Capacitor

1
C A P A C I T O R
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
dV
E 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
dV
E   ]
or,   

 
d
0
0
V
dV dx i.e., V d



So,
  d
A
d /
A
V
q
C


 

 












x  0 x  d
V  0
V
P
   
d

2
or
d
KA
C 0
 [as 0  K ]
SPHERICAL CAPACITOR :
We can derive the capacity of a spherical capacitor in a similar
way V=
4 0
q






b
1
a
1
;
C =
V
q
=
b
1
a
1
4 0


=
b a
4 0ab


If the radius of the outer sphere tends to infinity, b  , the
capacitance reduces to
C = 4 a 0  which is the capacitance of the isolated sphere.
CYLINDRICAL CAPACITOR :
E =
20r

a  r  b
V = Va Vb = - 
a
b
Edr or V =
20

ln
a
b
 C =
V
q
=
V

=
a
b
n
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
A
C 0

= 8. 85 x 10-12
1 x 10 m
200 x 10 m
x
m
F
-3
-4 2
= 0.177 x 10-9F
= 0.177nF.
The potential difference between the plates is
5.65
0.177nF
1nC
C
Q
V    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

b
a
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 = C1V1  C2V2  C3V3 and V = V1 V2 V3
 Effective capacitance of the combination C can be found from the relation.
C
1
=
C1
1
+
C2
1
+
C3
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 = Q1 + Q2 + Q3
C = C1 + C2 + C3
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
1 C 2 C 3 C
1 V 2 V 3 V
1 Q

1 -Q
2 Q 2 -Q


3 Q 3 -Q


A B
A B
A B

4
Ceq =
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
A
C 0
 then, the equivalent capacitance of the
system is given by
d
A
2
3
2
3C
C 0
eq

 
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 E0 ,
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
K0A
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
q
dq
[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
0
C
q
dq =
2C
Q2
=
2
QV
=
2
1
C 2 V
This work done is stored as electrostatic energy ie., U =
2
1
C 2 V =
2
1





 
d
0A  2 2  E d =
2
1
0 
2 E (Ad)
 Energy density (u) = energy per unit
Volume =
2
1
0  2 E
If dielectric is introduced then U =
2
1
K 0  2 E
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 + F W = 0
[Where F W denotes the work done in displacement
dx]
 F W = - Welec. = U
 - F dx =
2
Q2
d 



C
1
=
2
2
2C
Q
 dc
 F=
2
2
2C
Q
dx
dc
=
2
1
2 V
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 =
1 2
1 2
C C
C C

=
50 20
50x20

=
7
100
pF
 Charge on C1 = charge on C2 =
7
100
x 6 =
7
600
pC
 Potential difference across C1 50pC =
7x50
600
= 1.71 V
and across C2  20pC =
7x20
600
= 4.28 V
(B) Energy in C1 = E1 =
2
1
x 50x  2 1.71 = 73.5 pJ
Energy in C2 = E2 =
2
1
x 20 x  2 4.28 = 184 pJ
ILLUSTRATION : 05
A 5F 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 2 V
 W = 2x5x 6 10 x  2 12
= 1.44 mJ
ILLUSTRATION : 06
A capacitor stores 50C charge when connected across a battery. When the gap between
the plates is filled with a dielectric, a charge of 100C flows through the battery. Find the
dielectric constant of the material inserted.
SOLUTION :
Initial charge = 50C =Q1
Amount of charge flows = 100C
 With dielectric total charge = (50+100) =150C
20pF 50pF
6V

7
Initial capacity C =
V
Q
=
V
50C
Final capacity ' C =
V
Q'
=
V
150C
K =
C
C'
=
50/V
150/V
= 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.
4 f ,
C C
C .C
C
3 4
3 4
34  

 C2,3,4  8  4  12f
4.8 f ,
8 12
8 12
Ceq  


 q C V . C eq   4 810  48
The 'q' on 1 is 48C, thus 6V
c
q
V1   






 6V.
8 F
48 c
V1
 V V PQ  10  6  4
By symmetry of 3 and 4, we say, V V. AB  2
ILLUSTRATION : 08
What is VA  VB in the arrangement shown? What is the
condition such that VA VB  0
SOLUTION :
Let charge be as shown
(Capacitors in series have the same charge)
Take loop containing 1 C , 2 C and E
E 0
C
q
C
q
1 2
    





1 2
1 2
C C
C C
q E
From loop containing 3 4 C ,C and E
Similarly,
q
q'

8
E 0
C
q'
C
q'
3 4
  
 





3 4
3 4
C C
C C
q' E
Now,
2 4
A B
C
q'
C
q
V  V  
= 





 3 4
3
1 2
1
C C
C
C C
C
E.
  



 

 
1 2 3 4
1 4 3 2
A B
C C . C C
C .C C .C
V V E.
For   0 A B V V
 C1C4  C2C3  0 or
4
3
2
1
C
C
C
C

ILLUSTRATION : 09
A 8F capacitor C1 is charged to 0 V = 120volt. The charging
battery is then removed and the capacitor is connected in parallel to
an uncharged 4F 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 q0 be the charge on C1 initially Then q0  C1V0 when 1 C is connected to 2 C in
parallel, the charge 0 q is distributed between 1 C and 2 C . Let 1 q and 2 q be the charges on 1 C
and 2 C respectively. Now let V be the potential difference across each condenser.
Now q0  q1  q2 or C1V0  C1V  C2V
120V
8 F 4 F
8 F
V
C C
C
V 0
1 2
1
  



 
= 80volt.
(B) Initial energy stored
2
1
C V
2
1
U 2
0  1 0  (8 x 10-6) (120)2
= 5 .76 x 10-2joule
Final energy stored
S
1 C 2 0 C V

9
U = 2 2
1 2
1 1
C V C V
2 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 1F. 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 10 C is
3
8
. Capacitors C7 and 9 C 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

F
23
32
C  
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. V0 . Find
B
A
2 C
8 C
1 C
7 C 9 C
8 1
4
4 4
C
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., 12 32 C ,C 34 C and 54 C . The capacity of each capacitor is 0 C0
d
A
K  



 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
0 0
0 0
C 2C
C x 2 C

Further 34 C is again in parallel. Hence the effective capacity
=
d
A
K
3
5
C
3
5
C 2C
C x 2C
C 0 0
0 0
0 0
0   


(ii) Charge on the plate 5 = charge on the upper half of parallel combination
d
K AV
3
2
C
3
2
Q V 0 0
5 0 0

 



 
Charge on plate 3 on the surface facing 4
d
K AV
V C 0 0
0 0


Charge on plate 3 on the surface facing 2
= [Potential difference across (3 - 2)] 0 C
=
d
AV
C K
C C
C
V
2 3
0
0 0
0 0
0
0  

d
AV
K
d
K AV
Q
3
0
0
0 0
3  

  = 0 0
0 0 V
d
A
K
3
4
3
1
1
d
K AV
  

 


ILLUSTRATION : 12
(A) Find the effective capacitance between points X and Y in
the given figure. Assume that 10 2 C  F and other capacitors
are 4F 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 C2 , C3 and C4 are in series,
hence their equivalent capacitance = 2F Similarly the equivalent
capacitance of C1 and C5= 2F. Corresponding to points X and Y
these two are in a parallel combination. Hence the effective
capacitance between X and Y is 2 + 2 = 4F.
(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 3F, 9F and 18F 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 :
CP  3 9 18  30F
2
1
18
1
9
1
3
1
C
1
S
   
 CS  2F
Now
15
1
30 F
2 F
C
C
P
S 



EXAMPLE : 03
A number of capacitors each of capacitance 1F 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 2F 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 = 6
500
3000


13
The capacitance of series combination. = F
6
1

To obtain a capacitor of 2F, we should use 12 such combinations.
Total number of capacitors required = 12 x 6 = 72
EXAMPLE : 04
A capacitor of capacitance 1F withstands a maximum voltage of 6kV, while another
capacitor of capacitance 2F, 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
2 1
2 x 1
C 

 F and E
3
2
Q 
The potential of condenser C1 is given by
E 6kV
3
2
C
Q
V
1
1    E 9kv E 12KV
3
E
c
Q
v
2
2    
To avoid break down E  9KV
EXAMPLE : 05
Seven capacitors each of capacitance 2F are to be connected to obtain a capacitance of




11
10
F. 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 = 10F capacity. Further, two capacitors in series
gives a capacity 1F. When the two combinations are connected in series, they give a resultant
capacitance 



10 1
10 x 1
= 



11
10
F.
EXAMPLE : 06
Condenser A has a capacity of 15F when it is filled with a medium of dielectric
constant 15. Another condenser B has a capacity 1F 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 q1  C1 x V
= (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
1
15
10
15 x
K
C
C'
-6
1 
 


 


 



 F
Now when both condenser are connected in parallel their capacity will be
1F + 1F = 2F
Common potential V =
C
q
=   800V
2 x 10
15 x 10 (1 x 10 )
-6
-4 -4


.
EXAMPLE : 07
Two capacitors 2F and 4F 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 2F capacity is
(A)2V (B) 6V (C) 8V (D) 1V
Ans: (B)
SOLUTION :
Resultant capacitance of condensers of capacity 2F and 4F when connected in
parallel.
C' 2  4  6 F
This is connected in series with a capacitor of capacity 6F in series. The resultant capacity C is
given by
3
1
6
1
6
1
C
1
   or C  3 F
Charge on combination q = (3 x 10-6) x (12) = 36 x 10-6C
Let the charge on 2F capacitor be 1 q , then
4
q q
2
q1  1
 or
3
q
q1  q1  12 x 10-6C

15
Now potential across 2F condenser =  
-6
-6
-6
1
2 x 10
12 x 10
2 x 10
q
6V
EXAMPLE : 08
The capacitance of the system of parallel plate capacitor shown in the figure is
(A)
A A d
2 A A
1 2
0 1 2


(B)
A A d
2 A A
2 1
0 1 2


(C)
d
0A1
(D)
d
0A2
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
A
C 0 1
  (C)
EXAMPLE : 9
The charge flowing across the circuit on closing the key
K is equal to
(A) CV (B) V
C
2
(C)2CV (D) Zero
SOLUTION :
When the key K is kept open the charge drawn
from the source is Q  C'V
Where C' is the equivalent capacitance given by
2
C
C'
Therefore Q = V
2
C




Whey the key K is closed, the capacitor 2 gets short circuited and the charge in the
circuit 1 Q  CV
 Charge flowing is 1
C
Q Q Q V
2
   
 (B)
1 A
2 A
d
1 A
2 A
d 0 
 
 
E

16
EXAMPLE : 10
The figure shows a spherical capacitor with inner sphere earthed. The
capacitance of the system is
(A)
b a
4 0ab


(B)
b a
4 b2
0


(C)  b  a 0 4 (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,
b a
ab
C1 4 0

 
C2  40b
4 b
b a
ab
C 4 0  0

 

b a
4 b
C
2
0



 (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
Q
V  (C)
2C
Q
V  (D) ,
C
Q
V  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 Q CV  q for X and q CV
for Y, as shown in (B). Now, the outer faces must have equal charges.
a b
a b

1 C 2 C

17
 QCV  q  q CV
or 2q  2CV Q
or
2
Q
q  CV 
Potential difference
2C
Q
V
C
q
 
 (C)
EXAMPLE : 12
In an isolated parallel - plate capacitor of capacitance C,
the four surfaces have charges 1 2 3 Q ,Q ,Q and 4 Q as shown. The
potential difference between the plates is
(A)
2C
Q1 Q2 Q3 Q4
(B)
2C
Q2  Q3
(C)
2C
Q2 Q3
(D)
2C
Q1  Q4
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 =
 
2C
Q Q
2C
Q Q
2C
2Q
C
Q2 2 2 2 2  3

 
 
 (C)
* * *
1 Q 3 Q
2 Q 4 Q

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
1
0E2 (k - 1) C) U =
2
1
0E2 




k
1
1 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)

 0 AV
Q
d
B)

 0 KAV
Q
d
C) E =
Kd
V
D)
  
   
 
2
0 AV 1
W 1
2d 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
b a
ab

B) 4  0 a C) 4  0 b D) 40
b a
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) 80r B) 40r C) 40r 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) 3 0 A
d

2) 2 0 A
3d


21
3) 2 0 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 4F charged to 50V is connected to another capacitor of 2F charged to
100V. The total energy of the combination is
1) 4 2
x10 J
3
 2) 3 2
x10 J
2
 3) 2 3 x10 J  4) 8 2
x10 J
3

9. The radii of two charged metal spheres are 5cm and 10cm both having same charge
75c. If they are connected by a wire, the quantity of charge transferred through the
wire is
1) 75c 2) 50c 3) 25c 4) 15c
10. Two identical capacitors have equivalent capacity of 2F 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C
2K

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 10F 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 = 10F – 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 10F. 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 5F 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) 2C 2) 3C 3) 5C 4) 10C
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 5F. 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
Qd
V E d
A
Qd t 1
V 1 1
A d k
 

  
     
   

0
2 V t 1 1 1 3
1 1 ; 1
5 V d k 2 k 5
   
         
   
22. Two spheres A and B of radii 4cm and 6cm are given charges of 80C and 40C. If they
are connected by a wire, the amount of charge flowing from one to other is
1) 20C from A to B 2) 16C from A to B
3) 24C from B to A 4) 32C 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
 
 

24C from B to A
23. Three capacitor of capacitance 10F, 15F, 20F are in series with a cell. The charge
drawn from the cell is 60C. 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
p
s s s
q C E C 45
q 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 1
2
0 0
Qd Q 1 1 d d
d 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: C0 t 1 C0 6
C 1 1
t 1 d k C 7
1 1
d 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
5
d, t =
2
5
d & 2 1
2
1 2
C d 5 5
C 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) ½
30. A capacitor of capacity of 10F is charged to 40V and a second capacitor of capacity
15F 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 = 60C
31. A parallel plate capacitor of capacity 100F 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 = ½(C2 – C1)V2 & C2 = 2C
32. A parallel plate capacitor of capacity 5F 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) 2C 2) 3C 3) 5C 4) 10C
Hint: 1 0 Q  C V = 5C; Q2 = C2V = C0V
t 1
1 1
d k
 
   
 
= 10C; 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: 1 1 2 2
1 1 1 1
1 2 1 2
C V 1 C
V & 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 = A 0
1
d t 1
k

 
   
 
35. A 4F capacitor is charged by 200V battery. It is then disconnected from the supply and
is connected to another uncharged capacitor of 2F 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 =  1 2 2 1 1
1 2 2
1 2 1 2
1 C C C V
V 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
1
C V
2
, Potential on second capacitor in contact with the first one V2 = V/2;
U2 =
2
1 V E
C
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) V1 V2
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 3F, 10F and 15F are connected in series to a voltage
source of 100V. The charge on 15F is
1) 50C 2) 100C 3) 200C 4) 280C
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 10F 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) 4 0 Kab
a b


in CGS system
3)
 
4 0 Kab
a b
 

in SI system 4)
Ka b
ab

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) 2 0 A
d

2) 3 0 A
d

3) 4 0 A
d

4) 5 0 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
3
1 2
1 K K
2K
K K K

 

4) 1 3 2 3
1 3 2 3
K K K K
K
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) 20A/d 3) 30A/d 4) 40A/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) 20A/d
3) 30A/d 4) 40A/d
57. An infinite ladder is made as shown in figure using
capacitors C1 = 1 F and C2 = 2F. 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) C(V V )
4
1 2
2
2
1  2) C(V V )
4
1 2
2
3
1  3) 2
C(V1 V2 )
4
1
 4) 2
C(V1 V2 )
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) 2 CV 3) (25/6) 2 CV 4) (9/2) 2 CV
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)
V V
V V
 

2)
V
V V

 
3)
V
VV
4)
V
V V

 
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)
2C
(Q1 Q2 )
2)
C
(Q1 Q2 )
3)
C
(Q1 Q2 )
4)
2C
(Q1 Q2 )
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
0 A
,E 2)
(d )
0 A
 l

,E 3) 






d
, 1
(d )
0 A l
l
E 4) 





d
, 1
d
0 A 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)
2 d
A
n
0
2)
(2 1)d
A
n
0


3)
(2 2)d
A
n
0


4)
(2 1)d
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) E0A/d 2) E0A/2d 3) 2 E0A/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) 0
1 2
2 V
C C
C

2) 0
1 2
1 V
C C
C

3) 0
2
1 2 V
C
C  C
4) 0
1
1 2 V
C
C  C
80. The capacitance of a parallel plate capacitor is 16F. 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
0A
2)
d
30A
3)
d
A
2
3 0
4)
d
20A
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
1 k  2
2 k  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)
K b
K a
2
1
3)
K a
K b
1
2 4)
K b
K a
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) 0
1 2
2 U
C C
C

B) 0
1 2
1 U
C C
C

C) 0
2
1 2
1 2 U
C C
C C
 


 



 D) 0
1 2
1 2 U
2(C C )
C C

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) 2
C( 1 ~ 2 )
2
1
  B) 2
C( 1 2 )
2
1
  
C) 2
2
2
1 C
2
1
C
2
1
   D) 2
2
2
1 C
2
1
C
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)
1 2 3
1 1 2 2 3 3
C C C
C V C V C V
 
 
B) V1 + V2 + V3
C) 0 D)
2
1
3
1
3
2
3
2
1
C
C
V
C
C
V
C
C
V  
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
q q
2
1 2 3 B) 




 
C
q2 q3 C) 


 
C
q q
2
1 2 4 D) 


 
C
q2 q4
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)  


 

 

0 1 k 2
d t
k
t
A
Q
B)   

 

 


1 k 2
d t
k
t
A
4 Q
C)  


 





d t
k
t
k
A
4 Q 1 2 D)  


 

 

 2
1
0 k
d t
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)
1 2 2 1
1 2 0
d d
A
  
  
B)
1 1 2 2
1 2 0
d d
A
  
  
C)
0 1 2 1 2
1 2
( ) d d
A
   
 
D)
( d d )
A
1 2 0 1 1  2 2
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)  2 
2
2
C V1 V
4
1
 B)  2 
2
2
C V1 V
4
1
 C)  2
C V1 V2
4
1
 D)  2
C V1 V2
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
2
0
Ad
6 E
B)
3
2
0
d
4 AE
C)
3
3
0
2d
4 AE
D)
2
0
d
2 AE
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)
2d
AV2
0
B)
d
AV2
0
C)
d
2 AV2
0
D)
2d
3 AV2
0
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
4. 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 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 C2 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
1
C02 (K - 1) D) The change in energy is
2
1
C02





K
1
1
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
1
C0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) 40R
b) Capacity of spherical capacitor
f)
2
0
q
2 AK
c) Force between plates of capacitor
g)
1
2
0E2
d) Energy density of electric field h) q2/2C
PREVIOUS YEAR IIT QUESTIONS :
1. 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 one goes from 0 to 3d [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 V volts . The charge on plates 1 and 4
will be [IIT 1984]
(a)
d
AV
d
AV 0 0 2
.
  (b)
d
AV
d
AV 0 0 2
.
 
(c)
d
AV
d
AV 0 0 2
.
   (d)
d
AV
d
AV 0 0 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) V V V AB BC   100 (b) V V V V AB BC  75 ,  25
(c) V V V V AB BC  25 ,  75 (d) V V V AB BC   50
1 2 3 4 5
–
+
V
V A B
3F
3F 1F
1F
B
10
20 100V
A C
1F

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 2 CV (c)
2
3 2 CV (d)
2
9 2 CV
7. In an isolated parallel plate capacitor of capacitance C, the four
surface have charges 1 Q , 2 Q , 3 Q and 4 Q as shown. The potential
difference between the plates is [IIT-JEE 1999]
(a)
C
Q Q Q Q
2
1 2 3 4   
(b)
C
Q Q
2
2 3 
(c)
C
Q Q
2
2 3 
(d)
C
Q Q
2
1 4 
8. For the circuit shown, which of the following statements is true [IIT-JEE 1999]
(a) With 1 S closed, V 15 V, V 20 V 1 2  
(b) With 3 S closed V V 25V 1 2  
(c) With 1 S and 2 S closed 0 1 2 V  V 
(d) With 1 S and 3 S closed, V 30 V, V 20 V 1 2  
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) q / 2 (c) q (d)
2q
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 P,Q, R and S are
S1 + – S3 + – S2
V1=30V V2=20V
C1=2pF C2=3pF
A B
s
q
+
+
+
+
+
–
–
–
–
–
Q1
Q2
Q3
Q4
X
R
S Q
P
E


39
(a,b,0), (2a,0,0), (a, b,0) 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) qEa 2 (d) [(2 ) ] 2 2 qE a  b
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 :
1 2 3
1 1 1 1
C C C C p
  
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
* * *

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