Capacitor

1

CC AA PP AA CC II TT OO RR

Capacitance, Parallel Plate capacitor with and without

dielectric, capacitors in series and parallel, Energy stored in a

capacitor.

POSITION VECTOR : Capacitor is a device for storing electric charge and energy. It consists of a pair of

conductors carrying equal and opposite charges (generally). Magnitude of this charge is

known as the charge on the capacitor. Potential difference (V) between the two conductors is

proportional to the charge on the capacitor (Q).

Q V; Q = CV

Here the proportionality constant C is known as the capacitance of the capacitor.

Capacitance depends on the size and shape of the plates and the material between them. The SI

unit of capacitance is farad (F).

PARALLEL PLATE CAPACITORS :

A parallel plate capacitor consists of two equal flat parallel metal plates facing each

other and separated by a dielectric of electric permittivity .The plates may be square,

rectangular or circular in shape.

For calculating the capacity of a capacitor, we first calculate electric field at a point

between the plates and then using relation

dr

dVE compute the potential difference

between the plates. Finally dividing the magnitude of charge (given to one plate) by the

potential difference between the plates, we get the capacity.

In case of parallel plate capacitor as shown in figure. The field at P

E

2 2

or,

dx

dV [ as

dx

dVE ]

or,

d

0

0

V

dxdV i.e., dV

So, d

A

/d

A

V

qC

0x dx

V 0

VP

d

2

or d

KAC 0

[as

0K ]

SPHERICAL CAPACITOR :

We can derive the capacity of a spherical capacitor in a similar

way V=04

q

b

1

a

1;

C = V

q =

b

1

a

1

4 0

=

ab

ab4 0

If the radius of the outer sphere tends to infinity, b , the

capacitance reduces to

C = 4 a0 which is the capacitance of the isolated sphere.

CYLINDRICAL CAPACITOR :

E = r2 0

a br

V = ba VV = - a

bEdr or V =

02

ln

a

b

C = V

q =

V

=

a

bn

2 0

ILLUSTRATION : 01

A parallel plate capacitor has plates of area 200cm2 and separation between the plates

1.00mm. What potential difference will be developed if a charge of 1.00nC (i.e., 1.00 x 10-9C) is

given to it. Now if separation between the plates is increased to 2.00mm, what will be the new

potential difference?

SOLUTION : The capacitance of the capacitor is d

AC 0

= 8. 85 x 10-12m10 x 1

m10 x 200 x

m

F

3-

2-4

= 0.177 x 10-9F

= 0.177nF.

The potential difference between the plates is

65.5nF177.0

nC1

C

QV volts.

If the separation is increased from 1.00mm to 2.00mm the capacitance is decreases by a

factor of 2. If the charge remains the same, the potential difference will increase by a factor of 2.

q

ba

E

l

Q

a b

3

Thus, the new potential difference will be 5.65volts x 2 = 11.3 volts.

COMBINATION OF CAPACITORS

SERIES COMBINATION :

Capacitors connected as shown in the

figure are said to be connected in series. In

series combination the charges on individual

condensers are equal and the total p.d. across

the combination is to shared by the capacitors.

Q = 332211 VCVCVC and V = 321 VVV

Effective capacitance of the combination C can be found from the relation.

C

1=

1C

1 +

2C

1+

3C

1

PARALLEL COMBINATION :

In this combination p.d. across each of capacitors is same but the charge supplied at

points A and B is shared by capacitors.

V = 1

1

C

Q =

2

2

C

Q =

3

3

C

Q and total

charge

Q = 1Q + 2Q + 3Q

C = 1C + 2C + 3C

ILLUSTRATION : 02

Find the equivalent capacitance

between points A and B of the circuit

shown, each capacitance = C

SOLUTION : Equivalent circuit is

Each branch equivalent capacitance is 2

C.

There are four branches in parallel

Q Q Q Q Q Q

1C 2C 3C

1V 2V 3V

1Q

1Q-

2Q 2Q-

3Q 3Q-

A B

A B

A B

4

eqC = 2

C+

2

C+

2

C+

2

C = 2C

ILLUSTRATION : 03

The figure shown is a system of parallel conductors. Each plate is of equal area A and

equally separated by d. Find the equivalent capacitance of the system between a and b

SOLUTION : By joining the points of same potential, the

arrangement of conductors may be reduced as shown in

figure. If the capacitance between two successive plates is

given by d

AC 0

then, the equivalent capacitance of the

system is given by d

A

2

3

2

C3C 0eq

DIELECTRICS :

When a dielectric is introduced between conductors of a capacitor, its capacitance

increases. A dielectric is characterized by a constant 'K' called dielectric constant.

DIELECTRIC CONSTANT :

When a dielectric is placed in an external electric field, polarization occurs and it

develops an electric field in opposition to the external one. As a result total field inside it

decreases. If E is the total field inside the dielectric when it is placed in an external field 0E ,

then its dielectric constant 'K' is given as K = E

E0 ( k 1)

If a dielectric completely occupies the space between the conductors of a capacitor its

capacitance increases 'K' times. Hence in presence of a dielectric with dielectric constant ' K ',

the capacitance of a parallel plate capacitor = d

AK 0

ENERGY STORED IN A CAPACITOR :

The energy stored in a capacitor is equal to the work done to charge it. Let q be the

instantaneous charge on either plate of the capacitor and the potential difference between the

plate is V=C

q. The work done to transfer an infinitesimal charge dq from the negative plate to

the positive plate is dW = Vdq =

C

qdq

[The charge moves through the wires, not across the gap between the plates]

a

b

2

2

1

4

3

3

5

W = total work done to transfer charge Q = Q

0C

qdq =

C2

Q2 =

2

QV =

2

1C 2V

This work done is stored as electrostatic energy ie., U = 2

1C 2V =

2

1

d

A0 22dE =2

1 0

2E (Ad)

Energy density (u) = energy per unit

Volume =2

1 0

2E

If dielectric is introduced then U = 2

1K 0

2E

This energy is stored in a capacitor in the electric field between its plates.

FORCE ON A DIELECTRIC IN A CAPACITOR :

Let us consider a small displacement dx of the dielectric as shown in figure, keeping

the net force on it always zero.

Welectrostatic + FW = 0

[Where FW denotes the work done in displacement

dx]

FW = - .elecW = U

- F dx = 2

Q2 d

C

1=

2

2

C2

Q dc

F= 2

2

C2

Q

dx

dc =

2

1 2V

dx

dc

[Considering capacitor has battery connected to it, i.e., V = Q/C ]

ILLUSTRATION : 04

Two capacitors of capacitances 20pf and 50pf are connected in series with a 6-volt

battery, find

(A) The potential difference across each capacitor

(B) The energy stored in each capacitor

SOLUTION :

dx

x

F

a

b

1

2

3

4

6

(A) Equivalent capacitance C = 21

21

CC

CC

=

2050

20x50

=

7

100pF

Charge on 1C = charge on 2C = 7

100 x 6 =

7

600pC

Potential difference across pC50C1 = 50x7

600 = 1.71 V

and across pC20C2 = 20x7

600 = 4.28 V

(B) Energy in 1C = 1E = 2

1x 50x 271.1 = 73.5 pJ

Energy in 2C = 2E =2

1 x 20 x 228.4 = 184 pJ

ILLUSTRATION : 05

A 5F capacitor is charged to 12 volt. The positive plate of this capacitor is now

connected to the negative terminal of a 12 V battery and vice versa. Calculate the heat

developed in the connecting wires.

SOLUTION :

When capacitor is connected with battery the charge appears on one plate be Q = CV

and - Q on the other plate. If the capacitor is now disconnected and connected to the same

battery again with opposite polarity then - Q appear on first plate and + Q on second plate.

Total charge flown from battery is 2Q W= charge x potential = 2QV

Q = CV

W = 2C 2V

W = 2x5x 610 x 212

= 1.44 mJ

ILLUSTRATION : 06

A capacitor stores 50C charge when connected across a battery. When the gap between

the plates is filled with a dielectric, a charge of 100C flows through the battery. Find the

dielectric constant of the material inserted.

SOLUTION :

Initial charge = 50C = 1Q

Amount of charge flows = 100C

With dielectric total charge = (50+100) =150C

20pF 50pF

6V

7

Initial capacity C = V

Q =

V

C50

Final capacity 'C = V

Q ' =

V

C150

K = C

C ' =

V/50

V/150 = 3

ILLUSTRATION : 07

In the above circuit, find the potential difference

across AB.

SOLUTION :

Let us mark the capacitors as 1, 2, 3 and 4 for identification. As is clear, 3 and 4 are in

series, and they are in parallel with 2. The 2,3, 4 combination is in series with 1.

,f4CC

C.CC

43

4334

f1248C 4,3,2

,f8.4128

128Ceq

C.VCq eq 481084

The 'q' on 1 is 48C, thus V6c

qV1

.V6

F8

c48V1

VVPQ 4610

By symmetry of 3 and 4, we say, .VVAB 2

ILLUSTRATION : 08

What is BA VV in the arrangement shown? What is the

condition such that 0VV BA

SOLUTION :

Let charge be as shown

(Capacitors in series have the same charge)

Take loop containing 1C , 2C and E

0EC

q

C

q

21

21

21

CC

CCEq

From loop containing 43 C,C and E

Similarly,

q

q'

8

0EC

'q

C

'q

43

43

43

CC

CCE'q

Now, 42

BAC

'q

C

qVV

=

43

3

21

1

CC

C

CC

C.E

4321

2341BA

CC.CC

C.CC.C.EVV

For 0 BA VV

0CCCC 3241 or 4

3

2

1

C

C

C

C

ILLUSTRATION : 09

A 8F capacitor C1 is charged to 0V = 120volt. The charging

battery is then removed and the capacitor is connected in parallel to

an uncharged 4F capacitor C2.

(A) What is the potential difference V across the combination?

(B) What is the stored energy before and after the switch S is thrown

?

SOLUTION :

(A) Let 0q be the charge on 1C initially Then 010 VCq when 1C is connected to 2C in

parallel, the charge 0q is distributed between 1C and 2C . Let 1q and 2q be the charges on 1C

and 2C respectively. Now let V be the potential difference across each condenser.

Now 210 qqq or VCVCVC 2101

V120F4F8

F8V

CC

CV 0

21

1

= 80volt.

(B) Initial energy stored

2

1VC

2

1U 2010 (8 x 10-6) (120)2

= 5 .76 x 10-2joule

Final energy stored

S

1C 2C0V

9

U = 2 21 21 1

C V C V2 2

= 2

1(8 x 10-6) (80)2 +

2

1(4 x 10-6) (80)2

= 3.84 x 10-2joule.

Final energy is less than the initial energy. The loss of energy appears as heat in connecting

wires.

ILLUSTRATION : 10

From the given figure find the value of the capacitance C if the equivalent capacitance

between points A and B is to be 1F. All the capacitances are in F.

SOLUTION :

The capacitors C3 and C4 are in parallel, therefore

their resultant capacity C8 is 4. The capacitors C5 and C6 are

in series, therefore, their resultant capacity C9 is 4. These are

shown in figure (A)

Now the capacitor C2 and C8 are in series. Their

resultant capacity 10C is 3

8. Capacitors 7C and 9C are in

parallel. Their resultant capacity C11is 8. These are shown in

figure. (B)

C1 and C11 are in series. The equivalent capacitance is 8/9.

The parallel combination of 8/3 and 8/9 gives a resultant

capacitance 32/9 as shown in figure. (C)

32

9

C

1

1

1 or

32

23

C

1

F23

32C

ILLUSTRATION : 11

Five identical conducting plates 1, 2, 3, 4 and 5 are fixed

parallel to and equidistant from each other as shown in figure.

Plates 2 and 5 are connected by a conductor while 1 and 3 are

joined by another conductor. The junction of 1 and 3 and the

plate 4 are connected to a source of constant e.m.f. 0V . Find

B

A

2C

8C

1C

7C9C18

4

4 4C

A

10

(i) The effective capacity of the system between the terminals of the source

(ii) The charge on plates 3 and 5

Given d = distance between any two successive plates and

A = area of either face of each plate.

SOLUTION :

(i) The equivalent circuit is shown in figure (B). The system consists of four capacitors

i.e., 3212 ,CC 34C and 54C . The capacity of each capacitor is 00 Cd

AK

The effective capacity

across the source can be calculated as follow:

The capacitors C12 and C32 are in parallel and hence their capacity is C0 + C0 = 2C0. The

capacitor C54 is in series with effective capacitor of capacity 2C0. Hence the resultant capacity

will be 00

00

2C C

C 2 x C

Further 34C is again in parallel. Hence the effective capacity

= d

AK

3

5C

3

5

C2C

2C x CC 00

00

000

(ii) Charge on the plate 5 = charge on the upper half of parallel combination

d

AVK

3

2C

3

2VQ 00005

Charge on plate 3 on the surface facing 4

d

AVKCV 0000

Charge on plate 3 on the surface facing 2

= [Potential difference across (3 - 2)] 0C

= d

AVKC

CC

CV

32

0

00

00

0

0

d

AVK

d

AVKQ

3

0

0

00

3

= 0000 V

d

AK

3

4

3

11

d

AVK

ILLUSTRATION : 12

(A) Find the effective capacitance between points X and Y in

the given figure. Assume that 102 C F and other capacitors

are 4F each.

(B) Find the capacitance of a system of identical capacitors

between points A and B shown in figure.

11

SOLUTION :

(A) The circuit is redrawn in figure as the two arms are

balanced, no current flows through 2C , 3C and 4C are in series,

hence their equivalent capacitance = 2F Similarly the equivalent

capacitance of 1C and 5C = 2F. Corresponding to points X and Y

these two are in a parallel combination. Hence the effective

capacitance between X and Y is 2 + 2 = 4F.

(B) The arrangement of capacitors shown in figure is equivalent

to the arrangement shown in figure. The arrangement is connected

in parallel. Hence equivalent capacitance C is given by C = C1 + C2 +

C3

WORKED OUT OBJECTIVE PROBLEMS :

12

EXAMPLE : 01

A parallel plate capacitor is connected across a 2V battery and charged. The battery is

then disconnected and glass slab is introduced between the plates. Which of the following pairs

of quantities decrease?

(A) Charge and potential difference (B) potential difference and energy stored

(C) energy stored and capacitance (D) capacitance and charge

Ans: (B)

SOLUTION :

The introduction of a dielectric slab increases the capacitance. The charge remains

unchanged. Potential difference and energy stored decreases.

EXAMPLE : 02

Three capacitors of capacitances 3F, 9F and 18F are connected once in series and

then in parallel. The ratio of equivalent capacitances in the two cases(CS/CP) will be

(A) 1 : 15 (B) 15 : 1 (C) 1 : 1 (D) 1 : 3

Ans: (A)

SOLUTION :

F301893CP

2

1

18

1

9

1

3

1

C

1

S

F2CS

Now 15

1

F30

F2

C

C

P

S

EXAMPLE : 03

A number of capacitors each of capacitance 1F and each one of which get punctured if

a potential difference just exceeding 500volt is applied, are provided. Then an arrangement

suitable for giving a capacitor of capacitance 2F across which 3000 volt may be applied

requires at least

(A) 18 component capacitors (B) 36 component capacitors

(C) 72 component capacitors (D) 144 component capacitors

Ans: (C)

SOLUTION :

Number of capacitors required in series = 6500

3000

13

The capacitance of series combination. = F6

1

To obtain a capacitor of 2F, we should use 12 such combinations.

Total number of capacitors required = 12 x 6 = 72

EXAMPLE : 04

A capacitor of capacitance 1F withstands a maximum voltage of 6kV, while another

capacitor of capacitance 2F, the maximum voltage 4kV. If they are connected in series, the

combination can withstand a maximum of

(A) 6kV (B) 4kV (C) 10kV (D) 9kV

Ans: (D)

SOLUTION :

When the two condensers are connected in series. 3

2

1 2

1 x 2C

F and E

3

2Q

The potential of condenser 1C is given by

kV6E3

2

C

QV

11 kv9E KV12E

3

E

c

Qv

22

To avoid break down E 9KV

EXAMPLE : 05

Seven capacitors each of capacitance 2F are to be connected to obtain a capacitance of

11

10F. Which of the following combination is possible.

(A) 5 in parallel 2 in series (B) 4 in parallel 3 in series

(C) 3 in parallel 4 in series (D) 2 in parallel 5 in series

Ans: (A)

SOLUTION :

5 capacitors in parallel gives 5 x 2 F = 10F capacity. Further, two capacitors in series

gives a capacity 1F. When the two combinations are connected in series, they give a resultant

capacitance

110

1 x 10 =

11

10F.

EXAMPLE : 06

Condenser A has a capacity of 15F when it is filled with a medium of dielectric

constant 15. Another condenser B has a capacity 1F with air between the plates. Both are

charged separately by a battery of 100V. After charging, both are connected in parallel without

battery and the dielectric material being removed. The common potential now is

14

(A) 400V (B) 800V (C) 1200V (D) 1600V

Ans: (B)

SOLUTION :

Charge on capacitor A is given by V x Cq 11

= (15 x 10-6) (100) = 15 x 10-4C

Charge on capacitor B is given by q2 = C2 x V

= (1 x 10-6) (100) = 10-4C

Capacity of condensers A after removing dielectric

115

10 x 15

K

C'C

-61

F

Now when both condenser are connected in parallel their capacity will be

1F + 1F = 2F

Common potential V = C

q

=

V80010 x 2

)10 x 1(10 x 15

6-

4-4-

.

EXAMPLE : 07

Two capacitors 2F and 4F are connected in parallel. A third capacitor of 6 F capacity

is connected in series. The combination is then connected across a 12V battery. The voltage

across 2F capacity is

(A)2V (B) 6V (C) 8V (D) 1V

Ans: (B)

SOLUTION :

Resultant capacitance of condensers of capacity 2F and 4F when connected in

parallel.

642'C F

This is connected in series with a capacitor of capacity 6F in series. The resultant capacity C is

given by

3

1

6

1

6

1

C

1 or 3C F

Charge on combination q = (3 x 10-6) x (12) = 36 x 10-6C

Let the charge on 2F capacitor be 1q , then

4

qq

2

q 11 or 3

qq1 1q 12 x 10-6C

15

Now potential across 2F condenser = 6-

-6

6-

1

10 x 2

10 x 12

10 x 2

q6V

EXAMPLE : 08

The capacitance of the system of parallel plate capacitor shown in the figure is

(A) dAA

AA2

21

210

(B)

dAAAA2

12

210

(C) d

A10 (D)d

A20

Ans : (C)

SOLUTION :

Since the electric field between the parallel charge plates is

uniform and independent of the distance, neglecting the fringe effect,

the effective area of the plate of area A2 is A1. Thus the capacitance

between the plates is d

AC 10

(C)

EXAMPLE : 9

The charge flowing across the circuit on closing the key

K is equal to

(A) CV (B) VC

2

(C)2CV (D) Zero

SOLUTION :

When the key K is kept open the charge drawn

from the source is VCQ '

Where C' is the equivalent capacitance given by 2

C'C

Therefore Q = V2

C

Whey the key K is closed, the capacitor 2 gets short circuited and the charge in the

circuit 1Q CV

Charge flowing is 1C

Q Q Q V2

(B)

1A

2A

d

1A

2A

d 0

E

16

EXAMPLE : 10

The figure shows a spherical capacitor with inner sphere earthed. The

capacitance of the system is

(A)ab

ab4 0

(B)

ab

b4 20

(C) ab 04 (D) None of these

SOLUTION :

Let V be potential of the outer sphere. Thus we can consider two capacitors, one between the

outer sphere and inner sphere and the other between outer sphere and infinity.

Thus,

ab

ab4C 01

b4C 02

b4ab

ab4C 00

ab

b4C

20

(B)

EXAMPLE : 11

A capacitor of capacitance C is charged to a potential difference V from a cell and then

disconnected from it. A charge +Q is now given to its positive plate. The potential difference

across the capacitor is now

(A) V (B) C

QV (C)

C2

QV (D) ,

C

QV if V < CV

SOLUTION :

In the figure given below, left X and Y be

positive and negative plates. After charging

from the cell, the inner faces of X and Y have

charges ,CV as shown in (A). The outer

surfaces have no charge.

When charge Q is given to X, let the inner faces of X and Y have charges q Then, by the

principle of charge conservation, the outer faces have charges qCVQ for X and CVq

for Y, as shown in (B). Now, the outer faces must have equal charges.

a b

a b

1C 2C

17

CVqqCVQ

or QCV2q2

or 2

QCVq

Potential difference C2

QV

C

q

(C)

EXAMPLE : 12

In an isolated parallel - plate capacitor of capacitance C,

the four surfaces have charges 321 QQQ ,, and 4Q as shown. The

potential difference between the plates is

(A) C2

QQQQ 4321 (B)C2

QQ 32

(C) C2

QQ 32 (D) C2

QQ 41

SOLUTION :

Plane conducting surfaces facing each other must have equal and opposite charge

densities. Here, as the plate areas are equal, Q2 = - Q3

The charge on a capacitor means the charge on the inner surface of the positive plate-(in

this case Q2)

Potential difference between the plates

= charge on the capacitor capacitance.

Potential difference =

C2

QQ

C2

QQ

C2

Q2

C

Q 322222

(C)

* * *

1Q 3Q

2Q 4Q

18

SINGLE ANSWER OBJECTIVE TYPE QUESTIONS :

LEVEL - 1 :

1. A capacitor of capacitance C is charged to potential difference V0 from a cell and then

disconnected from it. A charge +Q is now given to its positive plate. The potential

difference across the capacitor is now

A) V0 B) V0 + (Q/C) C) V0 + (Q/2C) D) V0 -

(Q/C)

2. A dielectric of dielectric constant 3 fills up three fourths of the space between the plates

of a parallel plate capacitor. The percentage of energy stored in the dielectric is

A) 25% B) 50% C) 75% D) 100%

3. A parallel plate capacitor having capacitance C0 is connected to a battery of emf E. It is

then disconnected from the battery and a dielectric slab of dielectric constant k

completely filling the air gap of the capacitor is inserted in it. If U indicates the change

in energy, then

A) U = 0 B) U = 2

10E2 (k - 1) C) U =

2

10E2

k

11 D)U

2

1 0E2

1

k

1

4. The work done in increasing the voltage across the plates of the capacitor from 5V to

10V is W. The work done in increasing the voltage from 10V to 15V will be

A) W B) 4/3 W C) 5/3 W D) 2W

5. A parallel plate capacitor of plate area A and plate separation d is charged to potential

difference V and then the battery is disconnected. A slab of dielectric constant K is then

inserted between the plates of the capacitor so as to fill the space between the plates. If

Q, E and W denote respectively, the magnitude of charge on each plate, the electric field

between the plates (after the slab is inserted), and work done on the system, in

questions, in the process of inserting the slab, then

A)

0AV

Qd

B)

0KAV

Qd

C) E = Kd

V D)

2

0AV 1

W 12d K

6. When the capacitance in an oscillator circuit of frequency f is increased nine times, the

frequency of the oscillator is reduced to:

A) f/9 B) f/6 C) f/4 D) f/3

7. 64 small drops of water having the same charge & same radius are combined to form

one big drop. The ratio of capacitance of big drop to small drop is:

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

8. A parallel plate condenser is connected to a battery. The plates are pulled apart with a

uniform speed. If x is the separation between the plates, then the time rate of charge of

the electrostatic energy of the condenser is proportional to

19

A) x2 B) x C) 1/x D) 1/x2

9. A spherical condenser has inner and outer spheres of radii a and b respectively. The

space between the two is filled with air. The difference between the capacities of two

condensers formed when outer sphere is earthed and when inner sphere is earthed will

be

A) zero B) 4 0 a C) 4 0 b D) 4 0 a

[b/(b - a)]

10. The sphere shown in the figure are connected by a conductor. The

capacitance of the system is:

A) 4 0 ab

ab

B) 4 0 a C) 4 0 b D) 40

ab

a 2

11. A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative

plate is at X = 0 and positive plate is at X = 3d. The slab is equidistant from the plates.

The capacitor is given some charge. As X goes from 0 to 3d.

A) the electric potential increases at first, then decreases and again increases

B) the electric potential increases continuously

C) the direction of the electric field remains the same

D) the magnitude of the electric field remains the same

12. Two similar conducting balls are placed near each other in air.

The radius of each ball is r and the separation between the

centers is d (d >> r). The capacitance of two balls system when

they are connected by a wire is:

A) 80r B) 40r C) 40r loge (r/d) D) 4

loge 0 (r/d)

13. A hollow sphere of radius 2R is charged to V volt and another smaller sphere of radius R

is charged to V/2 volt. Then the smaller sphere is placed inside the bigger sphere

without changing the net charge on each sphere. The potential difference between the

two spheres would be

A) 3V/2 B) V/4 C) V/2 D) V

14. A capacitor is charged by using a battery which is then disconnected. A dielectric slab

is then slipped between the plates which results in:

A) reduction of charges on the plates and increase of potential difference across the

plates

B) increase in the potential difference across the plates, reduction in stored energy, but

no change in the charge on the plates

20

C) decrease in the potential difference across the plates, reduction in stored energy, but

no change in the charge on the plates

D) none of the above

15. Force acting on a charged particle kept between the plates of a charged condenser is F.

If one of the plates of the condenser is removed, force acting on the same particle will

become:

A) zero B) F/2 C) F D) 2F

16. A parallel plate air capacitor is connected to a battery. The quantities charge, voltage,

electric field and energy associated with this capacitor are given by Q0, V0, E0 and U0

respectively. A dielectric slab is now introduced to fill the space between the plates

with battery still in connection. The corresponding quantities now given by Q, V, E and

U are related in the previous ones as:

A) Q > Q0 B) V > V0 C) E > E0 D) U > U0

17. Figure shows two capacitors connected in

series and7joined to a battery. The graph

shows the variation in potential as one moves

from left to right on the branch containing the

capacitors:

A) C1 > C2 B) C1 = C2

C) C1 < C2

D) the information is not sufficient to decide the relation between C1 and C2

LEVEL - II :

1. Identical charged 103 oil drops each of radius 0.9nm are combined to form a single drop.

The electrical capacity of the drop is

1) 0.1 PF 2) 1 PF 3) 10 PF 4) 100 PF

2. A parallel plate condenser is charged end isolated. The distance between the plate is

increased by 2mm and a dielectric slab of thickness 3 mm is introduced between the

plates. If the potential difference between the plates remains same, the dielectric

constant of the dielectric slab is

1) 2 2) 3 3) 4 4) 5

3. Two identical parallel plate condensers are connected in series. A cell of e.m.f of 20V is

connected between their ends. A dielectric slab of constant 4 is placed between the

plates of one of the condensers. The potential difference across condenser with

dielectric slab is

1) 4V 2) 10V 3) 16V 4) 18V

4. Four identical parallel metal plates each of area A are placed with separation d

between adjacent plates as shown. The capacitance between the plates P and Q is

1) 03 A

d

2) 0

2 A

3d

21

3) 02 A

d

4) 0

A

2d

5. Two spherical conductors of radii 3cm and 6cm are in contact. A charge 10-9 is given to

them. The potential of the smaller sphere is

1) 67V 2) 33V 3) 50V 4) 100V

6. A parallel plate condenser is charged and isolated. The energy stored by the condenser

is E. The separation of the plate is doubled and then the space is completely filled with

a dielectric of constant 5. The energy stored by the condenser now is

1) E 2) 0.8E 3) 0.4E 4) 2.5E

7. Two condensers charged to potentials 50V and 80V are connected in parallel, the

common potential is 60V. The capacities of the condensers are in the ratio of

1) 2 : 1 2) 1 : 2 3) 3 : 4 4) 4 : 3

8. The capacitor of 4F charged to 50V is connected to another capacitor of 2F charged to

100V. The total energy of the combination is

1) 24

x10 J3

2) 23

x10 J2

3) 23 x10 J 4) 28

x10 J3

9. The radii of two charged metal spheres are 5cm and 10cm both having same charge

75c. If they are connected by a wire, the quantity of charge transferred through the

wire is

1) 75c 2) 50c 3) 25c 4) 15c

10. Two identical capacitors have equivalent capacity of 2F when they are connected in

series. If they are connected in parallel and charged to a potential of 200V, the energy

stored in the system is

1) 18 x 10-4 J 2) 18 x 10-4 J 3) 0.16 J 4) 0.36

11. The capacity of a parallel plate condenser is C. When half the space between the plates

is filled with a slab of dielectric constant K as shown in the figure. If the slab is removed

from the condenser, then the capacity of the

condenser becomes

1) 2KC

K 1 2)

K 1 C2K

3) K 1 C

2K

4)

KC

2K 1

12. Two parallel plate capacitors C and 2C are connected in parallel and charged to P.D V.

The battery is then disconnected and the region between the plates of the capacitor C is

completely filled with a material of dielectric constant 3. The P.D. across the capacitors

now becomes

1) V 2) 3V 3) 3V/5 4) 4V/5

13. A condenser of capacity 10F is connected between the terminals of a battery of

22

potential difference 100V and is charged. The amount of work done by the battery to

charge the condenser is

1) 0.05 J 2) 0.025 J 3) 0.1 J 4) 0.0125 J

14. Two condensers of capacities C1 = 5 F 100V and C2 = 10F 100V are connected in

series. The maximum potential difference that may be applied between them without

damaging the condensers is

1) 200 V 2) 175 V 3) 150 V

4) 300 V

15. n identical charged spheres combine together to form a large sphere. The ratio of the

potential of small sphere to potential of large sphere is 1 : 9. The ratio of the energy

stored in small sphere to the energy stored in the large sphere is

1) 1 : 3 2) 1 : 27 3) 1 : 81 4) 1 :

243

16. The capacity of parallel plate condenser with air between the plates is 10F. If the space

between the plates is completely filled with two dielectric slabs each of thickness is

equal to half of the separation between the plates, whose dielectric constants are 3 and

2. What will be the percentage change in capacity of the condenser?

1) 133.3 % 2) 140 % 3) 166.6 % 4) 280 %

17. The work done in charging a capacitor from 5V to 10V is W. The work done in charging

the

capacitor from 10V to 15V is

1) 4 W/3 2) 5 W/3 3) 2 W/5 4) 5 W/2

18. The voltages across C1 and C2 are in the ratio 2 : 3. When C2 is

completely filled with paraffin, the voltage ratio became 3 : 2. The

dielectric constant of paraffin is

1) 2.25 2) 13/6

3) 27/8 4) 6

19. A parallel plate capacitor of capacity 5F and plate separation 6cm is connected to a 1V

battery and is charged. A dielectric of dielectric constant 4 and thickness 4cm is

introduced into the capacitor. The additional charge that flows into the capacitor from

the battery is

1) 2C 2) 3C 3) 5C 4) 10C

20. A metal sphere A of radius a is charged to a potential V. What will be its potential if

it is enclosed by a spherical conducting shell B of radius b and the two are connected

by a conducting wire?

1) V 2) (a/b) V 3) (b/a) V 4) zero

21. The capacity of a parallel plate capacitor is 5F. When a glass plate of same area as the

plates but thickness half of the distance between the plates is placed between the plates

of the capacitor, its potential difference reduces to 2/5 of the original value. The

23

dielectric constant of the glass is

1) 1.5 2) 2.5 3) 5 4) 2s

Hint: 0 0

0

0

QdV E d

A

Qd t 1V 1 1

A d k

0

2 V t 1 1 1 31 1 ; 1

5 V d k 2 k 5

22. Two spheres A and B of radii 4cm and 6cm are given charges of 80C and 40C. If they

are connected by a wire, the amount of charge flowing from one to other is

1) 20C from A to B 2) 16C from A to B

3) 24C from B to A 4) 32C from A to B

Hint: Q = (C1 C2)V = 2 1 1 1 2 2 2 1 1 2

1 2 1 2

C C C V C V C C Q Q

C C C C

i.e. Q = 2 1 1 2

1 2

r r Q Q 2 x 120

r r 10

24C from B to A

23. Three capacitor of capacitance 10F, 15F, 20F are in series with a cell. The charge

drawn from the cell is 60C. If they are connected in parallel with the same cell, then

the charge drawn from the cell is

1) 385 C 2) 485 C 3) 585 C 4) 685 C

Hint: p p p

ps s s

q C E C 45q 6 x x13 585 C

q C E C 60

24. The plates of a parallel plate capacitor are horizontal and parallel. A thin conducting

sheet P is initially placed parallel to both the plates and nearer to the lower plate. From

t = 0 onwards, the sheet P is moved at constant speed vertically upwards so that it is

always parallel to the capacitor plates. At t = 20 milli seconds, it is nearer to the upper

plates. Then during the time interval from t = 0 to t = 20 milli seconds, the capacity of

the capacitor will

1) increase gradually 2) decrease gradually

3) remains constant 4) first increases and then decreases

Hint: Since the thickness of conducting plate is constant through out, capacity remains

constant

25. A capacitor is charged to 200V. A dielectric slab of thickness 4mm is inserted. The

distance between the plates is increased by 3.2mm to maintain the same potential

difference. Find the dielectric constant of the slab

1) 3 2) 4 3) 5 4) 6

Hint: V1 = V2; 1 2 120 0

Qd d dQ 1 1d t 1 1

A A k k t

26. A capacitor is charged with a dielectric to V volts. If the dielectric of constant K is

24

removed then ___ is true

a) capacity decreases by k times

b) electric field intensity decreased by k times

c) potential increases by k times

d) charge increases by k times

1) a, b, c 2) a, b, c, d 3) a, c 4) b, d

27. The capacitance of a capacitor becomes 7/6 times its original value if a dielectric slab of

thickness t = 2/3d is introduced in between the plates d is the distance between the

plates. The dielectric constant of dielectric field is

1) 14/11 2) 11/14 3) 7/11 4) 11/7

Hint: 0 0C Ct 1 6

C 1 1t 1 d k C 7

1 1d k

28. Between the plates of a parallel plate capacitor of capacity C, two parallel plates of the

same material and area same as the plate of the original capacitor are placed. If the

thickness of these plates is equal to I/5th of the distance between the plates of the

original capacitor, then the capacity of the new capacitor is

1) 5/3 C 2) 3/5 C 3) 3C/10 4) 10C/3

Hint: d1 = d, d2 = 3

5d, t =

2

5d & 2 1 2

1 2

C d 5 5C C

C d 3 3

29. A parallel plate capacitor of capacity Co is charge to a potential V0.

A) The energy stored in the capacitor when the battery is disconnected and the plate

separation is double is E1

B) The energy stored in the capacitor when the charging battery is kept connected and

the separation between the capacitor plates is doubled is E2, the E1/E2 value is

1) 4 2) 3/2 3) 2 4)

30. A capacitor of capacity of 10F is charged to 40V and a second capacitor of capacity

15F is charged to 30V. If they are connected in a parallel the amount of charge that

flows from the smaller capacitor to higher capacitor in C is

1) 30 2) 60 3) 200 4) 250

Hint: V = 1 1 2 2

1 2

C V C V&

C C

Q = (V1 V)C1 = 60C

31. A parallel plate capacitor of capacity 100F is charged by a battery of 50 volts. The

battery remains connected and if the plates of the capacitor are separated so that the

distance between them becomes half the original distance, the additional energy given

by the battery to the capacitor in joules is

1) 125 x 10-3 2) 12.5 x 10-3 3) 1.25 x 10-3 4) 0.125 x 10-3

Hint: V = (C2 C1)V2 & C2 = 2C

32. A parallel plate capacitor of capacity 5F and plate separation 6cm is connected to a I

25

volt battery and is charged. A dielectric of dielectric constant 4 and thickness 4cm

introduced into the capacitor. The additional charge that flows into the capacitor from

the battery is

1) 2C 2) 3C 3) 5C 4) 10C

Hint: 1 0Q C V = 5C; Q2 = C2V = 0C V

t 11 1

d k

= 10C; Q = Q2 Q1

33. A 20F capacitor is charged to 5V end isolated. It is then connected in parallel with an

uncharged 30F capacitor. The decrease in the energy of the system will be

1) 25 J 2) 100 J 3) 125 J 4) 150 J

Hint: 21 1 21 1 1 11 2 1 2

C V C1V & U C V U U

C C 2 C C

34. A dielectric of thickness 5cm and dielectric constant 10 is introduced in between the

plates of a parallel plate capacitor having plate area 500 sq cm and separation between

plates 10cm. The capacitance of the capacitor is (0=8.8 x 10-12 SI units)

1) 8 PF 2) 6PF 3) 4PF 4) 20PF

Hint: C = 0A

1d t 1

k

35. A 4F capacitor is charged by 200V battery. It is then disconnected from the supply and

is connected to another uncharged capacitor of 2F capacity. The loss of energy during

this process is _____

1) 0 2) 5.33 x 10-2 3) 4 x 10-2 4) 2.67 x 10-2

Hint: U = 21 2 1 1

1 2 21 2 1 2

C C C V1V V ; V

2 C C C C

36. Energy E is stored in a parallel plate capacitor C1. An identical uncharged capacitor C2 is

connected to it kept in contact with it fro a while and then disconnected. The energy

stored in C2 is ___

1) E/2 2) E/3 3) E/4 4) 0

Hint: U1 = 2

1

1C V

2, Potential on second capacitor in contact with the first one V2 = V/2;

U2 = 2

1 V EC

2 2 4

37. If the capacity of a spherical conductor is 1PF, then its diameter is

1) 9 x 10-15m 2) 9 x 10-3m 3) 9 x 10-5m 4) 18 x 10-7m

38. A 700PF capacitor is charged by a 50V battery. The electrostatic energy stored by it is

1) 17 x 10-5 J 2) 13.6 x 10-9 J 3) 9.5 x 10-9 J 4) 8.75 x 10-7 J

39. Two equal capacitors are first connected in parallel and then in series. The ratio of the

26

total capacities in the two cases will be

1) 2 : 1 2) 1 : 2 3) 4 : 1 4) 1 : 4

40. Two condensers of capacity 2C and C are joined in parallel and charged up to potential

V. The battery is removed and the condensor of capacity C is filled completely with a

medium of dielectric constant K. The potential difference across the capacitors will now

be

1) 3V

K 2)

3V

K 2 3)

V

K 2 4)

V

K

41. Two condensers C1 and C2 in a circuit are joined as

shown in figure. The potential at A is V1 and that

of B is V2. The potential of point D will be

1) 1 1 2 2

1 2

C V C V

C C

2) 1 2 2 1

1 2

C V C V

C C

3) 1 2

V V

2

4) 1 2 2 1

1 2

C V C V

C C

42. A number of capacitors are connected as

shown in figure. The equivalent capacity is

given by

1) nC 2) n(n + 1)C

3) 2n(n + 1)C 4) n n 1 C

2

43. Three capacitors of capacitances 3F, 10F and 15F are connected in series to a voltage

source of 100V. The charge on 15F is

1) 50C 2) 100C 3) 200C 4) 280C

44. In a parallel plate capacitor of capacitance C, a metal sheet is inserted between the

plates parallel to them. If the thickness of the sheet is half of the separation between the

plates, the capacitance will be

1) C/2 2) 3C/4 3) 4C 4) 2C

45. A 10 micro farad capacitor is charged to 500 V and then its plates are joined together

through a resistance of 10 ohm. The heat produced in the resistance is

1) 500 J 2) 250 J 3) 125 J 4) 1.25 J

46. A capacitor is charged to 200 volt. It has a charge of 0.1C. When it is discharged, energy

liberated will be

1) 1 J 2) 10 J 3) 14 J 4) 20 J

47. Half of the separation between two parallel plates of a capacitor is filled with a

dielectric medium. The capacitance of the capacitor becomes 5/3 times its original

value with full space dielectric. The dielectric constant of the medium K is

1) K = 2 2) K = 3 3) K = 4

4) K = 5

48. A 10F capacitor is charged to a potential difference of 50 V and is connected to another

uncharged capacitor in parallel. Now the common potential difference becomes 20 V.

27

The capacitance of second capacitor is

1) 10 F 2) 20 F 3) 30 F

4) 15 F

49. Capacity of a spherical capacitor having two spheres of radii a and b (a > b) separated

by a medium of dielectric constant K is given by

1) Kab

a b in SI system 2) 0

4 Kab

a b

in CGS system

3)

04 Kab

a b

in SI system 4)

K a bab

in CGS system

50. A capacitor of capacity C has charge Q. The stored energy is W. If the charge is

increased to 2Q, the stored energy will be

1) 2W 2) W/2 3) 4W 4) W/4

51. A D.C. potential of 100 volt is connected to the combination

as shown in figure. The equivalent capacity between A and

B will be equal to

1) 40 F 2) 20 F

3) 30 F 4) 10 F

52. The capacitance of four plates, each of area A arranged as shown in figure as

1) 02 A

d

2) 0

3 A

d

3) 04 A

d

4) 0

5 A

d

53. Identify the wrong statement of the following

a) the resultant capacity C is less than the capacitance of smallest capacitor in series

combination

b) the resultant capacity C is greater than greatest capacitance in parallel combination

c) In series combination, charge on capacitor plates is inversely proportional to

capacitance of capacitor

1) a is wrong 2) c is wrong 3) b is wrong 4) all are wrong

54. A parallel plate capacitor of area A, plate separation d with the

electric capacity C0 is filled with three different dielectric

materials with constants K1, K2 and K3 as in the figure. If these

three are replaced by a single dielectric, its dielectric constant K

is ___

1) 1 2 3

1 1 1 1

K K K 2K 2)

1 2 3

1 1 1

K K K 2K

28

3) 1 2 31 2

K K12K

K K K

4) 1 3 2 3

1 3 2 3

K K K KK

K K K K

55. Four metallic plates, each with a surface area of one side

A, are placed at a distance d apart. The outer plates are

connected to terminal X and the inner plates to terminal

Y. The capacitance of system between X and Y is

1) 0A/d 2) 20A/d 3) 30A/d 4) 40A/d

56. Four metallic plates, each with a surface area of one side A

are placed at a distance d apart, these plats are connected

as shown in figure. The capacitance of the system between

X and Y is

1) 0A/d 2) 20A/d

3) 30A/d 4) 40A/d

57. An infinite ladder is made as shown in figure using

capacitors C1 = 1 F and C2 = 2F. The equivalent capacitance

of the ladder, in F is

1) 1 2) 2

3) 0.75 4) 0.5

58. In the circuit segment shown VA - VB = 19V. The p.d. across 3 F capacitor is

1) 7V 2) 8V

3) 23V 4) 4V

59. A parallel plate capacitor with a dielectric constant K = 3 filling the space between the

plates is charged to a potential difference V. The battery is then disconnected and the

dielectric slab is withdrawn and replaced by another dielectric slab having K = 2. The

ratio of energy stored in the capacitor before and after replacing the dielectric slab by

new one is

1) 3 : 2 2) 9 : 4 3) 4 : 9 4) 2 : 3

60. Two parallel capacitors of capacitance C and 2C are connected in parallel and charged

to a potential difference V. The battery is then disconnected and the capacitor C is

completely filled with a material of dielectric constant k. The potential difference across

the capacitors is now

1) 2V/k 2) 3V/k 3) 3V/(k+2) 4)

2V/(k+3)

61. Initially the capacitors C1 and C2 shown in figure have equal

capacitances. If a dielectric plate (k = 2) is introduced in capacitor C2,

then potential difference across its plates and charge

1) both will decrease 2) both will increase

3) p.d. will increase but charge will decrease

4) p.d. will decrease but charge will increase

A B

29

62. Five identical capacitor plates, each of area A, are arranged such that adjacent plates are

at a distance d apart. The plates are connected to a source of emf V as shown in figure.

The charge on plate 1 is q and that on 4 is q', where

1) q' = q 2) q' = 2q

3) q' = -2q 4) q' = 3q

63. For the circuit shown in figure which of

the following statements is true

1) With S1 closed, V1 = 15V, V2 = 20V

2) With S3 closed, V1 = V2 = 25V

3) With S1 and S2 closed, V1 = V2 = 0

4) With S1 and S3 closed, V1 = 30V, V2 = 20V

64. Two identical capacitors, having the same capacitance C. One of them is charged to a

potential V1 and the other to V2. The negative ends of the capacitor are connected

together. When the positive ends are also connected, the decrease in energy of the

combined system is

1) )VV(C4

1 22

21 2) )VV(C

4

1 22

31 3)

221 )VV(C

4

1 4) 221 )VV(C

4

1

65. Each edge of a cube (figure) made of wire contains a capacitor of capacitance C. Find

the effective capacitance of this bank of capacitors between opposite

corners A and G.

1) 5C/6 2) 4C/3

3) 3C/4 4) 6C/5

66. Consider the situation shown in figure. The capacitor A has charge q

on it whereas B is uncharged. The charge appearing on the capacitor

B a long time after switch is closed is

1) zero 2) q/2 3) q 4) 2q

67. A parallel plate capacitor of capacitance C is connected to a battery and is

charged to a potential difference V. Another capacitor of capacitance 2C is

similarly charged to potential differences 2V. The charging battery is now

disconnected and the capacitors are connected in parallel to each other in such

a way that the negative terminal of one is connected to the negative terminal of

the other. The final energy of the configuration is

1) zero 2) (3/2) 2CV 3) (25/6) 2CV 4) (9/2) 2CV

68. You are given thirty two capacitors each having capacity 4 F. How do you connect all of them to

prepare a composite capacitor having capacitance 8 F?

1) 4 Condensers in series 8 such groups in parallel

2) 2 Condensers in series and 16 such groups in parallel

3) 8 Condensers in series and 4 such groups in parallel 4) All of them in series.

69. Find out the effective capacitance between points P and Q. It will

30

be

equal to

1) 9 F 2) 4.5 F

3) 1 F 4) 6 F

70. An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar

air filled capacitor charged to a potential V. The two share the charge and the common potential is

V'. The dielectric constant K is

1) VV

VV

2)

V

VV

3)

V

VV 4)

V

VV

71. Two condensers each having capacitance C and breakdown voltage V are joined in series. The

capacitance and the breakdown voltage of the combination will be

1) 2C and 2V 2) C/2 and V/2 3) 2C and V/2 4) C/2 and 2V

72. Two identical metal plates are given positive charges Q1 and Q2 (< Q1) respectively. If they are

now brought close together to form a parallel plate capacitor with capacitance C, the potential

difference between them is

1) C2

)QQ( 21 2) C

)QQ( 21 3) C

)QQ( 21 4) C2

)QQ( 21

73. Three very large plates are given charges as shown in the figure. If the

cross sectional area of each plate is the same, the final charge distribution

on plate C is:

1) +5 Q on the inner surface, +5 Q on the outer surface




74. Two identical sheets of metallic foil are separated by d and capacitance of the system is C and is

charged to a potential difference E. Keeping the charge constant, the separation is increased by l.

Then the new capacitance and potential difference will be:

1) d

A0 ,E 2) )d(

A0

l

,E 3)

d1,

)d(

A0 l

lE 4)

d1,

d

A0 l E

75. n conducting plates are placed face to face as shown in

figure. Distance between any two plates is d. Area of the

plates is A, (n 1)

A A A A, , ......

2 4 8 2 . The equivalent

capacitance of the system is

1) d2

A

n

0 2) d)12(

A

n

0

3)

d)22(

A

n

0

4)

d)12(

A

n

0

76. The adjoining figure shows two identical parallel plate

capacitors connected to a battery with switch S

close(4). The switch is now opened and the plates are

filled with a dielectric of dielectric constant 3. The ratio

d

31

of the total electrostatic energy stored in both the capacitors before and after the

introduction of the dielectric is

1) 2 : 5 2) 3 : 5 3) 5 : 2

4) 5 : 3

77. A parallel plate capacitor has two layers of dielectric as

shown in figure.

This capacitor is connected across a battery, then the

ratio of potential

difference across the dielectric layers

1) 4/3 2) 1/2

3) 1/3 4) 3/2

78. Five conducting plates are placed parallel to each other.

Separation between them is d and area of each plate is A.

Plate number 1, 2 and 3 are connected with each other and at

the same time through a cell of emf E. The charge on plate

number 1 is

1) E0A/d 2) E0A/2d 3) 2 E0A/d 4) zero

79. A capacitor of capacity C1, is charged by connecting it across a battery of emf V0. The battery is

then removed and the capacitor is connected in parallel with an uncharged capacitor of capacity

C2. The potential difference across this combination is:

1) 021

2 VCC

C

2) 0

21

1 VCC

C

3) 0

2

21 VC

CC 4) 0

1

21 VC

CC

80. The capacitance of a parallel plate capacitor is 16F. When a glass slab is placed

between the plates, the potential difference reduces to 1/8th of the original value.

What is dielectric constant of glass ?

1) 4 2) 8 3) 16 4) 32

81. The equivalent capacity across M and N in the given figure is:

1) 5C/3 2) 2/3C 3) C 4) 3/2C

82. Three plates of common surface area A are connected as shown.

The effective capacitance between points P and Q will be:

1) d

A0 2) d

A3 0

3) d

A

2

3 0 4) d

A2 0

83. A dielectric slab of dielectric constant K = 5 is covered from all sides with a metallic foil. This

system is introduced into the space of a parallel plate capacitor of capacitance 10 F. The slab

fills almost the entire space between the plates, but does not touch the plates. The capacitance

will become nearly:

1) 2) zero 3) 2 pF 4) 50 Pf

1k 2

2k 6

32

84. A capacitor of capacitance 1 F can withstand the maximum voltage 6 kV while a capacitor of

capacitance 2.0 F can withstand the maximum voltage 4 kV. If the two capacitors are connected

in series, then the two capacitors combined can take up a maximum voltage of:

1) 2.4 kV 2) 5 kV 3) 9 kV 4) 10 kV

85. A spherical conductor of radius 2m is charged to a potential of 120 V. It is now placed inside

another hollow spherical conductor of radius 6 m. Calculate the potential of bigger sphere if the

smaller sphere is made to touch the bigger sphere:

1) 20 V 2) 60 V 3) 80 V 4) 40 V

86. A parallel plate capacitor has two layers of dielectrics as shown in figure. Then the ratio of

potential difference across the dielectric layers when connected to the battery is:

1) 2

1

K

K 2)

bK

aK

2

1

3) aK

bK

1

2 4)

bK

aK

1

2

LEVEL - III :

1. A parallel plate capacitor C is connected to a battery and it is charged to a potential

difference of V. Another capacitor of capacitance 2C is similarly charged to a potential

difference of 2V. The charging battery is now disconnected and the capacitors are

connected in parallel to each other in such a way that the positive terminal of one is

connected to positive of the other. The final energy of the configuration is

A) zero B) 3/2 CV2 C) 25/6 CV2 D) 9/2 CV2

2. The amount of heat liberated when a capacitor of C farads charged to a potential

difference of V volts is discharged through a resistor of R ohms is H joules. The same

capacitor is now charged to a potential difference of 2V and discharged through a resistor

of 2 R ohms, then heat liberated is

A) 4H B) 2H C) H D) H/2

3. A capacitor of capacity C1 is charged to a potential V0. The electrostatic energy stored in

it is U0. It is connected to another uncharged capacitor of capacitance C2 in parallel. The

energy dissipated in the process is

A) 021

2 UCC

C

B) 0

21

1 UCC

C

C)

0

2

21

21 UCC

CC

D) 021

21 U)CC(2

CC

4. In the circuit shown in figure, if the key is turned so

that instead of 1, 2 terminals 1, 3 are connected, then

the heat liberated in resistor R is

33

A) 221 )~(C2

1 B) 221 )(C

2

1

C) 222

1 C2

1C

2

1 D) 22

21 C

2

1C

2

1

5. Three capacitors C1, C2, C3 are connected as

shown in figure to one another and to points

P1, P2, P3 at potentials V1, V2 and V3. If the total

charge on the capacitors is zero, the potential

of the point O is

A) 321

332211

CCC

VCVCVC

B) V1 + V2 + V3

C) 0 D) 2

13

1

32

3

21

C

CV

C

CV

C

CV

6. A parallel plate capacitor having capacitance C has two

plates of same area A and thickness t. Figure shows the

charges available on the four surfaces of the plates. The

potential difference V between the two plates is given by

A)

C

qq

2

1 32 B)

C

qq 32 C)

C

qq

2

1 42 D)

C

qq 42

7. The plates of a parallel plate capacitor are separated by d cm. A plate of thickness t cm

with dielectric constant k1 is inserted and the remaining space is filled with a plate of

dielectric constant k2. If Q is the charge on the capacitor and area of plates is A cm2

each, then potential difference between the plates is

A)

210 k

td

k

t

A

Q B)

21 k

td

k

t

A

Q4 C)

td

k

t

k

A

Q4 21 D)

2

1

0 k

td

t

k

A

Q

8. Find the capacitance of a system of three parallel plates each of area A separated by

distances d1 and d2. The space between them is filled with dielectrics of relative

dielectric constants 1 and 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

9. Two identical capacitors, have the same capacitance C, One of them is charged to

potential V1 and the other to V2. The negative ends of the capacitors are connected

together. When the positive ends are also connected, the decrease in energy of the

combined system is

34

A) 2221 VVC4

1 B) 2221 VVC

4

1 C) 221 VVC

4

1 D) 221 VVC

4

1

10. One plate of a capacitor is connected to a spring as shown in the

figure. Area of both the plates is A. In steady state, separation

between the plates is 0.8 d (spring was unstretched and the distance

between the plates was d when the capacitor was uncharged). The

force constant of the spring is approximately.

A) 3

20

Ad

E6 B)

3

20

d

AE4 C)

3

30

d2

AE4 D)

2

0

d

AE2

11. A slab of copper of thickness b is inserted in between the plates of

parallel plate capacitor as shown in figure. The separation of the

plates is d. If b = d/2, then the ratio of capacities of the capacitor

after and before inserting the slab will be:

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

12. Consider a parallel plate capacitor of capacity 10 F with air filled

in the gap between the plates. Now one-half of the space between

the plates is filled with a dielectric of dielectric constant 4, as

shown in the figure. The capacity of the capacitor changes to:

A) 25 F B) 20 F

C) 40 F D) 5 F

13. Consider the arrangement of three plates X, Y and Z each of area A and separation d.

The energy stored when the plates are fully charged is:

A) d2

AV20 B) d

AV20

C) d

AV2 20 D) d2

AV3 20

MULTIPLE ANSWER OBJECTIVE TYPE QUESTIONS :

1. In the arrangement shown in Fig, the charge on capacitor C2 is 1 C and on capacitorC3

is 2 C. If the capacitance of capacitor C2 is 1 F, then

A) p.d across C1 is 2 V B) Charge on C1 is 3 C

C) Energy stored in system is 4.5 J D) Energy supplied by battery

is 4.5 J

2. In the arrangement shown in Fig, all capacitors have equal capacities equal to

k = 4

35

1 F. If the emf of the battery is 2 V

A) The charge on capacitor C1 is 1 C

B) The potential difference across C2 is 1 V

C) The energy stored in C3 is 2 J D) Energy supplied by battery is 4 J

3. In a parallel plate capacitor, the area of each plate is A and the plate separation is d. The

capacitor carries a charge q and the force of attraction between the two plates is F. Then

A) F q2 B) F d C) F 1/A D) F 1/d


plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates.

The capacitor if given some charge. As x goes from o to 3d

A) the magnitude of electric field remains the same

B) the direction of electric field remains the same

C) the electric potential increases continuously

D) the electric potential increases at first, then decreases and again increases

5. In the circuit shown, some potential difference is

applied between A and B. If C is joined to D,

A) no charge will flow between C and D

B) some charge will flow between C and D

C) the equivalent capacitance between C and D will

not change

D) the equivalent capacitance between C and D will change

6. The two plates X and Y of a 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 = Q/C

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 plate X will be 2Q

C) The total charge on the plate Y will be zero

D) The cell will supply C2 amount of energy

7. A parallel-plate capacitor is charged from a cell and then disconnected from the cell.

The separation between the plates is now doubled

A) The potential difference between the plates will become double

B) The field between the plates will not change

C) The energy of the capacitor doubles

D) Some work will have to be done by an external agent on the plates

8. In the circuit shown, each capacitor has a capacitance C.

The emf of the cell is . If the switch S is closed

36

A) some charge will flow out of the positive terminal of the cell

B) some charge will enter the positive terminal of the cell

C) the amount of charge flowing through the cell will be C

D) the amount of charge flowing through the cell will be 4/3 C

9. A parallel-plate air capacitor of capacitance C0 is connected to a cell of emf and then

disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air

gap of the capacitor, is now inserted in it

A) The potential difference between the plates decreases K times

B) The energy stored in the capacitor decreases K times

C) The change in energy is 2

1C02 (K - 1) D) The change in energy is

2

1C02

K

11

10. When a charged capacitor is connected with an uncharged capacitor, then flows

A) the change always flows from the changed to the unchanged capacitor

B) a steady state is obtained after which no further charge flow occurs

C) the total potential energy stored in the capacitors remains conserved

D) the charge conservation always holds true

MATCHING TYPE QUESTIONS :

A parallel-plate air capacitor of capacitance C0 is connected to a cell of emf and then

disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air

gap of the capacitor, is now inserted in it

A) The potential difference between the plates decreases K times

B) The energy stored in the capacitor decreases K times

C) The change in energy is 2

1C0

2 (K - 1)

1.

List I List II

a) energy stored in capacitor by external

source

a) remain same

b) field inside the dielectric when is placed in

between plates of capacitor battery still

connected

b) half of energy supplied by battery

c) charge on capacitor by placing dielectric

and battery connection is removed c)

C

Q

2

1

d) force between two parallel plates when d) decreases

37

separation is increased

2.

List I List II

a) Energy stored in capacitor e) 40R

b) Capacity of spherical capacitor f)

2

0

q

2 AK

c) Force between plates of capacitor g)

1

20E2

d) Energy density of electric field h) q2/2C

PREVIOUS YEAR IIT QUESTIONS :


plate is at 0x and positive plate is at dx 3 . The slab is equidistant from the plates.

The capacitor is given some charge. As one goes from 0 to d3 [IIT-JEE 1998]

(a) The magnitude of the electric field remains the same

(b) The direction of the electric field remains the same

(c) The electric potential increases continuously

(d) The electric potential increases at first, then decreases and again increases

2. A parallel plate capacitor is charged to a potential difference of 50 V. It is discharged through a

resistance. After 1 second, the potential difference between plates becomes 40 V. Then [Roorkee

1999]

(a) Fraction of stored energy after 1 second is 16/25

(b) Potential difference between the plates after 2 seconds will be 32 V

(c) Potential difference between the plates after 2 seconds will be 20 V

(d) Fraction of stored energy after 1 second is 4/5

3. Five identical plates each of area A are joined as shown in the figure. The distance

between the plates is d. The plates are connected to a

potential difference of voltsV . The charge on plates 1 and 4

will be [IIT 1984]

(a) d

AV

d

AV 00 2.

(b) d

AV

d

AV 00 2.

(c) d

AV

d

AV 00 2.

(d) d

AV

d

AV 00 2.

4. In the figure below, what is the potential difference between the point

A and B and between B and C respectively in steady state [IIT 1979]

(a) VVV BCAB 100 (b) VVVV BCAB 25,75

(c) VVVV BCAB 75,25 (d) VVV BCAB 50

1 2 3 4 5

+

V

B A V

3F

3F 1F

1F B

10

20 100V

A C

1F

38

5. Figure given below shows two identical parallel plate capacitors connected to a battery

with switch S closed. The switch is now opened and the free space between the plate of

capacitors is filled with a dielectric of dielectric constant 3. What will be the ratio of total

electrostatic energy stored in both capacitors before and after the introduction of the

dielectric [IIT 1983]

(a) 3 : 1 (b) 5 : 1

(c) 3 : 5 (d) 5 : 3

6. A parallel plate capacitor of capacitance C is connected to a battery and is charged to a

potential difference V. Another capacitor of capacitance 2C is connected to another

battery and is charged to potential difference 2V. The charging batteries are now

disconnected and the capacitors are connected in parallel to each other in such a way

that the positive terminal of one is connected to the negative terminal of the other. The

final energy of the configuration is [IIT 1995]

(a) Zero (b) 6

25 2CV (c)

2

3 2CV (d)

2

9 2CV

7. In an isolated parallel plate capacitor of capacitance C, the four

surface have charges 1Q , 2Q , 3Q and 4Q as shown. The potential

difference between the plates is [IIT-JEE 1999]

(a) C

QQQQ

2

4321 (b) C

QQ

2

32

(c) C

QQ

2

32 (d) C

QQ

2

41

8. For the circuit shown, which of the following statements is true [IIT-JEE 1999]

(a) With 1S closed, VVVV 20,15 21

(b) With 3S closed VVV 2521

(c) With 1S and 2S closed 021 VV

(d) With 1S and 3S closed, VVVV 20,30 21

9. Consider the situation shown in the figure. The capacitor A

has a charge q on it whereas B is uncharged. The charge

appearing on the capacitor B a long time after the switch is

closed is

[IIT-JEE (Screening) 2001]

(a) Zero (b) 2/q (c) q (d)

q2

10. Point charge q moves from point P to point S along the

path PQRS (figure shown) in a uniform electric field E

pointing co-parallel to the positive direction of the X axis.

The coordinates of the points RQP ,, and S are

S1 S3 S2 + +

V1=30V V2=20V

C1=2pF C2=3pF

A B

s

q

+

+

+

+

+

Q1

Q2

Q3

Q4

X

R

Q S

P

E

39

)0,,(),0,0,2(),0,,( baaba and )0,0,0( respectively. The work done by the field in the above

process is given by the expression [IIT 1989]

(a) qEa (b) qEa

(c) 2qEa (d) ])2[( 22 baqE

ASSERTION & REASON :

Read the assertion and reason carefully to mark the correct option out of the options

given below :

(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 assertion is false but reason is true.

1. Assertion : If three capacitors of capacitance C1 < C2 < C3 are connected in parallel then

their equivalent capacitance Cp > Cs

Reason : 321

1111

CCCCp

2. Assertion : If the distance between parallel plates of a capacitor is halved and dielectric

constant is made three times, then the capacitor becomes 6 times.

Reason : Capacity of the capacitor does not depend upon the nature of the

material.

3. Assertion : Dielectric breakdown occurs under the influence of an intense light beam.

Reason : Electromagnetic radiations exert pressure.

4. Assertion : The capacity of a given conductor remains same even if charge is varied on

it.

Reason : Capacitance depends upon nearly medium as well as size and shape of

conductor.

5. Assertion : The whole charge of a conductor cannot be transferred to another isolated

conductor.

Reason : The total transfer of charge from one to another is not possible.

6. Assertion : Conductors having equal positive charge and volume, must also have same

potential.

Reason : Potential depends only on charge and volume of conductor.

7. Assertion : The lightening conductor at the top of high building has sharp pointed

40

ends.

Reason : The surface density of charge at sharp points is very high resulting in

setting up of electric wind.

8. Assertion : Circuit containing capacitors should be handled cautiously even when there is

no current.

Reason : The capacitors are very delicate and so quickly break down.

9. Assertion : The tyres of aircraft's are slightly conducting.

Reason : If a conductor is connected to ground, the extra charge induced on conductor will flow

to ground.

10. Assertion : A bird perches on a high power line and nothing happens to the bird.

Reason : The level of bird is very high from the ground.

11. Assertion : Two capacitors are connected in series to a battery. If the dielectric medium

is inserted between the plates of one of the capacitors, the energy stored in the system

will increase

Reason : On inserting the dielectric medium, the capacity of the capacitor increases

* * * * *

K E Y S

SINGLE ANSWER TYPE QUESTIONS

LEVEL I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

C B D C C D A D C C BC A B C B A C

LEVEL II

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2 2 1 2 4 3 1 1 3 3 2 3 3 3 4 2 2 1 3 2

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

3 3 3 3 3 3 1 1 3 2 1 3 3 1 4 3 2 4 3 4

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3 4 3 4 4 2 3 3 3 3 4 2 2 4 2 3 2 2 4 3

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

4 3 4 3 4 1 2 1 1 4 4 4 3 3 3 2 4 4 2 2

81 82 83 84 85 86

1 4 1 3 1 4

LEVEL III

1 2 3 4 5 6 7 8 9 10 11 12 13

41

B A A B A A B A C B B B B

MULTIPLE ANSWER OBJECTIVE TYPE QUESTIONS

1 2 3 4 5 6 7 8 9 10

ABC ABD AC BC AC ABCD ABCD AD ABD ABD

MATCH THE COLUMN :

01. a-bc, b-a, c-a, d-a 02. a h, b e, c f, d g

PRIVIOUS YEAR IIT QUESTIONS

1 2 3 4 5 6 7 8 9 10

BC AB C C C C C D A B

ASSERTION & REASON

1 2 3 4 5 6 7 8 9 10 11

C B B A D D A C B C C

* * *

Documents

Capacitor