgF

oy2

Now range 2Fox F x1R V t a t2

Where xqEam

Now, Calculate range.

(38) P e ro Calculate P..

(39) As tantan ,

2 Shown in fig 90 tan( )

tan902

cot tan 2

12tan

tan

tan2 2

tan ( )1 2 52 53to(40) PE sin = q(2q)E sin

( ) sinq

2a E

Now find out q.

(41) Theory related quesition.(42) As the drop is stationary, weight of drop = froce due to electric field.

43

3 r g = neE So, 3 neEr4 g

now find out r..

(43) Theory related question.

(44) = 3 3

0 00

Q enclosed Q enclosed f ( 8 10 4 10 )

Now find Q.

(45) Applysing gauss law

E x.4 2 3q v 4 x3

= E x

(46) Applying gauss law 0

q

(47) total = A B Cq

Assume b = and A = C=1

So, 2

= 12 0

q

42

(48) . qE da

q.0

E 2 rl

qE2 rl

0

Er

Now find out E.

(49) Edvdr

0

dvr

2 r

dvdr

vb b

va a

1dv dr2 r

Now calculate.(50) maximum length of string = 3l

maximan enclosed charge = 3 l l

(51) (A) W = 100e (-4-10) = -1400ev= -1400(-1.6 10-19) J = 2.24 10-16 J

(52) (A) The electric Potential V ( , , )x y z x 4 2 Volt

Now dv dv dvE i j kdx dy dz

Now dvdx =

8x , dvdy

0 and dvdz

0

Hence E

= 8xi , So at Point (1m,0,2m)

E

= 8i Volt/metre or 8 along negative x-axis

(53) (c) Potential at the centre o, q1V 4 4 2

Where Q = 103 109 C and a = 8cm = 8 10 2 m

So = 4 9 10103

109 9

8 102

2 = 1500 2 Volt

(54) Obviously, from charge configuration, at thecentre electric field is non - zero. Potential

at the centre due to 2q charge 2qqVr

and

Potential due to q Charge qV q r

(r = distance of centre Point)

Total Potential 2q q qV V V V = 0

43

(55) ABCDE is an equipotential surface, on equipotential surface no work is done inshifing a chrge from one place to another.

(56) V a b cA

( )

V ab

b cB FHG

IKJ

2

VC = a

cb

c C2 2

e jon Putting C = a +b VA = VC VB

(57) Edv

dxxy zx

2 3

Ey dvdy

x 2

Ez dvdz

xz 3 2

E 3 2 2x y zE i E j C k xy z i x j 3xz k

(58) (B) For Pair of Charge

U = 14

10 10 10 1010

100

6 6

L

NMM

OQPP +

10 10 10 1010

100

6 6 LNMM

OQPP

+ 10 10 10 10

10100

6 6 LNMM

OQPP

= 3 9 10 100 10 10010

9 2 = 27J

(59) (B) Potential at Centre o of the square Vo = a2Q4

4

Work done in shifting (-Q) Charge from Centre to infinity

00W Q V V QV

2 2Q Q

4 a a

(60) (D) Let Q1, and Q2 are the Charges on Sphere of radii R1 and R2 respectively

Surface Charge density ch eArea

arg

According to given Problem, 1 2

= QR

QR

1

2

2

24 4

QQ

1

2 =

RR

12

22 .....(1)

44

In Case of a charged sphere, vs = 1

4 QR

V1 = 1

4

QR

1

1 , V2 =

14

QR

2

2

VV

QR

RQ

1

2

1

1

2

2

= QQ

RzR

1

2 1

= RR

RR

RR

1

2

2

2

1

1

2

FHG

IKJ .....(using (i) )

(61) Usystem = 1

4

( )( ) ( )( ) ( )( )

q 2q 1 2q q 1 q qq 4 a 4 2a

= o

27q8 a

(62) Work done indisplacing charge of 5lic from B to C is W V Vc b 5 109 ( ) where

V vB

9 10 100 10

0 494

109 6

6

.

V vC

9 10 100 10

0 595

109 6

6

.

So W J FHGIKJ

5 10 95

10 94

10 94

6 6 6

(63) 2dv dE 5x 10x 9 10x 10dx dx

( )E xv10 20m

(64) Energy density ue = 121

2 8 86 102 12

2

Evr

FHGIKJ

. = 2 83 3. /J m

(65) Potenti al i nsi de the Sphere w i l l be same as that on i ts Surf ace i .e. v = V surface

= q volt

10

Vout = q

15 volt

vout

v23

Vout V23

(66) Length of each side of square is 2m

so distance of its centre from each cornet is 22

1 m

Potential at the centre

V LNM

OQP

9 10 10 101

5 101

3 101

8 101

96 6 6 6

5V 1.8 10 V

45

(67) W Uf U Q Qr r

LNM

OQP1

91 2

2 1

9 10 1 1

= W

LNM

OQP

9 10 12 10 8 10 14 10

110 10

9 6 62 2

= 12 96 10 13. J J

(68) By using W = . Q E r

. 1 2 3 1 2W Q e i e j e k ai bj Q e a e b (69) K.E. = ( ) . ( )6 180 A Bq V V 1 6 70 50 10 J

(70) Net electrostatic energy 2KQq Kq KQqU 0

a a a 2

Kq QQ qa 2

Now find out Q.(71) Point P will lie near the Charge which is smaller in magnitude i.e. -6lic Hence

Potential at P.

( ) ( )( . )

6 66 1 12Vx 4 0 2 x

x m 0 2.

(72) Calculate as MCQ 67.

(73) Calculate as MCQ 66.

(74) (C) AB+AC = 12 cm .......(i)= AB . AC = 32 cm2

= AB AC AB AC AB AC ( ) .2 4= AB AC 4From equation (i) and (ii)AB = 8 cm; AC = 4cmPotential energy at Point A

A 1 21 1V q q

AB AC

V JA 1 35.

(75) Use the equation 12 m V V12

22d i = QV

46

(76) Potential energy of the system

U kQql

kql

kqQl

2

0

( )KQ Q q Q 0

l

qQ2

(77) ( )

xdvE 5

dx also find Ey an Ez

Enet = 2 2 2

x y zE E E = ( ) ( )5 3 15 72 22

d i(78) Van - d - glaph generater principal

(79) U Q Qr

Q Qr

Q Qr

LNM

OQP

14

1 2

1

2 3

2

1 3

3

Unet = 2

0

134

. q l

(80) Length of the diagonal of a cube having each side b is 3b. So distance of centre

of cube from each vertex is 32

b .

Hence Potential energy of the given system of charge is

U = 8 0

1 ( )( )4 3 2

q qb =

24q3 b

(81) When a negatively charged Pendylum oscillates overa Positively charged Plate

then effective Value of 9 increases so, according to 2Tg

decreases

(82) When charge q is released in uniform electric field E then its acceleration

a = qEm (is constant) so its motion will be uniformly accelerated motion and itss

Velocity after time is given by

tqEV atm

= K = 12 mv2

2 2 2 21 qq q E tt2 m 2m

(83) Electric Potential at P

R2

KQ Kq Q qVR 4 R 4 R

47

(84) Potential at P due to (+q) charge

. ( )1 0

qVz a

Potential at P due to (-q) Charge

= .( )2

1 qV4 z a

Total Potential at P due (AB) electric dipole V V V 1 2Now calculate

(85) (C) Potential will be zero at two Points .....

At internal Point(M) = 1

42 10

61 10

06 6

L

NMM

OQPP

( )l lc h

l 2So distance of M from origin; x 6 2 4 At exteriot Point (N)

( ) '( )

6 61 2 1 l4 6 l l'

So distance of N from origin x 6 6 12(86) Potential at the centre of rings are

. ( )

1O 2 2

k q k qVR R d

, ( )

2

O 2 2

k q kqVR R d

1 2O O 2 2 2 2

1 1 q 1 1V V 2kqR 2 RR d R d

(87) (A) Change in Potential energy (u) = uf - udNow calculate

(88) Theory base Question

(89) Potential at C, VC = 0

Potential difference VD -VC = 23

kqL

( ) D CW Q V V put the values

(90) V N V N 2

32

340 10

N N N2

3 24 64 8 (91) C C1 2

Ad

Ad

1

1

2

2

d AA

d2 21

1 Now find d1.

48

(92) Here s 1 p 1C 3l F and C 16 l F Now in Parallel connection C C Cp 1 2So, C C1 2 16 11

in series connection CC C

C C51 2

1 2

So, =

C CC C

1 2

1 2 .....(2)

or C C1 2 Now, C C1 22

b g = C C C C1 2 2 24 b g , orC C1 2 8 ........(3)Adding the question (1) and (3) we haveC C1 2b g+ C C1 2b g16+8

1 & C 2a F C F (93) Suppose that the techinician makes a combination use of N Capacitors and

connects them in m rows, each row having m Capacitors Then N=mnCapacitance of each capacitor = 1 l F1 required Capacitance of the combinationC = 2l F1Voltage rating of each < apalitor = 400Vrequired Voltage rating of the combination = 103VWhen capacitars are connected in series P.d. a cross their Plates get added. forn capacitorsVoltage ...to 400 nv 400 103n

n 10400

2 53

. or n 3

The total Capucitae 1 1

111

11

31C ' 1C

3

The total Capacitanae of m rous C ' OR '

Cmc mC

(94) Common Potential VCV C V

C Cr v r v

r r

1 1 2 2

1 2

1 1 2 2

1 2

4 44 4

V r v r vr r

1 1 2 2

1 2

(95) U C V J1 1 121

20 121 .

Total charge on the two Capacitors q CV C V C 1 1 2 2 411 10C C V l F l F l F F 1 2 1 1 1

65 2 5 7 5 7 5 10. . .

VC

V 9 4403

U CV J221

20 081 . Now, energy lost = U U1 2 find it.

49

(96) Apply wheatstone bridge law.

(97) CairAd

with dielectlic slab C

Ad t t k

1

( / ) Now C =

43 C

FH

IK

A

d t tk

Ad

43

= K = 4 4( / 2)

4 4( / 2 )

t q

t d d d = 2

(98) As P.d. remains the same, Capacity must remain the same,

x = t11

k x = 1.5 mm t= 2mm Now find out k.

(99) CAdo

18 C k A

d

372 Now, find out K.

(100) C = 4RRk

. Put the Values of R&K.

(101) 1 0 1 01 2

2

k A k AC d d

C k d2 22

2

Now, 1 1 1

3 1 2C C C

(102) Apply lawa of series & Parallel conection of Capacitor

(103)1 1 1 1

5 1 2 3C C C C

C C C Cp 1 2 3 Now fiud out s

p

CC

(104) Number of Capacitors to be connected in series

V voltage rat g requiredvoltage rat g required

intint

.700200

3 5

i e. .4

C r Feq 104

2 5 1.

Number of rows required = Capacityrequired

Capacityof each row 102 5

4.

Total number of Capacitor 4 4 = 16

(105) U C V U C V U U U1 1 2 2 2 2 1 212

12

&

50

(106) Work done = 1 22 12 1

q q 1 1U U4 r r

Now Calculate.

(107) Volume of big drop = 1000 volume of small drop 43

1000 43

3 2 R l

Now find out initial energy

U qC12

10002

then final energy U qC2

2

1

10002

b g then UU

2

1

R = 10r so, C C1 10(108) minimum capacity is Cs (Series Connection) & maximum Capaciy is CP (Parallel

Connection) Now p

s

CC Calculate

(109) Theory base question(110) With S S1 3& Closed , the Capacitors C C1 2& are in series arrangenent. So

111

2

VV

CC

V V V V V21

21

21

1 232

30 20 50 & Now simplify..

(111) EQA

QA

1 2 1 1

2 2 2 2 Now Simplify..

(112) C F23 30 30 60 Now,,1 1 1 1

1 23 4C C C C

C pf120

7 Total charge Q =CV

V QC1 1

, V V V QC

V QC2 3 23 23

44

&

(113) The arrangement can be redrawn asshown in figule Now find out.

(114) V = 4x2 E =

dvdr = 8x Now Put the value of x.

(115)1 1 1

5 1 2C C C and q C V 5

(116) CA

dPF 9 1 01

3

k ACd and

2 02

32

k AC

Now 1 1 1

3 4 2C C C

51

(117) Knowledge base question.(118) Knowledge base question.(119) Knowledge base question.

(120) Use equation EdVdx

(121) W QV CV V CV ( ) 2 and 12

2CV Now find Uw

(122) When Spheres are connected by a conducting wire their Potentials become equal.

1 1 1 1 1

2 2 2 2 2

C r q C V C1 1= = = = =C r 2 q C V C 2

Now, 1

21 1

2222

KqE r

KqEr

Now find out rativ..

(123)

(124) Q = CV = 5c

= CA

d t tk

1 FH

IK

= A d

t t kd

/

1F

HGGIKJJ

Now Put the value.

(125) Knowledge base question.

(126)qc

qc

qc

qc

10 or

CV10

42 5.

Now AV 0 = 7.5 V VA 7 5.Again V VN B ..... O VB 2 5. V VB 25

(127) V = 64

4q

R =

644 4

qr ( )

C A d

(128) CA

d tk

1

1 1

FHIK

Use this equation

52

(129) CA

d11

1

54

and C265

Now C C CC C

1 2

1 2

(130) C = 32

Ad and V

QC

(131) Use wheatstons bridge equation eqC C and Q CVCharge on Capacitor between the terminals

A and B is Q CV2 2 = Enegy stored in capacitor =

2Q22C

(132) Theory base question.

(133) Work done = Final energy - initial energy = QC

QC

2

1

2

2 2

(134) U C V Vi 12 1

22

2d i and 1 2 1 21 2

q + q V +VV = =c + c 2

U C Vf 12

2 2( ) Now find U Ui f

(135) CAd1 10

C A d2 2

C C553

Percentage increase in Capacitance = C C

C5 100 %

(136) Use Series and Parallel Connection law.(137) Theory base question.(138) Theory base question.

(139)1000n = = 2.8 = 3350

S1C = F3

m= F3

m F = 2F3

m = 6total no = mn = 3 6 = 18

53

Unit - 12Curreent Electricity

54

SOME IMPORTANT POINTS1. Current I

dQdt

If current is steady, then IQ net t

2. If a point charge q is moving in circle with constant speed and frequency f, then corrosponding current.

I fq q2

3. Current density at any point of conductor.

dIJda cos

dI J.da I J.da

If the cross-sectional area is perpendicular to the current and if J is constant over the entire cross-section, then

IJA

4. Ohm's law VRI

where R= resistance

1 Ohm volt1Ampere

V= potential difference

I= current flowing through the conductor

1R is called the conductance of material.

Its unit is 1 or mho or seimen(s)

5. Resistivity R A

resistivity

RA

unit Ohm.m ( m)

Dimension formula 1 3 3 2M L T A

6. Conductivity 1

unit mho.m

1

1 3 3 2Dimension M L T A

55

7. Drift velocity d deEV and I neAVm

dI J E E VV

neA ne ne ne ne

where, = Number of electrons per unit volume of the conductorA = Area of cross-sectionV = Potential difference across the conductorE = electric field inside the conductorI = CurrentJ = Current density = Specific resistance

= Conductivity 1

= relxation time between cons. collisan

8. Resistivity 2m

ne

9. Mobility dE

ne

2mUnit

volt.sec

(1) For conductor e en e

(2) For Semiconductor e e h hn e n e

10. Temperature Dependence of Resisitivity

0 0

1 where, = resistivity at a temperature

0 = resistivity at a proper reference temperature 0

temperature co-efficient of resistivity 0 1(. C )

0 0

R R 1

If 1R and 2R are the resistance at 1t C and 2t C respectively then 1 1

2 2

R 1 tR 1 t

and 2 1

1 2 1

R RR t t

56

11. The emf of a Cell and Terminal Voltage: when unit positive charge is driven form negative terminalto the positive terminal due to non-elecrical forces, the energy gained by the charge (or work done bythe non-electrical forces) is called an emf ( ) of a battery..The net potential difference between the two terminals of a battery is called the terminal voltage (V).

The terminal voltage of a battery is, V Ir12. Secondary Cell: The cell which can be restored to original condition by reversing chemical processes

(i.e. by recharging) are called secondary cells. e. g. lead accumulator.13. Charging: If the secondary cell is connected to some other external d.c. source of larger emf, current

may enter the cell through the positive terminal and leave it at the negative terminal. The electrical energyis then converted into chemical energy. This is called charging of the cell.For the charging of a laed storage cell (lead accumulator),

2 2 VVIt It I Rt I rt and Ir R

where I = charging current

14. Junction or branch Point: It is the point in a network at which more then two conductors (minimumthree) meet.

15. Loop: A closed circuit formed by conductors is known as loop.16. Kirchhoff's Rules:

First rule: ` ` The algebraic sum of all the electric currents meeting at the junction is zero.''

I 0 Second Rule: ` ` For any closed loop the algebraic sum of the products of resistances and the respectivecurrents flowing through them is equal to the algebraic sum of the emfs applied along the loop.''

IR 17. Connections of Resitors:

Series Connection:

S 1 2 3 nR R R R ...... R

where, SR Equivalent resistance of n resistors connected in series.

Parallel connection:

p l 2 3 n

1 1 1 1 1......R R R R R

where, pR Equivalent resistance of n resistors connected in parallel.

18. Series Connection of Cells: For the series connection of two cells of emfs 1 and 2 and internal

resistances 1r and 2r ,

eq1 2

1 2 eq

IR r r R r

(for helping condition)

where, I= Current flowing through the external resistance R connected across the series connection.

57

Equivalent emf eq 1 2

Equivalent internal resistance eq 1 2r r r

19. Parallel Connection of cells: When n cells of equal emf E and internal resistance r are connected inseries in helping condition.

1 2

1 2 1 2 2 1

1 2 1 2

1 2

r r r rI R R R r r r r1r r

1 2 2 1

eq1 2

1 2 eq

1 2

r rr r

I r r R rRr r

Equivalent emf 1 2 2 1eq1 2

r rr r

Equivalent internal resistance 1 2

eq1 2

r rrr r

(1) Series grouping: In series grouping of one cell is connected to cathode of other cell and so on, Ifn identical cells are connected in series.

(i) Equivalent emf of the combination eqE nE

(ii) Equivalent internal resistance req = nr

(iii) main current = Current from each cell nEi

R nr

(iv) Potential difference across external resistance V iR

(v) Potential difference across each cell VV'n

(vi) Power dissipated in the external circuit 2nE R

R nr

58

(vii) Condition for maximum power 2

maxE: R nr and P n4r

(viii) This type of combination is used when nr R.(2) Parallel grouping: In parallel grouping all anodes are connected at one point and all cathodes areconnected together at other point. of n identical cells are connected in parallel.

(i) Equivalent emf eqE E

(ii) Equivalent internal resistance eqrRn

(iii) Main current Ei

R r / n

(iv) Potential difference across external resistance = p.d across each cell = V= iR

(v) Current form each cell ii 'n

(vi) Power dissipated in the circuit 2EP R

R r / n

(vii) Condition for max. power is 2

maxr ER and P nn 4r

(viii) This type of combination is used when r >> nR(3) Mixed Grouping: If n identical cells are connected in a row and such m rows are connected inparallel as shown, then

59

(i) Equivalent emf of the combination eqE nE

(ii) Equivalent internal resistance of the combination eqnrrm

(iii) main current flowing through the load nE mnEi nr mR nrRm

(iv) Potential difference across load V = iR

(v) Potential difference across each cell VV 'n

(vi) Current form each cell ii 'n

(vii) Condition for maximum power 2

maxnr ER and P mnm 4r

(viii) Total number of cells = mn20. Wheatsone Bridge: For a balanced wheatstone

bridge, P R P QorQ S R S

For Practical circuit 11 2 2

P Q PorQ

60

21. Potentiometer:

Current I R L r

where, r = internal resistance of battery

L = length of potentiometer wire resistance per unit length of potentiometer wire

L resistance of potentiometer wire

emf of batteryR = resistance connected in series

Potential difference between two points on wire separated by distance

will be, V I( )R L r

Potential gardient on wire will be , where 1V OR

R L r

(i) If the length of a Potentiometer wire required to balance the cell of emf 1 is 1 , then 1 1

(ii) If the length of a potentiometer wire required to balance the cell of emf 2 is 2 , then 2 2

2 2

l 1

22. On Passing electric current in a conductor:Electric energy consumed = Heat enrgy generated (in joule)

22 V tW VQ Vlt l Rt ,

R where

V = Potential difference between two ends of a conductorQ = electric chargeI = electric currentR = ohmic resistancet = time in seconds

61

23. Heat or thermal energy:

Heat (calorie) = 2I RtJ

, where J= Joule's constant = 4.2 J/cal

Heat or thermal energy:H (joule) = 2I Rt Heat (H) per unit time I2

24. Electric power (or electrical energy consumed in unit time):2

2W VP VI I Rt R

2P I (Joule's Law)

25. Star (Y) Delta () arrangment: Here three ressistances Ra, Rb, Rc are replaced by R1 R2 and R3 asshown, then

1RaRcR

Ra Rb Rc

2RaRbR

Ra Rb Rc

3RbRcR

Ra Rb Rc

62

Cur

rent

Ele

ctri

city

63

QuestionFor the answer of the following questions choose the