150099533-DPP-25-to-31-Electrostatics-7-Capacitance-15-06-2013-HOMEWORK.pdf

7/25/2019 150099533-DPP-25-to-31-Electrostatics-7-Capacitance-15-06-2013-HOMEWORK.pdf

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DPP No. #25 TO 31/HOMEWORK/17/05/2013 Target IIT-JEE 2014

Page #1

VACATIONS

HOMEWORKREVISION

Electrostatics & Capacitance

CONTENTS

DPP#25 to 30 Single Answer Type Page 225

DPP#31 Multiple Answer Type Page 2632


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Page #2

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#25: 17/06/2013 Monday Time Allotted 1 Hour Single Answer Correct

1. In the figure shown the plates of a parallel plate capacitor have unequal charges. Its capacitance is C P is a pointoutside the capacitor and close to the plate of charge Q. The distance between the plates is d select incorrectalternative

P

Q2Q

(A) A point charge at point P will experience electric force due to capacitor(B) The potencial difference between the plates will be 3Q/2C

(C) The energy stored in the electric field in the region between the plates isC8

Q9 2

(D) The force on one plate due to the other plate is2

0

2

d2

Q

2. Three capacitors A,B and C each of capacitance 1F are connected as shown. The charge on capacitor C is

CBA

18 V

6V

(A) 4 C (B) 6 C (C) 8 C (D) 2 C

3. Separation between the plates of a parallel plate capacitor is 5 mm. This capacitor, having air as the dielectric mediumbetween the plates, is charged to a potential difference 25 V using a battery. The battery is then disconnected and a

dielectric slab of thickness 3 mm and dielectric constant K = 10 is placed between the plates, as shown.Potential difference between the plates after the dielectric slab has been introduced is -

3mm

5mm

(A) 18.5 V (B) 13.5 V (C) 11.5 V (D) 6.5 V

4. Current versus time and voltage versus time graphs of a circuit element are shown in figure.

4.0

sec

1.0

amp

t(s)

I(A)

4.0Volt

t(s)

V(Volt)

4.0

sec The type of the circuit element is :

(A) capacitance of 2 F (B) resistance of 2(C) capacitance of 1 F (D) a voltage source of e.m.f 1 V


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Page #3

5. A circuit element is placed in a closed box. At time t = 0, a constant current generator supplying a current of I amp isconnected across the box. Potential difference across the box varies according to graph shown in the figure. The elementin the box is :

2

8

3t/s

V (volts)

(A) a resistance of 2 ohm (B) a battery of e.m.f 6 V (C) an inductance of 2 H (D) a capacitance of 0.5 F

6. A,B,C,D,E,F are conducting plates each of area A and any two consecutive plates separated by a distance d. The netenergy stored in the system after the switch S is closed is :

A B C D E F

(A)d2

A3 0 V2 (B)d12

A5 0 V2 (C)d2

A0 V2 (D)d

A0 V2

7. Three identical metal plates of area 'A' are at distance d1& d2from each other. Metal plate A is uncharged, while plate B& C have respective charges +q & q. If metal plates A &C are connected by switch K through a consumer of unknownresistance, what energy does the consumer give out to its surrounding ?Assume d1= d2= d

A

B

C

+q

q

K

(A)A4

dq

0

2

(B)

A

dq

0

2

(C)

A2

dq

0

2

(D)

A

dq2

0

2

8. Initially K1is closed, now if K2is also closed,find the heat dissipated in the resistances of connecting wires

C

CCC

K2

K1V

(A)2

1CV2 (B)

3

2CV2 (C)

3

1CV2 (D)

4

1CV2

9. Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere. The ratio of their

radii is


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Page #4

(A)1n

n2

(B)

1n

n

(C)

1n

n2

+ (D)

1n

1n2

+

+

10. A capacitor is composed of three parallel conducting plates. All three plates are of same area A. The first pair of plates are kepta distance d1apart and the space between them is filled with a medium of a dielectric 1. The corresponding data for the secondpair are d2& 2respectively. What is the surface charge density on the middle plate ?

d1 d2

1 2

V0

(A)

+

2

2

1

10 ddV (B)

+

2

2

1

10 ddV (C)

+

2

2

1

10 ddV2 (D)

+

2

2

1

10 ddV2

11. A thin conducting plate is inserted in half way between the plates of a parallel plates capacitor of capacitance C.

onducting plate

What does the value of capacitance, if both the plate of capacitor is shortened ?

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

12. Following figure represents a parallel plate capacitor with a grid halfway with the voltages shown. An electron starting

from plate P1will :+100V

60V

0V1

G

P2

(A) not be able to reach the plate P2 (B) reach P2with 100eV kinetic energy

(C) reach P2with 40 eV kinetic energy (D) reach P2with 140 eV kinetic energy

13. The distance between the plates of a circular parallel plate condenser of diameter 40 mm, in order to make its capacityequal to that of a metallic sphere of radius 1m, will be (A) 0.1 mm (B) 10 mm (C) 0.01 mm (D) 1 mm

14. Five identical plates each of area A are joined as shown in the figure the distance between the plates is d. The plates areconnected to a potential difference of V volts. The charges on plates 1 and 4 will be

1 2 3 4 5 +

V

(A) d

AV0

, d

AV2 0

(B) d

AV0

, d

AV2 0

(C) d

AV0

, d

AV2 0

(D) d

AV0

, d

AV2 0


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Page #5

15. Four equal capacitors , each with a capacitance (C) lare connected to a battery of E.M.F 10 volts as shown in the adjoiningfigure. The mid point of the capacitor system is connected to earth. Then the potentials of B and D are respectively

C

B D

Earth

(A) + 10 volts, zero volts (B) + 5 volts, 5 volts (C) 5 volts, + 5volts (D) zero volts, 10 volts

ANSWER KEY

1. [D]

000 A2Q3E

A2Q

A2Q2E

=

+

=

VC2

Q3Ed

Cd

Q

2

3E ===

(ii) F = EQ/2

0

2

0 A

Q

1

)Q(

A2

Q2F

=

=

0

2

A

QF

=

(iii) Energy =

2

10E

2Ad

2

0cd2

Q3

2

1

= Ad =C

Q

8

9 2

2. [A]

Equivalent circuit

AB

C

12V

3. [C]

The capacitor is charged by a battery of 25 V. Let themagnitude of surface charge density on each plate be

. Before inserting the dielectric slab, electric fieldstrength between the plates,

E =0

=

d

V

or E =0

=

3105

25

= 5000 N/C

The capacitor is disconnected from the battery but

charge on it will not change so that has the same

value. When a dielectric slab of thickness 3mm is

placed between the plates, the thickness of air between

the plates will be 5 3 = 2 mm. Electric field strength

in air will have the same value (5000 N/C) but inside

the dielectric, it will beK

5000=

10

5000

= 500 N/C

so potential difference = Eairdair+ Emeddmed

= 5000 (2 103) + 500 (3 103)

= 11.5 V

4. [C]

In case of a capacitorq = CV

i =dt

dq= C

dt

dV

dt

dV=

0.4

0.4V/s = 1.0 V/s

Therefore, if C = 1 F then i = 11 = 1A (constant)5. [D]6. [C]

Ceff=d

A0 since effective capacitance between plates

A and E is zero

U =2

1CV2=

d2

A0 V2

7. [A]

+q q

Energy loss =CC

C

2

1 2

+V2=

2

C

2

1

2

2

C

q

=C4

q2

=A4dq

0

2

8. [C]


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Page #6

When K1is closedC

V

+Q Q

Q = CV

energy Ui=2

1CV2

When K2is also closed

V

12 5

6

43

Equivalent circuit

1

C

524

C 3

CC

6

Ceq= C +3

C2=

3

C5

Energy Uf=2

1

3

C5V2=

6

5CV2

Charge supplied by battery after closing K2

= 3

5

CV CV = 3

2

CVEnergy supplied by battery = Uf Ui+ H

3

2CV2=

6

5CV2

2

1CV2+ H

H =3

1CV2

9.. [B]

R1

C1

R1

R2

C2

C1= 40R1

and C2 = 40

12

21

RR

RR

Given that C2= nC1

or12

12

RR

RR

= nR1

or1R/R

R/R

12

12

= n

or1

2

R

R=

1n

n

10. [A]

Equivalent circuit

2, 2'

V0

2 C2V0

C1V0

1

1 1'2

2'3 3'

Middle plate

11' 33'

Total charge on 2 & 2' plate = Vd

A

d

A

2

02

1

01

+

= 0V

+

2

2

1

1

dd

11. [D]

d/2

1

1

2

3

3

2

1

1

3

3

Cl 22

Cl

= 2 d

2)A( 0 = 4 .d

A0 = 4C

12. [A]13. [A]

14. [C]15. [B]


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Page #7

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#26: 18/06/2013 Tuesday Time Allotted 1 Hour Single Answer Correct

1. What is the capacitance of the capacitor of square plates of area A, Shown in figure

K3

K1

d

d

B

(A)d4

A0

21

21

KK

KK

+ (B)

21

2110

KK3

)KK(K

d

A

+

+ (C)

21

2110

KK

)K3K(K

d4

A

+

+ (D)

)K3K(d4

A

21

0

+

2.

A dielectric slab of area A and thickness d is inserted between the plates of a capacitor of area 2A and distance betweenplates d with a constant speed v as shown in the fig. The capacitor is connected to a battery of emf E. The current in thecircuit varies with time as

v E

(A)

I

t

(B)

I

t (C)

I

t (D)

I

t3. Find the capacitance of a system of three parallel plates each of area A separated by distance d1 and d2. The space

between them is filled with dielectrics of relative dielectric constants 1and 2. The dielectric constant of free space is 0

(A)1221

021

dd

A

+

(B)

2211

021

dd

A

+

(C)21210

21

dd)(

A

+

(D)

)dd(

A

2211021 +

4. For making a parallel plate capacitor , two plates of copper, a sheet of mica (thickness = 0.1 mm, K = 5.4), a sheet of

glass (thickness = 0.2 mm, K = 7) and a slab of paraffin (thickness = 1.0 cm, K = 2) are available. To obtain the largest

capacitance, which sheet should you place between the copper plates ?

(A) Mica (B) Glass (C) Paraffin (D) None of these

5. The capacity of a parallel plate condenser is C0. If a dielectric of relative permittivity rand thickness equal to one fourth

the plate separation is placed between the plates, then its capacity becomes C. Then value of0C

Cwill be-

(A) 14

5

rr+

(B) 13

4

rr+

(C) 12

3

rr+

(D) 1

2

rr

+


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Page #8

6. Two metal plates form a parallel plate condenser. The distance between the plates is d. A metal plate of thickness d/2 and

of the same area is inserted completely between the plates. The ratio of capacitances in the two cases (later to initial) is -

(A) 2 : 1 (B) 1 : 2 (C) 1 : 1 (D) 1 : 4

7. A parallel plate capacitor is completely filled by an insulating material 3 mm thick and of relative permittivity 4. The

distance between the plates is increased to allow the insertion of a second sheet 5 mm thick and of relative permittivity

r. If the capacitance of the capacitor so formed is one-half of the original capacitance, then the value of r -

(A)3

20 (B)

3

16 (C)

3

10 (D) None of these

8. A positive charge q is given to each plate of a parallel plate air capacitor having area of each plate A and separationbetween them, d -(A) Since both the plates are identically charged, therefore, capacitance becomes equal to zero

(B) Energy stored in the space between the capacitor plates is equal toA

Aq

0

2

(C) No charge appears on inner surface of the plates

(D) Potential difference between the plates is equal toA

qd2

0

9. Two identical capacitors are joined in parallel, charged to a potential V, separated and then connected in series, i.e., the

positive plate of one is connected to the negative of the other-

(A) The charge on the plates connected together are destroyed

(B) The charge on free plates are enhanced

(C) The energy stored in the system increases

(D) The P.D. between the free plates is 2V

10.

Two spherical conductors A1and A2of radii r1and r2are placed concentrically in air. The two are connected by a copper wire

as shown in fig. Then the equivalent capacitance of the system is-

A2

A1

r1

r2

(A)12

210

rr

r.rk4

(B) 40(r1+ r2) (C) 40r2 (D) 40r1

11. Three concentric thin spherical shells are of radii a , b and c [a < b < c]. The first and third are connected by a fine wire

through a small hole in the second, and the second is connected to earth through a small hole in the third, the capacity of

the capacitor so formed is

(A) 40

+

bcc

ab

ab 2 (B) 40

++

+ bac

ab

ab 2

(C) 40

+

2c

bc

ab

ab

(D) 40

+

+

+2c

bc

ab

ab


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Page #9

12. A parallel plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is

charged by a battery and then battery is disconnected. Now the slab is started to pull out slowly at t = 0. If at time t,

capacitance of the capacitor is C, then which of the following graphs is correct ?

C

O t

(A)

C

O t

(B)

C

O t

(C)

C

O t

(D)

13. If the current, charging a capacitor, is kept constant then the potential difference V across the capacitor varies with time t

as

V

O

(A)

V

O

(B)

V

O

(C)

V

O

(D)

14.

A capacitor of capacitance 160 F is charged to a potential difference of 200V and then connected across a discharge

tube which conducts until the potential deference across it has failed to 100 V. The energy dissipated in the tube is -

(A) 6.4 J (B) 4.8 J (C) 3.2 J (D) 2.4 J

15. Two capacitors each having capacitance C and breakdown voltage V are joined in series. The capacitance and the

breakdown voltage of the combination will be

(A) 2C and 2V (B) C/2 and V/2 (C) 2C and V/2 (D) C/2 and 2V

ANSWER KEY1. [C]

2. [B]

3. [A]

4. [A]

5. [A]

6. [A]

7. [A]

8. [C]

9. [D]

10. [C]

11. [A]

12. [D]

13. [C]

14. [D]

15. [D]


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Page #10

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#27: 19/06/2013 Wednesday Time Allotted 1 Hour Single Answer Correct

1. Two metal plates having charges Q, Q face each other at some separation and are dipped into an oil tank. If the oil ispumped out, the electric field between the plates will -

(A) increase (B) decrease (C) remain the same (D) become zero2. A parallel plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery

and the smaller plate to its negative terminal. Let Q+and Qbe the charges appearing on the positive and negative plates

respectively -(A) Q+> Q (B) Q+= Q (C) Q+< Q

(D) The information is not sufficient to decide the relation between Q+and Q

3. A parallel plate capacitor without any dielectric has capacitance C0. A dielectric slab is made up to two dielectric slabs of

dielectric constants K and 2K and is of same dimensions as that of capacitor plates and both the parts are of equaldimensions arranged serially as shown. If this dielectric slab is introduced (dielectric K enters first) in between the platesat constant speed, then variation of capacitance with time will be best represented by-

A AA

V

LL L

K 2K

(A)

C

C0

t

(B)

C

C0

t

(C)

C

C0

t

(D)

C

C0

t 4. The metal plate on the left in the fig. carries a charge +q. The metal plate on the right has a charge of 2q. What charge

will flow through S when it is closed if the central plate is initially neutral ?

+

+

+

+

+

+

q 2q

(A) zero (B) q (C) + q (D) + 2q

5. You have a parallel plate capacitor, a spherical capacitor and cylindrical capacitor. Each capacitor is charged by and thenremoved from the same battery. Consider the following situations(i) separation between the plates of parallel plate capacitor is reduced(ii) radius of the outer spherical shell of the spherical capacitor is increased

(iii) radius of the outer cylinder of cylindrical capacitor is increased

Which of the following is correct ?

(A) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same and potential difference

across it also remains the same

(B) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same but potential difference, insituations (i) and (iii), decreases, and in situation (ii), increases


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Page #11

(C) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same but potential difference, insituations (i), decreases, and in situations (ii) and (iii), increases

(D) Charge on the capacitor in each situation changes. It increases in all these situations but potential difference remains

the same

6. A closed body, whose surface F is made of metal foil, has an electrical capacitance C with respect to an uniformly distantpoint. The foil is now dented in such a way that the new surface F*is entirely inside or an the original surface as shownin the figure. Then

F*

F

(A) Capacitance of F*> capacitance of F (B) Capacitance of F*< capacitance of F(C) Capacitance of F*= capacitance of F (D) Nothing can be concluded from given

7. Two capacitor C1& C2, charged with q1& q2are connected in series with an uncharged capacitor C, as shown in figure.As the switch S is closed-

+ q1

+

C

C2C1

S

q2

(A) C gets charged in any condition (B) C gets charged only when q1C2> q2C1(C) C gets charged only when q1C2< q2C1 (D) C gets charged when q1C2q2 C1

8. An electron with a kinetic energy of 100 eV enters the space between the plates of plane capacitor made of two densemetal grids at an angle of 30 with the plates of capacitor and leaves this space at an angle of 45 with the plates. What isthe potential difference of the capacitor

30

45

(A) 100 V (B) 50 V (C) 150 V (D) 200 V9. In the given fig. the work done by battery after the switch S is closed

10 F4 V

10 F

S

(A) 100 J (B) 100 J (C) 80 J (D) 80 J

10. In the condenser show in the circuit is charged to 5V and left in the circuit, in 12 s the charge on the condenser willbecome


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Page #12

6

2F

(A)e

10C (B)

10

eC (C)

2e

10 (D)

10

e2C

11.

Two capacitors are joined in series as shown in figure. The area of each plate is A. The equivalent of the combination is

a b

d

d

(A)21

0

dd

A

(B)

ba

A0

(C)

b

1

a

1A0 (D)

210

d

1

d

1A

12. The two spherical shells are at large separation one of them has radius 10 cm and has 1.25 C charge. The other is of 20cm radius and has 0.75 C charge. If they are connected by a conducting wire of negligible capacity, the charge on theshells are-

(A) 1 C, 1C (B)3

2C,

3

4C (C)

3

4C,

3

2C (D) 0.25 C, 0.25 C

13. The net capacitance between A and B isC C

C C

CCC

A

B

(A) 6 C (B) 5

C2 (C) 3

C2 (D) None of these

14. In the following circuit composed of identical capacitor, across which terminals would you connect a battery in order forall capacitors to charge up

B

A

CD

(A) AB (B) AC (C) BD (D) None of these

15. Five identical plates of equal area A are placed parallel to and at equal distance d from each other as shown in figure. Theeffective capacity of the system between the terminals A and B is-

B

A

(A)5

3

d

Ao (B)

4

5

d

Ao (C)3

5

d

Ao (D)

5

4

d

Ao


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Page #13

ANSWER KEY1. [A]2. [B]3. [B]

4. [C]

5. [C]

Each capacitor is charged and then removed from the

battery. Changing the plate separation in a parallel

plate capacitor or the radius of any shell or cylinder in

the spherical or the cylindrical capacitors will not

change the charge on any capacitor. Each capacitor, in

the disconnected state, is an isolated system.

In situation (i), since C =d

A0 , capacity will increase

as d is reduced. Therefore, V =C

Qdecreases, Q being

the same.

In situation (ii), C = 40ab

ab

= 40

b/a1

a

a and b are the radii of the inner and the outer

spherical shells, respectively.

As b is increased, capacity will reduce and

V =C

Qincreases, Q being the same.

In situation (iii), C = 20)a/b(n

L

l

L is the length of cylinders; a and b are the radii of

inner and outer cylinders, respectively.As b is increased, capacity will decrease and

V =C

Qincreases, Q being the same.

6. [B]

Ui=i

2

C2

Q

Uf=f

2

C2

Q

As surface was deformed in such a way that charge onoriginal surface are coming closer or moving

perpendicular to electric force acting on them totalenergy of foil get increase.Uf> Ui

fC2

Q2>

i

2

C2

Q

Ci> Cf7. [D]

Charge in the circuit flows only when potentialdifference across C1is either greater or less than thatacross C2

ie.1

1

C

q

2

2

C

qq1C2q2C1

8. [B]

v1

v2

Horizontal velocity is constantv1 cos 30 = v2 cos 45

v12

3= v2

2

1

4

v3 21 =2

v22

21mv

2

1

2

3 = 22mv

2

1

KEf =2

3 KEi

= 1.5 100 = 150 eV

P.d. = e

KE= e

eV)100150( = 50 V

9. [C]

Before the switch S is closed

Qi= CeqV

= 5 4 = 20 C

When the switch S is closed

Qf = CV

= 10 4 = 40 CW(cell) = QE = (Qf Qi) E

= 20 4 = 80 J

10. [A]

During discharge

qc=

RC

t

eCE

= 2 5

12

12

e

=e

10

11. [B]

When two capacitors are in series

x1 x2

eqC

1=

A

x

A

x

0

2

0

1

+

=

A

xx

0

21

+

Ceq=21

0

xxA

+


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Page #14

=platesbetweensseparationofSum

A0

Now in given arrangementCapacitors are in series& sum of separations = a b

Ceq=ba

A0

12. [A]

Total charge = 1.25 C + 0.75 C = 2 Cq1' : q2' = R1: R2= 1 : 2

==

==

C3

42

3

2'q

C3

22

3

1'q

2

1

13. [B]

Use Junction method

A

BX

X

Y

X

X

X YB

eqC

1=

C

1+

C2

1+

C

1

Ceq=5

C2

14. [D]

A

CB

D

Battery is connected between A and B

A

DB

C

i

x x

x

x

x

xi

Potential across C and D is same. Capacitance between

C and D is uncharged.

Battery is connected across AC

A

DB

i

iC

Now B and D will remain uncharged.

Battery is connected across BD

A

DB

C

i 2x

xx

x

xi

x

i

A and C are at same potentialCapacitance between A and C is uncharged.

15. [C]

5

4

3

2

1

B

A

A B

1 2

23 5 4

3 4

The capacity of each capacitor is, C0=

d

A0

From fig. it is clear that Ceq =3

5C0 =

3

5

d

Ao


15/32


Page #15

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#28: 20/06/2013 Thursday Time Allotted 1 Hour Single Answer Correct

1. A capacitor consists of two parallel metal plate of area A separated by a distance d. A dielectric slab of area A, thicknessb and dielectric constant k is placed inside the capacitor. If CKis the capacitance of capacitor with dielectric, how muchK and b be restricted so that CK= 2C, where C is capacitance without dielectric

(A) K =db2

b4

&

3

d< b d (B) K =

db2

b2

&

2

d< b d

(C) K =db2

b2

&

2

db 2d (D) K =

db2

b2

&

4

db d

2. If area of each plate is A and the successive separations are d, 2d and 3d, then equivalent capacitances across Aand B is -

d

2d

3d

A

B

(A)d6

A0 (B)d4

A0 (C)d4

A3 0 (D)d3

A0

3. n conducting plates are placed face to face as shown. Distance between any two plates is d. Area of the plates is A,

)1n(2

A....

4

A,

2

A

2

A

4

A

A

d d The equivalent capacitance of system is -

(A)d2

An

0 (B)d)12(

An

0

(C)

d)22(

An

0

(D)

d)12(

A1n0

4. Six plates of equal area A and plate separation as shown are arranged equivalent capacitance between A and B is -

d

2d

3d

2d

d

4B

56

3

2

1

A

(A)d

A0 (B)d

A2 0 (C)d

A3 0 (D)d4

A0

5. In an adjoining figure are shown three capacitors C1, C2 and C3 joined to a battery. The correct condition will be(Symbols have their usual meanings)

V1C1 Q1

V2C2 Q2

V3 C3Q3

+

V


16/32


Page #16

(A) Q1= Q2= Q3and V1= V2= V3= V (B) Q1= Q2+ Q3and V = V1+ V2+ V3

(C) Q1= Q2+ Q3and V = V1+ V2 (D) Q2= Q3and V2= V3

6. Four condensers are joined as shown in the adjoining figure. The capacity of each is 8 F. The equivalent capacitybetween the points A and B will be

B

A

(A) 32 F (B) 2 F (C) 8 F (D) 16 F

7. Assuming capacitance of each capacitors equals C, find the effective capacitance between A and B.

B

A

(A) C (B)2

C (C)

8

C5 (D)

8

C3

8. What physical quantities may X and Y represent?

X

Y

(A) pressure v/s temperature of a given gas (constant volume)

(B) kinetic energy v/s velocity of a particle

(C) capacitance v/s charge at a constant potential

(D) potential v/s capacitance at a constant charge

9. An infinite number of identical capacitors each of capacitance 1F are connected as in adjoining figure. Then theequivalent capacitance between A and B is-

8 capacitor

16 capacitor

A B

(A) 1F (B) 2F (C) 1/2F (D)

10. A1 is a spherical conductor of radius (r) placed concentrically inside a thin spherical hollow conductor A2of radius (R).A1is earthed and A2is given a charge +Q then the charge on A1is -(A) Q (B) Qr/R (C) rQ/R (D) Q (Rr)/R

11. A capacitor of capacitance 0.1 F is charged to certain potential and allow to discharge through a resistance of 10M. How long will it take for the potential to fall to one half of its original value-(A) 0.1s (B) 0.2346 s (C) 1.386 s (D) 0.693 s

12. Calculate the charge on the plates of the capacitor C in the given circuit -


17/32


Page #17

E r

R1

R2

A B

(A) C rR

ER

2

2

+ (B) C rR

ER

1

1

+ (C) C 21

21

RR

R.RE

+ (D) C rR

RE

2

1

+

13. In the adjoining circuit diagram E = 5 volt, r = 1 ohm , R2= 4 ohm, R1= R3= 1 ohm and C = 3F. Then the numericalvalue of the charge on each plate of the capacitor is

R2

R1

R3

E,r

C C

C C

(A) 24C (B) 12C (C) 6C (D) 3C

14. Two condensers of capacities 2C and C are joined in parallel and charged upto potential V. The battery is removed andthe condenser of capacity C is filled completely with a medium of dielectric constant K . The p.d. across the capacitorswill now be -

(A)2K

V3

+ (B)

K

V3 (C)

2K

V

+ (D)

K

V

15. 0.2F capacitor is charged to 600V by a battery. On removing the battery. It is connected with another parallel platecondenser (1.0F). The potential decreases to-(A) 100 volts (B) 120 volts (C) 300 volts (D) 600 volts

ANSWER KEY1. [B]

CK=

Kbbd

A0

+

We set b = 0

CK=d

A0 = C if CK= 2C

Then,

K

bbd

A0

+

=

d

A2 0 K =db2

b2

K > 0 and b d

=db2

b2

and 2b d > 0

2

d< b d b >

2

d

2. [B]3. [C]

4. [A]

5. [C]

6. [A]

7. [A]

8. [D]9. [B]

10. [C]

11. [D]

12. [A]

13. [C]

14. [A]

15. [A]


18/32


Page #18

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#29: 21/06/2013 Friday Time Allotted 1 Hour Single Answer Correct

1. Two capacitors of capacities C1and C2 are charged to voltages V1and V2 respectively. There will be no exchange ofenergy in connecting them in parallel . If-

(A) C1= C2 (B) C1V1= C2V2 (C) V1= V2 (D)1

1VC =

2

2VC

2. Two spheres of radii R1and R2 have equal charge are joint together with a copper wire. If the potential on each sphere

after they are separated to each other is V, then initial charge on any sphere was (k =04

1

)

(A)k

V(R1+ R2) (B)

k2

V(R1+ R2) (C)

k

V(R1+ R2) (D)

21

21

RR

)RR(

k

V

+

3. Calculate the reading of voltmeter between X and Y then (V x Vy ) is equal to -

1F

1F

X2F

3F 6F

20V

A BV

Y

(A) 10 V (B) 13.33V (C) 3.33 V (D) 10.33 V

4. In the figure shown, the capacity of the condenser C is 2F. The current in 2resistor is -

6V

2F 4

2.8

2

3

+

(A) 9 A (B) 0.9 A (C)9

1A (D)

9.0

1A

5. In the circuit shown here C1= 6F, C2= 3F and battery B = 20V. The Switch S1is first closed. It is then opened andafterwards S2is closed. What is the charge finally on C2

C2 3F

C1 6F

B=20V

S2

S1

(A) 120C (B) 80C (C) 40C (D) 20C

6. Three identical capacitors are given a charge Q each and they are then allowed to discharge through resistance R1, R2andR3. Their charges, as a function of time shown in the graph below. The smallest of the three resistance is -


19/32


Page #19

R3R2

R1

Q

t (A) R3 (B) R2 (C) R1 (D) Cannot be predicted

7. The work done in placing a charge of 8 1018coulomb on a condenser of capacity 100 micro-farad is

(A) 3.1 1026J (B) 4 1010J (C) 32 1032J (D) 16 1032J

8. A fully charged capacitor has a capacitance 'C'. It is discharged through a small coil of resistance wire embedded in a

thermally insulated block of specific heat capacity 's' and mass 'm'. If the temperature of the block is raised by 'T', the

potential difference 'V' across the capacitance is

(A)s

TCm2 (B)

s

TCm (C)

C

Tms (D)

C

Tms2

9. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d.

The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1= 3 and

thickness3

dwhile the other one has dielectric constant k2= 6 and thickness 3

d2. Capacitance of the capacitor is now

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

10. A series combination of 0.1 Mresistor and a 10 F capacitor is connected across a 1.5V source of negligible resistance. The

time required for the capacitor to get charged up to 0.75 V approximately (in seconds) is

(A) (B) loge2 (C) log102 (D) zero

11. A capacitor of capacity C is charged in RC circuit. The variation of log I Vs time is shown in the figure by dotted line

when net resistance of circuit is X. When resistance changes to 2X the variation is now shown by

Log I

S

R

Q

P

t (A) P (B) Q (C) R (D) S

12. A capacitor of capacitance 4F is charged through a resistor 2.5 M connected in series to a battery of emf 12 volthaving negligible internal resistance . Then time in which potential drop across capacitor is 3 times the potential dropacross the resistor -(A) 13.86 sec (B) 6.93 sec (C) 27.72 sec (D) 3. 46 sec

13. Time constant for the given circuits are


20/32


Page #20

1

2

2F 4F

12V

2F 4F

1 2

12V

2F

4F1 2

12 V

(A) 18 s,9

8s, 4s (B) 18 s, 4 s,

9

8s (C) 4s,

9

8s, 18 s (D)

9

8s, 18s, 4s

14. A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount ofcharge that flows from Y to X is

3F

3

6F

6

X

Y

9V

S

(A) 0 (B) 54 C (C) 27 C (D) 81 C

15. Calculate the equivalent capacitance between a & b -

d/2

A/3

d/2

K=2

K1=3 K3=9K2=6

aA/3 A/3

b

(A) 3d

A0 (B) 2d

A0 (C)d

A0 (D)d2

A0


21/32


Page #21

ANSWER KEY

1. [C]

2. [B]

3. [C]

4. [B]

5. [C]

6. [C]

7. [C]

8. [D]

9. [B]

10. [B]

11. [B]

12. [A]

13.

[A]

14. [C]

15. [A]

C1=

2

d3

A0

K1= 2C0

C2=

2

d3

A0

K2= 4C0

C3=

2

d3

A0

K3 = 6C0

C4=

2d

A0 K4= 4C0

d/2

A/3

d/2 C1

aA/3 A/3

b

C2 C3

C4

C1,C2 & C3 are in parallel and C4 is in series with

C1,C2& C3

C1|| C2|| C3 2C0+ 4 C0+ 6C0= 12C0

Ceq =0

00

C16

C4C12 = 3C0 =

d

A3 0


22/32


Page #22

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#30: 22/06/2013 Saturday Time Allotted 1 Hour Single Answer Correct

1. The ratio of potential difference between 1 F and 5 F capacitors

3 F

2 F

1 F

2 F

5 F

10 V

(A) 1 : 2 (B) 3 : 1 (C) 1 : 5 (D) 10 : 1

2. Two parallel plate capacitors of capacitance C and 3C are connected in parallel and charged to a potential difference Vwith the help of a battery. The battery is disconnected and the space between these two capacitors are filled with

dielectric of constant K and K/2 respectively. The voltage across the combination will be -(A)

K3

V4 (B)

K3

V6 (C)

K5

V8 (D)

K5

V3

3. In the given system a capacitor of plate area A is charged upto charge q. The mass of each plate is m2. The lower plate isrigidly fixed. Find the value of m1so that the system is in equilibrium

+ + + +

qm1

(A) m2+Ag

q

0

2

(B) m2 (C)

gA2

q

0

2

+ m2 (D) None of these

4. Find the amount of charge that will flow through the switch when it is closed

3F 6F+200V

S

6F 3Fa

b

V = 0

(A) 300 C (B) 400 C (C) 500 C (D) 100 C

5. A slab of copper of thickness 'b' is inserted in between the plates of parallel plate capacitor. The separation of the plates is

d. If b =2

d, then the ratio of the capacities of capacitor after and before inserting the slab is -

(A) 2 : 1 (B) 2 : 1 (C) 1 : 1 (D) 2 : 2

6. An electron is first placed at A and then at B between the two plates of a parallel plate capacitor charged to a potentialdifference of V volt as shown. The electrostatic potential energy of electron at A is -

+

+

++

+

+

+

A

B

(A) more than at B (B) less than at B (C) equal to that at B (D) nothing can be said

7.

Find the charge on each capacitor during steady state -


23/32


Page #23

3F

3F

110 V

3F

3F

6

R = 4

3

3

3

6

6

(A) 3C (B) 6C (C) 9C (D) 12C

8. In the given circuit switch K is open. The charge on the capacitor is 'C' in steady state is q1. Now key is closed and steadystate charge on C is q2. The ratio of charges q1/q2is -

R K

2RCE

(A) 3/2 (B) 3/2 (C) 1 (D) 1/2

9. If each plate has area A and separation between successive plates is d from equivalent capacitance between A and B is -

B

A

(A)d

A 0 (B)d2

A 0 (C)d

A4 0 (D)d

A3 0

10. In the circuit shown in figure switch S is at position 1 for long time. The total heat generated in resistors 2r0and r0when

switch is shifted from position 1 to position 2.C0r0

21

S

E0

2r0

(A)2

EC 200 (B)3

EC 200 (C)0

200

r3

EC (D) None

11. In the given circuit diagram. Find the heat generated on closing the switch S (Initially the capacitor of capacitance C is

uncharged) -

S

C 2C

3CV

(A) 2CV2

3 (B) CV2 (C)

2

1CV2 (D) 2 CV2

12. If each capacitor has capacitance is C then equivalent capacitance between A & B is -


24/32


Page #24

B

A

(A)3

C4 (B)

3

C8 (C) 12 C (D)

12

C5

ANSWSER KEY1. [C]

4 F1 F

5 F

10 V

V4F

2 F & 2 F are reduced to 1 capacitor of 1 F and 3

F & 1 F is reduced to 4 F.

F4

V

=5

110= 2

(potential difference across 4 F capacitor is

calculated by voltage division Rule)

F5

V

= 10 V

(potential difference across 5 F is same as Battery)

F

F

5

1

V

V

=

10

2=

5

1

2. [C]

V

3C

C q1= CV

q2= 3CV

K

+

++

K/2

+

+

+

Common potential =21

21

CC

qq

+

+=

C32

KKC

CV3CV

+

+

=

2

KC5

CV4=

K5

V8

3. [C]

+ + + +

Fem1g

m2g

T T

T = Fe+ m2g .(1) (for upper plate)

T = m1g .(2) (for m1)

m1g =0

2

A2

q

+ m2g

m1=gA2

q

0

2

+ m2

4. [A]

When switch is open

3F 6F+200V

6F 3F

V = 0

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

q = Ceq V (for both branches)

q = 2 200 = 400

Hence charge on each capacitor is 400 C.

When switch's closed

3F 6F+200V

6F 3F

V = 0

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ Equivalent 6F

43F 6F

3F

200 V100V 100V

q6= 600 C q3= 300 C

Hence final arrangement

Initial was


25/32


Page #25

3F, 300C 6F, 600C

600C 300C

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

6F 3Fa

b

400F 400C

400C 400C

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

Final charge on both plates Initial charge on bothis 300 plates is zero

Hence charge flow is 300C.

5. [B]

Cpartial medium=

r

0

t)td(

A

+

6. [B]

7. [D]

B

3F

3F

10 V

3F

3F

A

1

4

I=.eqR

V=

5

10= 2A; VA VB = IR = 2 4 = 8 V

P.D across each capacitor is 4 V hence q = 4 3 = 12 C

8. [A]

Initially when switch is open

R

CE q1= CE

Finally when switch is closed

R

2RC

AI

B

I =R3

E; VA VB= I 2R = E/3R 2R = 2E/3

Charge on capacitor = CV ; q2= 3E2C

2

1

q

q=

CE3/2

CE= 3 : 2

9. [A] It is a Wheatstone bridge10. -

11. [C]

SV

C 2C

3C

Before closing switch Ui=2

1

C2C3

C2C3

+

V2

=5

3CV2

After closing switch Uf=2

1CV2+

5

3CV2

Energy supply by battery = CV V = CV2

CV2= Uf Ui+ H

CV2=2

1CV2+ H

H =2

1CV2

12. [B]

B

5 3

1A

104

912

78

2

11

6

8 11 109

B

A

(1 to 7)

2C C

C

C

C

2C

2C

2C

Ceq.= 4 CC2

CC2

+

=

3

C24=

3

C8


26/32


Page #26

Physics For IITJEE by Shiv R. Goel (B.Tech., IITDelhi) DPP#31: 24/06/2013 Monday Time Allotted 1 Hour Multiple Answer Correct

1. Three capacitors each having capacitance C = 2F are connected with a battery of emf 30 V as shown in figure. Whenthe switch S is closed :

C

30 V

C

C

S

(A) the amount of charge flown through the battery is 20 C

(B) the heat generated in the circuit is 0.6 mJ

(C) the energy supplied by the battery is 0.6 mJ

(D) the amount of charge flown through the switch S is 60C

2.

In the circuit shown in figure.1

120V

2 3

2 1 3

C1 C2

C1= C2= 2F. Then charge stored in :(A) capacitor C1is zero (B) capacitor C2is zero(C) both capacitors is zero (D) capacitor C1is 40 C

3. Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a battery. Now -(A) The facing surfaces of the capacitor have equal and opposite charges

(B) The two plates of the capacitor have equal and opposite charges(C) The battery supplies equal and opposite charges to the two plates

(D) The outer surfaces of the plates have equal charges

4. A charge Q is imparted to two identical capacitors in parallel. Separation of the plates in each capacitor is d0. Suddenly,

the first plate of the first capacitor and the second plate of the second capacitor starts moving to the left with speed v,then

(A) Charge on the two capacitor as a function of time are0

0

d2

)vtd(Q ,

0

0

d2

)vtd(Q +

(B) Charge on the two capacitors as a function of time are)vtd(2

Qd

0

0

,

)vtd(2

Qd

0

0

+

(C) Current in the circuit will increase as time passes

(D) Current in the circuit will be constant

5. Two plates of a parallel plate capacitors carry charges q and q and are separated by a distance x from each other. Thecapacitor is connected to a constant voltage source V0. The distance between the plates is changed to x + dx. Then in

steady state :V0

+q q

x

(A) Change in electrostatic energy stored in the capacitor isx

Udx


27/32


Page #27

(B) Change in electrostatic energy stored in the capacitor isdx

Ux

(C) Attraction force between the plates is 1/2 qE(D) Attraction force between the plates is qE

(where E is electric field between the plates)6. A parallel plate condenser is charged by a battery. The battery is removed and a thick glass slab is placed between the

plates. Now-

(A) the capacity of the condenser is increased(B) the electrical energy stored in the condenser is decreased

(C) the potential across the plates is decreased

(D) the electric field between the plates is decreased

7. Identical dielectric slabs are inserted into two identical capacitors A and B. These capacitors and battery are connected asshown in figure. Now the slab of capacitor B is pulled out with battery remaining connected-

BA

a b

(A) during the process charge flows from a to b

(B) final charge on capacitor B will be less than on capacitor A

(C) during the process, work is done by external force F which appears as heat in the circuit

(D) during the process, battery receive energy

8. The two plates x and y of parallel plate capacitor of capacitance C are given a charge of amount Q each. x is now joined to the

positive terminal and y to the negative terminal of a cell of emf e =C

Q. Then

(A) a charge of amount Q will flow from the positive terminal to the negative terminal of the cell through the capacitor

(B) the total charge on the x will be 2Q

(C) the total charge on the plate y will be zero

(D) the cell will supply Ce2amount of energy

9. The plates of a parallel plate capacitor are not exactly parallel then -(A) surface charge density is therefore higher at the closer end

(B) the surface charged density will not be uniform

(C) each plate will have the same potential at each point

(D) the electric field is smallest where the plates are closest

10. The figure shows three infinite thin non-conducting charged plates perpendicular to the plane of the paper with chargeper unit area +, +2 and 3. As we move from plate 1 to plate 2 magnitude of potential change occured is V12, thatfrom plate 2 to 3 is V23and that from plate 1 to 3 is V13. Then-

+

+++

+

2

+

+

+

3

2m 2m

4m 6m

A B

1 2 3

Plate

(A) Ratio of net electric field at point A to that at point B is 1/3(B) 9V12= 2 V23

(C) 2V13= 7 V12

(D) 3V13= 5V23


28/32


Page #28

11. A uniformly charged ring charge +q has radius R. A uniformly charged solid sphere (over its total volume) has charge Q is

placed on the axis of ring at a distance x = R3 from centre of ring as shown. Radius of sphere is also R, then

RR

q Q

OO +

+++

+

+ + +++

+

+

+

++

+ +++

+

+

+

+

+

+ ++

+++

+

+++

+

+

+

+++

+

+++

+

+

++

++

+

++

+

+

+

+

+

+

++

R3x =

(A) Electric force on ring is2R8

kQq3

(B) Electric force on ring is2R2

kQq

(C) The increase in tension in ring due to sphere is2

R16

kQq

(D) The increase in tension in ring due to sphere is2R8

kQq

12. Four sphere each of different radius named 'a', 'b', 'c', 'd' are given, each are solid insulating uniformly charged and

carrying equal total charge. Variation of electric field with distance r from the centre is given. Then

E

b

a

c

d

r

(A) Radius of sphere a > Radius of sphere b

(B) Radius of sphere a < Radius of sphere b

(C)Volume charged density of c > volume charged density of b

(D)Volume charged density of c < volume charged density of b

13. We have an infinite non-conducting sheet of negligible thickness carrying a uniform surface charge density and next

to it, an infinite parallel slab of thickness D with uniform volume charge density +. All charges are fixed.

+

D

(A) Magnitude of electric field at a distance h above the negatively charged sheet is02

D

(B) Magnitude of electric field inside the slab at a distance h below the negatively charged sheet (h < D) is

02)h2D(

+


29/32


Page #29

(C) Magnitude of electric field at a distance h below the bottom of the slab is04

D

(D) Magnitude of electric field at a distance h below the bottom of the slab is02

D

14. Three charged particles are in equilibrium under their electrostatic forces only

(A) The particles must be collinear (B) All the the charges cannot have the same magnitude

(C) All the charges cannot have the same sign. (D) The equilibrium is unstable

15. Two infinitely large plane sheets are separated by a distance l and carry a uniform charge of surface density

+and . The planes have coaxial holes of radius R (l>> R). Find the potential f and field E at a point on the axis of

the holes at a distance x from the midpoint O between the holes -

+ + + ++

+

+

+++++

++

++

+ +

+

xl

O P

(A)2/122

0 )xR(x2 +

= (B)

2/3220

2

)xR(2

RE

+

=

l (C)

20x2

= (D)

50R2

E

=

16. If at distance r from a positively charged particle, the electric field strength, potential and energy density are E, V and U

respectively, which of the following graphs are correct?

(A)

O E

V (B)

O E

V2

(C)

O U

(D)

O U

V2

17. Two large conducting plates having surface charge densities + & are fixed d distance apart. A small test charge q

of mass m is attached to two identical springs as shown in the adjacent figure. The charge q is now released from rest

with springs in natural length. Then q will [neglect gravity] -

+

m kq

k

(A) perform SHM with angular frequencym

k2 (B) perform SHM with amplitude

0k2

q

(C) not perform SHM but will have a periodic motion (D) remain stationary

18. Consider three infinite line charge kept in XY Plane parallel to X-axis, wire with density +is along X-axis and other

two wires with density passes through (0, a) and (0, a) respectively. Now choose the correct alternative(s)


30/32


Page #30

+ + + + + + + +

Z

(0, a)

(0, a)

Y

XO

(A) E at point (0, 0, a) is zero

(B) work done in displacing +q charge from (0, 0. a) to (0, 0, 2a) is02

log

4

5

(C) work done in displacing +q charge from (0, 0, a) to (0, 0, 3a)02

log

3

5

(D) Electric field at (0, 0, 2a) is E = a20

3

0

k

19. Five point charges, each of charge +q coulomb are placed on five vertices of a regular hexagon of side h as shown infigure. Then

ED

FO

A B+q +q

+q

+q +q

qC

(A) the forces on (q) at O due to charges +q at A and D are balanced

(B) the forces on (q) due to charges at D and E are balanced

(C) the resultant force on q at O is04

1

2

2

h

qalong OE

(D) the resultant force on q at O is04

1

2

2

h

qalong OC


31/32


Page #31

ANSWER KEY1. [A,C,D]

The charges stored in different capacitors before and

after closing the switch S are

+

30 V

40C+ 20C

+

20C

+

30 V

60C

before after

The amount of charge flown through the battery is q =

20 C

Energy supplied by the battery is

U = qV = (20 106) (30) J

U = 0.6 mJ

Energy stored in all the capacitors before closing the

switch S is

Ui=2

1CnetV

2=

610

3

4

2

1(30)2

= 0.6 mJ

and after closing the switch

Uf=

2

1CnetV

2=

2

1(2 106) (30)2

= 0.9 mJ

Heat generated H = U (Uf Ui) = 0.3 mJ and

charge flown through the switch is 60 C.

2. [B,D]

Potential difference across C1= 20 V

Potential difference across C2= 0 V

Charge stored on C1 = 40C

and Charge stored on C2= 0 C

1

120V

2 3

2 1 3

20V 40V 60V

40V 20V 60V

C1 C2

3. [A,C,D]

4. [A,D]

5. [A,C]

6. [A,B,C,D]

7. [A,D]

QKCKC

+Q

+Q Q BA

a b

E

Q =2

KCE

on removal of dielectric from B

Q+xKC

Qx

Q xC

A

a bE

Q+x

x

x x

Applying kirchoff

KC

xQ +

C

xQ = E

Q x = CE1K

K

+

from x is coming = positive

Charge will flow from a to b, (A) is right

answer.

Final charge on B = Final charge on A, B iswrong answer

During the process energy received by battery

= E x. (D) is right answer.

8. [A,B,C,D]

Q

x

x

QQ

+x x Q

Q/C

Q+x Qx

x=C

Q C = Q

Total charge on plate x = Q + x

= Q + Q = 2Q

Total charge on plate y = Q x

= Q Q = 0

Cell will supply = CQ x = CQ

2


32/32


=C

eC 22=Ce

2

9. [A,B,C]

As distance between plate decreases C is higher on

that point.

More charge will accumulate.

a is correct

E =d

V when distance between plate is less, E is

higher.10. [A,B]

11. [A, C]

12. [B,C]

13. [A,B,D]

At a distance h above the sheet

E = Esheet+ Eslab

=

000 2

D

2

D

2

=

+

At a distance h below the top surface of slab

Eslab=02

)h2D(

E = Esheet+ Eslab=02

+

02

)h2D(

=02

)h2D(

+

At a distance h below the bottom surface of the slab =

000 2

D

2

D

2

=

+

14. [A,B,C,D]

15. [A,B]

16. [B,C]

17. [B]

Electric field between plates is uniform hence

electrostatic force due to this field is constant. Angular

frequency does not change by constant force.

Equilibrium position will be at the point where 2kX0

= q 0

X0=

0k2

q

X0is also the amplitude of oscillation.

18. [A,B,D]

19. [A,D]

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