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The following questions deal with the basic concepts of this section. Answer the following briefly. Go to
the next section only if your score is at least 80%. Do not consult the Study Material while attempting
these questions.
1. When a dielectric is inserted to fill the space between a charged parallel plate capacitor, does the
stored energy increase or decrease given that (a) the battery remains connected; or (b) the battery
is first disconnected?
2. The potential difference across a capacitor is doubled. How does each of the following quantities
change: (a) the capacitance; (b) the stored energy; (c) the stored charge?
3. Given a battery, how would you connect two capacitors, in series or in parallel, for them to store the
greater; (a) total charge; (b) total energy
4. A parallel plate capacitor with large plates is charged and then disconnected from the battery. As
the plates are pulled apart, does the potential difference increase, decrease or remain the same?
How is the stored energy affected?
5. A parallel-plate capacitor is connected to a battery. Consider what happens as you move the plates
closer together.
(a) How are the charge, potential difference, and energy affected?
(b) Would you do positive or negative work in moving the plates?
6. Two identical capacitors are connected as shown in the
above diagram. A dielectric slab is inserted between the
plated of one capacitor, the battery remaining
connected so that a constant potential difference V is
maintained. Describe qualitatively what happens to the
charge, the capacitance, the potential difference for
each capacitor.
V
K
A
B
7. Given two capacitors, C1 = 1 F and C2 = 2 F, and a 12 V battery, find the charge and potential
difference for each if they are connected in series.
8. All the capacitors in the above diagram
are identical, with C = 3 F. What is their
equivalent capacitance?
C
C
C
C
9. Consider the combination of capacitor in
the diagram. The energy stored in the 5
F capacitor is 200 mJ. What is the
energy stored in the 4 F capacitor.
4
F
5
F
3
F
6
F
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10. Find the equivalent capacitance and charge on
5F capacitor
12F
10F
5F
9F
8F
+
–
60V
ANSWERS
1. (a) Increase
(b) Decrease
2. (a) No changed
(b) Increases four times
(c) Increases two times
3. (a) Parallel
(b) Parallel
4. (a) Potential difference increases
(b) Energy stored increases
5. (a) Charge increase, potential difference does not change, energy increases
(b) Negative work
6. Charge increases for each capacitor: the capacitance of capacitor A does not change while that of B
increase: potential difference across A increases and that across B decreases.
7. 8C for C1 & C2 : 8 V for C1 & 4 V for C2
8. 4 F
9. 160 mJ
10. 4F, 50C
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SOLVED OBJECIVE EXAMPLES
Example 1:
A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in
equilibrium if q is equal to
(a)
2
Q
(b)
4
Q
(c)
4
Q
(d)
2
Q
Solution:
Let 2l = distance between the equal charges. For equilibrium of each outer charge,
2
0
2
2
0)2(44 ll
QQq
= 0 q +
4
Q
= 0
q = –
4
Q
(b)
Example 2:
Three point charges 4q, Q and q are placed on a straight line of length l at points distant 0,
2
l
and l respectively. The
net force on charge q is zero. The value of Q is
(a) –q (b) –2q (c)
2
1
q (d) 4q
Solution:
Force between charges 4q and q =
2
2
0
4
4
1
l
q
Force between charges Q and q =
2
0
2
4
1
l
Qq
2
2
0
2
0
4
4
14
4
1
ll
qQq
Q = – q
(a)
Example 3:
A charge Q is placed at each of the two opposite corners of a square. A charge q is placed at each of the other two
corners. If the resultant electric force on Q is zero, then Q is equal to
(a)
q
22
(b)
22
q
(c)
q22
(d)
q22
Solution:
Obviously Q and q should be of opposite signs and the resultant intensity
0
321
EEE
2
0
21 4
1
|||| a
Qq
EE
where ‘a’ is the side of the square.
2
2
0
3)2(
4
1
|| a
Q
E
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Now
||2|| 3121
EEEE
which gives Q = –2
q2
(c)
Example 4:
The wedge-shaped surface in figure is in a region of uniform electric
field E0 along x axis. The net electric flux for the entire closed
surface is
(a)9 E0 (b) 15 E0
(c) 12 E0 (d) zero
4 m
3 m
5 m
Z
X
Y
E
o
Solution:
Since field is uniform, the net flux for the closed surface is zero.
(d)
Example 5:
A charge Q is placed at the centre of a cube. The flux of the electric field through the six surfaces of the cube is
(a)
0
6
Q
(b)
0
Q
(c)
2
6L
Q
(d)
2
3L
Q
Solution:
From Gauss’s law
0
enc
E
Q
(b)
Example 6:
A block of mass m carrying a positive charge q is placed on a smooth
horizontal table, which ends in a vertical wall situated at a distance d
from block. An electric field E is switched on towards right. Assuming
elastic collisions, find the time period of resultant oscillation.
(a)
m
qEd2
(b)
qE
md8
(c)
qE
md2
(d)
qE
md
m
E
d
Solution:
Acceleration of the block a =
m
qE
d =
2
2
1at
Required time = 2t =
qE
8md
(b)
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Example 7:
An electric dipole is placed in an electric field generated by a point charge. Then
(a) the net electric force on the dipole must be zero
(b) the net electric force on the dipole may be zero
(c) the torque on the dipole due to the field may be zero
(d) the torque on the dipole due to the field must be zero
Solution:
The field is not uniform. However, the torque on the dipole can be zero if it is aligned along the line of force.
(c)
Example 8:
An electron having a charge – e located at A in the presence of a point charge +Q located at B is moved to a point C
so that ABC is an equilateral triangle. The work done in this process is
(a)
AC
Q
o
4
1
(b)
AC
Qe
o
4
1
(c)
AB
Qe
o
4
1
(d) zero
Solution:
Electron is moved from A to C. A and C are equidistant from B and hence the potential at A due to charge +Q = potential
at C due to the same charge. Since there is no potential difference between A and C no work is done in moving a charge
from A to C.
(d)
Example 9:
An infinite number of charges each equal to q are placed along the x-axis at x = 1, x = 2,
x = 4, x = 8 and so on. The resultant potential at x = 0 will be
(a)
0
2
q
(b)
0
4
q
(c)
0
8
q
(d)
0
q
Solution:
V =
32
02
1
2
1
2
1
1
4
q
=
q
4 1 1
2
0
=
0
2π
q
(a)
Example 10:
A solid conducting sphere of charge Q is surrounded by an uncharged concentric conducting spherical shell. The
potential difference between the sphere and the shell is V. If the shell is now given a charge of –3Q, the new
potential difference between them will be
(a) V (b) 2 V (c) 4 V (d) –2 V
Solution:
The potential difference depends only on the charge on the inner sphere.
(a)
Example 11:
In a parallel plate capacitor, the plate separation of 10 mm is very small compared with the size of the plates. A
potential difference of 5.0 kV is maintained across the plates. The electric field intensity between the plates is
(a) 500 V/m (b) 2.5 105 V/m (c) 5 105 V/m (d) 2.5 103 V/m
Solution:
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3
3
1010
105
d
V
E
= 5 105 V/m
(c)
Example 12:
Three uncharged capacitors of capacities C1 , C2 , C2 are connected
as shown in figure to one another and to points A, B and C at
potentials V1 , V2 and V3 . Then the potential at O will be
(a)
321
332211
CCC
CVCVCV
(b)
321
321
CCC
VVV
(c)
)(
)(
321
321
CCC
VVV
(d)
321
321
CCC
VVV
O
B
C
A
C
1
C
2
C
3
Solution:
Taking into account the relation between capacitance, voltage and charge of a capacitor, we can write the following
equations for the three capacitors.
1
1
01 C
q
VV
,
2
2
02 C
q
VV
,
3
3
03 C
q
VV
where C1, C2 and C3 are the capacitances of corresponding capacitors and q1, q2 and q3 are charges on the plates.
According to charge conservation law, q1 + q2 + q3 = 0 and hence the potential V0 of the common point is
321
332211
CCC
CVCVCV
0
V
.
(a)
Example 13:
Two capacitors A (2 F) and B(5 F) are connected to two batteries as
shown in the figure. Then the potential difference in volts between
the plates of A is
(a) 2 (b) 5
(c)11 (d)18
A
B
18 V
11 V
5
F
2 F
Solution:
(18 11) =
F
Q
F
Q
F
Q
10
7
52
Q = 10C
F
C
C
Q
V
A
A
2
10
= 5 V
(b)
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Example 14:
The effective capacitance between A and B
is ( each capacitor is of 1 F)
(a)
μF
2
15
(b)
μF
3
17
(c)
μF
8
13
(d)
μF
8
19
A
B
K
M
N
L
O
P
Solution:
Circuit can be redrawn as
8
13
eq
C
F
(c)
B
A
K
M
O
N
L
P
Example 15:
Two identical thin rings, each of radius R metres
are coaxially placed at a distance R metres apart.
If Q1 and Q2 charges are spread uniformly on the
two rings, the work done in moving a charge q
from the centre of one ring to that of the other is
(a) zero
(b) q(Q1 Q2) (
R
0
(421)/2
)
(c)
)(4 R)/Q(Q2q 021
(d)
)(4 0R2/1)2()Qq(Q 21
R
Q1
Q2
1
2
B
R
R
A
q
Solution:
VB =
R
KQ
R
KQ
V
R
KQ
R
KQ
A2
,
2
2112
VA – VB =
1
2
1
2
1
121
R
KQ
R
KQ
VA–VB =
)(
2
1
121 QQ
R
K
, where
0
4
1
K
W = q (VA – VB)
(b)
Example 1:
Two charged balls are attached by silk threads of length l to the same point. Their velocity is
x
K
, where K is a constant and
x is the distance between the balls, x is very small in comparison to l. Find the rate of leakage of charge in 10–5 C/s.
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(take
10
mg
l
, k =
24
)
Solution:
Let T be the tension in each of the silk threads.
T sin = F, T cos = mg
tan =
mg
q
mg
F1
42
0
2
x
Since is small, tan = sin =
l
x
2
O
F
F
mg
mg
x
x =
2
0
2
4
22
x
ll
q
mgmg
F
2
00
2
3
24
2q
mg
q
mg
ll
x
x =
3/2
3/1
0
2q
mg
l
… (i)
3
1
3/1
03
2
2
q
mgdtdq
dtd
dq
dx l
x
3/1
0
3/1
23
2
mgdt
d
q
dt
dq lx
… (ii)
It is given,
3/1
6/1
0
2q
mg
KK
dt
d
l
x
x
… (iii)
From equations (2) and (3), we get,
2/1
0
23
2
mg
K
dt
dq
l
=
2/1
0
2
2
3
l
mg
K
2 10–5
20 C/s
Example 2:
A rigid insulated wire frame in the form of a right-angled
triangle BAC is set in a vertical plane as shown in the Figure.
Two beads of equal masses m = 1 kg each and carrying
the charges q1 =10C and q2 =100C are connected by a cord
of length l = 1m and can slide without friction on the wires.
Considering the case when the beads are stationary
determine (1) angle , (2) tension in cord and (3) normal
reaction on beads. (
1.73
)
C
60°
Q
q2
90°
T-F
P
60°
mg
30°
B
A
R1
q1
Solution:
The bead is at P, having charge q1and weight mg acting vertically downwards. The tension in the string is acting along
PQ. The electrical force F between the beads acting along length PQ is
F =
2
21
0
4
1
l
qq
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R1 is the normal reaction of the wire on the bead. The forces acting are resolved along and perpendicular to AB.
For the equilibrium of bead at P,
mg cos 60 = (T F) cos (parallel to AB) … (i)
R1 = mg cos 30 + (T F) sin … (ii)
For equilibrium of bead at Q ,
mg sin 60 = (T F) sin … (iii)
R2 = mg sin 30 + (T F) cos … (iv)
Dividing equation (iii) by equation (i) tan 60 = tan
This gives = 60
From equation (3), T F = mg
or
2
0
21
4l
qq
T
= mg
or T =
2
0
21
4l
qq
mg
= 19 N … (v)
From equations (2) and (4)
R1 = mg cos 30 + (T F) sin 60
= mg cos 30 + mg sin 60 =
3
mg = 17 N
R2 = mg sin 30 + mg cos 60 = mg = 10 N.
Example 3:
Four charges + q, + q, – q and – q are placed respectively at the corners
A, B, C and D of a square of side a =
cm15
arranged in the given
order. If E and P are the midpoints of sides BC and CD respectively,
what will be the work done in carrying a charge q0 from O to E and from
O to P?
(take q = 10 C, q0 =
5
C)
A
D
C
B
+q
+q
–q
–q
O
E
P
Solution:
ABCD is the given square of side a. The charges are placed at the corners as shown. O is the midpoint of square.
OA = OB = OC = OD = r (say) =
2
a
Potential at O due to the charges at the corners =
r
q
r
q
r
q
r
q
o
4
1
= 0
Therefore O is at zero potential. The electric field at O due to charge at A
=
2
4
1
r
q
o
along OC.
To find the work done in carrying a charge e from O to E
Potential at O = 0
Potential at E =
CEDEBEAE
q
o
1111
4
Since AE = DE and BE = CE the summation in bracket vanishes. So potential at E = 0.
Hence no work is done in moving the charge from O to E.
To find the work done in carrying the charge from O to P
Potential at P =
CPDPBPAP
q
o
1111
4
=
DPAP
q
o
11
4
2
Now AP =
22 DPAD
=
2
2
2
a
a
=
a
2
5
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DP =
2
a
Potential at P
V =
a
a
q
o
2
5
2
4
2
=
a
q
o5
522
4
2
=
a
q
o5
)51(4
4
Potential difference between O and P =
a
q
o5
514
4
0
=
a
q
o5
154
4
Work done in carrying a charge e from O to P =
a
qe
5
154
4
1
0
J = 36 J
Example 4:
A particle of positive charge Q = 8q0, is having a fixed position P. Another charged particle of mass m and charge q =
10 C moves at a constant speed in a circle of radius r1 = 2 cm with centre at P. Find the work that must be done to
increase the radius of circle to r2 = 4 cm.
Solution:
Let q orbit round Q in a circle of radius r.
K.E. of orbiting particle =
2
1
mv2. ... (i)
where v is orbital velocity.
Potential energy of q =
r
qQ
o
4
1
.... (ii)
P.E. is negative since q is negative.
Electrostatic attraction on q =
2
4
1
r
Qq
o
.... (iii)
This is used as centripetal force required for circular motion.
r
mv 2
=
2
4
1
r
Qq
o
r
Qq
mv
o
4
1
2
.... (iv)
From (1) and (4)
K.E. =
2
2
1mv
=
r
Qq
o24
1
Total energy of the orbiting charge
= K.E. + P.E.
=
1
2
r
Qq
r
Qq
oo
4
1
4
1
= –
2
1
.
r
Qq
o
4
1
The total energy of q when in orbit of radius r1
E1 = –
2
1
.
1
4
1
r
Qq
o
When it is in orbit of radius r2
E2 = –
2
1
.
2
4
1
r
Qq
o
The work done on q = change in energy
= E2 E1
= –
2
1
.
12 4
1
2
1
4
1
r
Qq
r
Qq
oo
=
21
11
8rr
Qq
o
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=
210
2
011
8
8
rr
q
= 90 J
Example 5:
A ball of mass m = 100 gm with a charge q can rotate in a vertical
plane at the end of a string of length l = 1 m in a uniform
electrostatic field whose lines of force are directed upwards. What
horizontal velocity must be imparted to the ball in the upper
position so that the tension in the string in the lower position of
the ball is 15 times the weight of the ball? (given qE = 3 mg)
E
B
v1
T1
mg
T2
qE
A
v2
mg
Solution:
As per principle of conservation of energy,
K.E. at B + P.E. at B = K.E. at A + P.E. at A.
Gain in K.E. = K.E. at A K.E. at B
=
2
1
2
2
2
1vvm
… (i)
Loss in P.E. = P.E. at B P.E. at A.
= loss in gravitational P.E. at B gain in electrical energy at A
= mg(2 l ) (qE) 2l = (mg qE)2 l … (ii)
P.E. at B P.E. at A = K.E. at A K.E. at B
i.e., (mg qE) 2 l =
2
1
2
2
2
1vvm
… (iii)
Centripetal force at A =
2
2
mv
= (T2 + qE mg) … (iv)
From equation (3)
2
2
mv
= 2(mg qE)2 l +
2
1
mv
From equation (4)
2
2
mv
= l (T2 + qE mg)
i.e., 2(mg qE)2 l +
2
1
mv
= l (T2 + qE mg)
i.e., 4 mg 4qE +
l
2
1
mv
= T2 + qE mg … (v)
Given in problem, T2 = 15 mg
4 mg 4qE +
2
1
v
m
l
= 15 mg + qE mg
or
2
1
v
m
l
= 10 mg + 5qE
or
m
vl
2
1
(10 mg + 5qE)
Horizontal velocity to be imparted to the ball,
1/2
1qE)5mg(10
m
l
v
= 50 m/s
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Example 6:
In the figure shown alternative positive and negative charges
of magnitude q = 10C are placed at the corners of a cube of
side length a = 1m. What is the work done (in mJ) in moving
the charges far from each other.
–q
+q
–q
+q
–q
q
+q
–q
Solution:
Initial electrostatics potential energy of the system
a
Kq
a
Kq
a
Kq
Ui3
4
2
12
12 2
2
2
=
3
4
2612
2
a
Kq
=
431266
3
2
a
Kq
+q
–q
+q
–q
+q
–q
–q
+q
Final electrostatics potential energy of the system is zero.
i.e., UF = 0
W =
a
Kq
3
2
431266
work done =
63236
a3
2Kq2
= 5357 J
Example 7:
A capacitor is formed by two square metal plates of edge a
separated by a distance d = 0.061m. The dielectrics of dielectric
constants K1= 20 and K2 = 40 are filled within the gap, as shown in
Figure. Find the equivalent capacitance in nF. (loge 2 = 0.69, 0=
8.85 20–12)
A
B
f
e
a
C
D
g
h
d
dx
x
K1
K2
Solution:
Let us consider a capacitor efgh at distance x from C and of width dx.
The capacitor is made of two small capacitors in series, one of
dielectric constants K1 and the other of dielectric constant K2. Let dC1
and dC2 be the capacitances of the small capacitors.
y
x
y
daK
dC
yd
daK
dC xx 02
2
01
1;
)(
… (i)
y = x tan =
a
d
x
)(
2
0101
1x
x
x
x
ad
daK
a
d
d
daK
dC
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d
daK
a
d
daK
dC x
x
xx2
0202
2
The equivalent capacitance of efgh
=
x
x
x
x
daK
d
daK
ad
dCdCdC 2
02
2
01
21
)(111
=
x
xx
daKK
dKadK
2
021
12 )(
i.e. dC =
x
x
xx
x
dKKdaK
daKK
dKadK
daKK
)()( 212
2
021
12
2
021
=
x
x
)( 212
2
021
KKaKd
daKK
The differential capacitors are in parallel and x varies from 0 to a. The effective equivalent capacitance C is
C =
a
KKaK
d
d
aKK
0212
2
021
)( x
x
=
a
e
KK
KKaK
d
aKK
0
21
212
2
021 )(log
x
=
aKaKKaK
dKK
aKK
ee 2212
21
2
021 log)(log
)(
=
aK
aK
dKK
aKK
e
2
1
21
2
021 log
)(
=
2
1
21
2
021 log
)( K
K
dKK
aKK
e
or C =
1
2
e
12
2
021
K
K
log
)dK(K
aεKK
= 4 nF
Example 8:
Five capacitors, two batteries and two switches are connected as shown in the Figure. Initially S1 and S2 are open and
all the capacitors are uncharged. After S1 and S2 are closed and steady state is attained, find the p.d. between the
terminals of the 3 F and 5 F capacitor.
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13 V
E
2
4 F
e
3 F
d
4 F
c
55 V
E
1
S
1
2 F
a
b
5 F
S
2
Solution:
Assume that the p.d. across the capacitor C connected in the middle is V.
Effective p.d. across left branch = (55 V) V
Equivalent capacity C =
F
5
6
32
32
charge in 2 F capacitor Q = CV =
5
6
)55(V
Effective p.d. across 5 F capacitor = (13 + V) V
Equivalent capacity of the right branch =
F
9
20
45
45
Charge in 5 F capacitor =
)13(
9
20 V
Equating the charges in the capacitors,
VVV 4)13(
9
20
5
6
)55(
i.e.,
)55(
5
6
4)13(
9
20 VVV
5
6330
9
3620260 VVV
or 1300 + 100 V + 180 V = 2970 54 V or 334 V = 1670 or V = 5
P.d. across 3 F capacitor =
C
Q
= (55 – 5) ×
5
2
= 20 V
P.d. across 5 F capacitor =
9
4
)513(
= 8 V
Example 9:
Find the electric flux crossing the wire frame ABCD of length
l = 1m width b and whose center is at a distance OP = d (=b/2) from an
infinite line of charge with linear charge density
= 10–9 c/m. Consider that the plane of frame is perpendicular to
D
C
l
b
P
d
B
A
O
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line OP.
Solution:
Flux through the element of width dx as shown in figure is
ldxds
d
EdsE
and
sec2
,.
0
ldx
d
b
b
sec
cos
20
2/
2/
dx
dx
d
d
lb
b
2
22
2/
2/
0
2
2d
b
tan
l1
0
= 90
d
ds
E
x
dx
Example 10:
A capacitor of capacitance C1 = 1 F can withstand a maximum voltage of V1 = 6kV and another capacitor of
capacitance C2 = 2 F can withstand a maximum voltage of V2 = 4 kV. If they are connected in series what maximum
voltage (in volts) will the system withstand.
Solution:
Maximum charge C1 and hold,
36
111 106101
VCQ
,
C1063
1
Q
and maximum charge C2 can hold
36
222 104102
VCQ
,
C1083
2
Q
when connected in series, both will have equal charges and so
each can have charge Q1 which is smaller of the two.
In this case
Voltage across C1 = 6 kV
And voltage across
6
3
2
1
2102
106
C
Q
C
3 kV
maximum voltage across the system = (6 + 3) kV = 9000 V
MIND MAP
1. Coulomb’s Law
2
21
0
4
1
r
qq
F
where
0
4
1
=
9
109
Nm2C–2
2. (i) Electric field intensity due
to a point charge
3. Electric flux through a surface
SdE
E.
4. Gauss’s law
0
.
q
SdE
5. Electric field intensity
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MIND MAP
ELECTRIC FIELD
6. Electric field intensity due to a uniformly
charged spherical shell or a solid
conducting sphere
(i) At an external point
2
0
4
1
r
Q
E
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
O
r
P
R
(ii) At an internal point
E = 0
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
P
r
O
7. Electric field intensity due to a uniformly
charged non-conducting sphere
(i) At an external point
2
0
4
1
r
Q
E
+ + +
+ + +
+ + +
+
+
P
r
O
(ii) At an internal point
r
R
Q
E3
0
4
1
+
+ + + +
+ + +
+
r
P
8. Energy Density of an electric field
=
2
0
2
1E
1. (i) Electric potential at a point due to a
point charge
r
q
V
0
4
1
+q
O
r
A
The electric potential at A is positive, if the
point charge q is positive and negative if
the point charge is negative.
(ii) Electric potential
0
q
W
Vext
(iii) The p.d. between two points, A and B,
is given by
B
A
AB drEVV .
2. Electric potential at an axial point of a
uniformly charged ring.
V =
22
0
4
1
rR
Q
+
+
+
+
+
+
+
+
+
+
R
O
r
P
3. Electric potential at an axial point of a
uniformly charged non-conducting disc
of surface charge density .
rrRV 22
0
2
+
+
+
+
+
+
+
+
+
+
P
r
R
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MIND MAP
4. Electric potential due to a uniformly
charged spherical shell or conducting
sphere at
(i) an external point
r
Q
V
0
4
1
+
+
+
+
+
+
+
+
+
+
+
+
+
P
O
R
r
(ii) an internal point
R
Q
V
0
4
1
(iii) Variation of Electric Potential with
distance (r )
V
O
r = R
r
R
Q
0
4
1
5. Electric potential due to a uniformly
charged non-conducting sphere at
(i) an external point
r
Q
V
0
4
1
+ + +
+ + +
+ + +
O
R
A
r
(ii) an internal point
3
02
4
1
R
Q
V
[3R2 – r2]
+ + +
+ + + +
+ + + +
+ +
A
O
r
R
6. Electric potential energy of a system of
two point charges
r
qq
U21
0
4
1
ELECTRIC POTENTIAL
1. Electric dipole
When two equal and opposite point charges
are placed at a very short distance it forms
an electric dipole. The magnitude of electric
dipole moment
p = q 2a
p
+q
–q
2a
Electric dipole moment is a vector quantity
and is directed along the axis of the dipole
from the negative to the positive charge.
3. Dipole in an uniform electric field
(i) Torque on a dipole
=
Ep
(ii) Potential Energy of a Dipole
U = –
Ep .
.
(iii) Work-done by the external agent
Wext = pE [cos1 – cos2]
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MIND MAP
2. Electric potential and electric field due to
an electric dipole
(i) End-on position
2
0
4
1
r
p
V
P
–q
O
a
r
+q
3
0
2
4
1
r
p
E
(along
p
)
(ii) Broad-side-on-position
3
0
4
1
0
r
p
E
V
(opposite to
p
)
–q
+q
E
P
r
4. (iii) At any point (r, )
–q
O
+q
r
E
P
2
0
cos
4
1
r
p
V
2
3
0
cos31
4
1
r
p
E
tan =
2
1
tan
ELECTRIC DIPOLE
1. Capacitance of capacitor, C =
v
Q
Capacitance of
(a) Parallel plate capacitor, C =
d
A
0
(b) Spherical capacitor, C =
ab
ab
0
4
(b) Cylindrical capacitor, C =
a
b
nl
l
0
2
2. Energy stored in a charged capacitor
U =
2
2
1CV
=
qV
C
q
2
1
2
2
(a) Energy density of charged capacitor
U =
2
0
2
1E
(b) Force between the plates of capacitor
F =
A
q
0
2
2
1
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EXERCISE – I
IIT JEE & NEET-SINGLE CHOICE CORRECT
1. In induction, the charge induced in the near surface of a dielectric is
(a) equal and similar (b) greater and dissimilar
(c) lesser and dissimilar (d) equal and dissimilar
2. A soap bubble is given a negative charge. Then its radius
(a) decreases
(b) increases
(c) remains unchanged
(d) will change but the information is insufficient to predict whether it will increase or decrease.
3. 64 charged drops of capacity C and potential V are put together to form a bigger drop. If each small drop had
a charge q, then the charge on bigger drop will be
(a) q (b) 4q (c) 16q (d) 64q
4. Charges 2Q and –Q are placed as shown. The point at which electric
field intensity is zero will be
3. Effect of dielectric
(i) When battery is disconnected
C = KC0
K
V
V0
q = q0
E =
K
E0
(ii) When battery is connected
C = KC0
V = V0
q = Kq0
E = E0
4. Grouping of capacitors
(i) When capacitors are in series
...
1111
321 CCCC
(ii) When capacitors are in parallel
C = C1 + C2 + C3 ….
CAPACITOR
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(a) somewhere between –Q and 2Q
(b) somewhere on the left of –Q
(c) somewhere on the right of 2Q
(d) somewhere on the right bisector of line joining –Q and 2Q
–
+
–Q
B
+2Q
5. A positively charged pendulum is oscillating in a uniform electric
field as shown in figure. Its time period as compared to that when it
was uncharged
(a) will increase (b) will decrease
(c) will not change (d) will first increase then decrease
+ + + + + + +
– – –
– – –
+
6. In which of the following states is the potential energy of an electric dipole maximum?
(a)
–q
+q
E
(b)
–q
+q
E
(c)
+q
E
–q
(d)
+q
–q
E
7. The equivalent capacitance between A and B in the figure is
1F. Then the value of the capacitance C is
(a) 1.4 F (b) 2.5 F
(c) 3.5 F (d) 1.2 F
2.5F
1F
A
C
B
8. Three capacitors each of 1 F are connected as shown. The
capacitance between the points A and B is
(a) 3 F (b) 1 F
(c) (2/3) F (d) (1/3) F
A
B
1F
1F
1F
9. A hollow charged sphere of radius R has a constant surface charge density . The variation of the electric
field strength E with distance x from the centre of the sphere is
(a)
x =R
E
O
(b)
x =R
E
O
(c)
x =R
E
O
(d)
x =R
E
O
10. In the figure, the potential at X due to the charges +Q and –Q
is, using SI units,
2d
d
+Q
–Q
X
(a)
d
Q
0
9
2
(b)
d
Q
0
6
(c)
d
Q
0
4
3
(d)
d
Q
0
6
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11. The three capacitors in figure, store a total energy of
(a) 12 J (b) 36 J
(c) 48 J (d) 80 J
3F
4V
6F
6F
12. Four metallic plates, each having area A, are placed as shown.
The distance between the consecutive plates is d. Alternate
plates are connected to points A and B. The equivalent
capacitance of the system between A and B is
A
B
(a) 0A/d (b) 20A/d (c) 30A/d (d) 40A/d
13. A particle of mass m and charge q is placed at rest in a uniform
electric field E as shown and released. The kinetic energy it
attains after moving a distance y is
(a)
qEy
2
1
(b) qEy
(c) qE2y (d)
)(
2
1qEym
q
+ + + + +
– – – – –
14. A and B are two concentric spheres. If A is given a charge Q while
B is earthed as shown in figure,
(a) the charge density of A and B are same
(b) the field inside and outside A is zero
(c) the field between A and B is not zero
(d) the field inside and outside B is zero
A
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
15. A capacitor connected to a 10V battery collects a charge 40 microcoulomb with air as dielectric and 100
microcoulomb with oil as dielectric. The dielectric constant of the oil is
(a) 4 (b) 2.5
(c) 0.4 (d) 1.0
16. A dielectric slab is inserted between the plates of an isolated capacitor. The force between the plates will
(Thickness of slab is less than separation between plates)
(a) increase (b) decrease
(c) remain unchanged (d) become zero
17. A thin metal plate P is inserted between the plates of a parallel-
plate capacitor of capacitance C in such a ways that its edges
touch the two plates (see the figure). The capacitance now
becomes
(a) C/2 (b) 2C
(c) 0 (d)
P
18. Three identical metallic uncharged spheres A, B and C of radius a are kept at the corners of an equilateral
triangle of side d (d >>a). The fourth sphere (of radius a) which has a charge q touches A and is then
removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed.
The charge on C is
(a)
d
ad
d
qa
2
2
2
(b)
d
ad
d
qa 2
2
(c)
d
ad
d
qa
2
(d)
d
ad
d
qa
2
2
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19. Two similar conducting balls of mass m are hung from silk threads of
length L and carry similar charges q as shown in the figure. Assuming
to be small, the distance x between the balls is
(a)
3/1
0
2
4
mg
Lq
(b)
3/1
0
2
2
mg
Lq
m
m
q
q
x
L
L
(c)
2/3
0
2
4
mg
Lq
(d)
2/1
0
2
2
mg
Lq
20. A charge Q is placed at each of the two opposite corners of a square. A charge q is placed at each of the
other two corners. If the resultant force on Q is zero, then
(a)
qQ 2
(b)
qQ 2
(c)
qQ 22
(d)
qQ 22
21. If there are n capacitors in parallel connected to V volt source, then the energy stored equal to
(a) CV (b)
2
2
1nCV
(c)
2
CV
(d)
2
2
1CV
n
22. Three charges –q1, +q2 and –q3 are placed as shown in the figure.
The x-component of the force on –q1 is proportional to
(a)
sin
2
3
2
2
a
q
b
q
(b)
cos
2
3
2
2
a
q
b
q
(c)
sin
2
3
2
2
a
a
b
q
(d)
cos
2
3
2
2
a
q
b
q
a
–q3
–q1
+q2
b
y
23. If the electric flux entering and leaving an enclosed surface respectively is 1 and 2, electric charge inside
the surface will be
(a)
0
21 )(
(b)
0
12 )(
(c) (1 + 2)0 (d) (2 – 1)0
24. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the
shell. The electrostatic potential at a point P a distance R/2 from the centre of the shell is
(a)
R
q
R
Q
00 4
2
4
2
(b)
R
q
R
Q
00 44
2
(c)
R
Qq 2
4
)(
0
(d)
R
Q
0
4
2
25. A charged particle q is shot from infinity towards another charged
particle Q, which is fixed, with a speed v. It approaches Q upto a
closest distance r and then returns. If q were given a speed of 2v,
the closest distance of approach would be
q
v
Q
r
(a) r (b) 2r
(c) r/2 (d) r/4
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EXERCISE – II
IIT-JEE-SINGLE CHOICE CORRECT
1. Two small balls with like charges are suspended by light strings of equal length L from the same point. When
taken to a place where they are in a state of weightlessness the separation between the balls will be
(a) 2 L (b)
2
L
(c)
2
)1( LL
(d)
)1( LL
2. A particle of mass m and charge q starts moving from rest along a straight line in an electric field E = E0 – ax
where a is a positive constant and x is the distance from starting point. Find the distance travelled by the
particle till the moment it came to instantaneous rest
(a)
a
E0
2
(b)
a
E0
(c)
m
qE0
(d)
q
E0
3. The charge on a drop of water is 3 10–8 C. If its surface potential is 500 V, its radius must be equal to
(a) 81 cm (b) 54 cm (c) 27 cm (d) 108 cm
4. A and B are two thin concentric hollow conductors having radii a and b and charges Q1 and Q2 respectively.
Given that a > b and P is a point between the two spheres and distance of P from the common centre is r (b
< r < a). The potential at P is proportional to
(a)
r
QQ 21
(b)
r
Q
a
Q21
(c)
b
Q
a
Q21
(d)
a
Q
b
Q21
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5. How should 5 capacitors each of value 1 F be connected so as to produce a total capacitance
7
3
F?
(a) Two capacitors in parallel and the combination in series with other three capacitors
(b) Three capacitors in parallel and the combination in series with other two capacitors
(c) Four capacitors in parallel and combination in series with fifth capacitor
(d) All capacitors in parallel
6. In the network shown, we have three identical
capacitors. Each of them can withstand a
maximum 100 V p.d. What maximum voltage can
be applied across A and B so that no capacitor
gets spoiled?
(a) 150 V (b) 120 V
(c) 180 V (d) 200 V
B
A
C
C
C
7. Three point charges q, q, –2q are placed on an equilateral
triangle of side a. The magnitude of dipole moment of the
arrangement is
(a)
qa3
(b)
qa
2
3
(c)
qa32
(d) 2qa
–2q
q
q
a
8. Four plates of area A are arranged as shown. The equivalent
capacitance between A and B is
(a)
d
A
3
20
(b)
d
A
2
30
(c)
d
A
3
40
(d) none
A
B
d
d
d
9. Three positive and three negative charges of equal magnitude are
placed at the corners of a regular hexagon PQRSTU. If electric field at
O due to all the charges is twice the field at O due to a positive charge
at R only, the order in which the charges are placed at PQRSTU is
P
Q
R
S
T
U
O
(a) + + + (b) + + + (c) + + + (d) + + +
10. Three charges q1, -q1 and q2 are placed as shown. S is a spherical Gaussian
surface. Electric field at any point on S is
(a) due to q2 only (b) uniform on all the points
(c) zero on all the points (d) due to all charges
q1
-q1
q1
S
q2
11. One plate of a capacitor having charge Q, and plate area A, is pulled
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by a man keeping one plate at fixed position , as shown in figure
.What force should be applied by the man such that , plate moves
with constant velocity.
(a)
0
2
A
Q
(b)
0
2
3
2
A
Q
(c) zero (d)
A
Q
0
2
2
12. A particle A has charge +q and particle B has charge + 4q with each of them having the same mass m, when
allowed to fall from rest through the same electrical potential difference in a gravity free space, the ratio of
their speeds
BA vv /
will become
(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1
13. In the circuit shown, a potential difference of 60 V is
applied across AB. The potential difference between
the points M and N is
(a) 10 V (b) 15 V
(c) 20 V (d) 30 V
C
C
B
A
2C
M
N
2C
60 V
14. A conducting sphere of radius 10 cm is charged with 10C. Another uncharged sphere of radius 20 cm is
allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on
the spheres will be in the ratio of
(a) 1 : 4 (b) 1 : 3 (c) 1 : 2 (d) 1 : 1
15. Five vertices of a regular hexagon of side L are occupied by five point charges. The value of each point charge
is +q. Another point charge –q is placed at the centre of the hexagon. What is the magnitude of the force on
–q due to all the charges placed at the vertices of hexagon?
(a)
2
0
2
34 L
q
(b)
2
0
2
4
3
L
q
(c) zero (d)
2
0
2
4L
q
16. A, B, C, D corners of a square are occupied by q, –q, 2Q and Q charges respectively. The side of square is 2a.
The field at the mid point of side CD is zero. What is the value of
Q
q
?
(a)
2
55
(b)
5
22
(c)
5
2
(d)
2
5
17. The variation of electric field between the two charges q1 and q2
along the line joining the charges is plotted against distance
from q1 (taking rightward direction of electric field as positive)
as shown in the figure. Then the correct statement is
(a)
1
q
and
2
q
are positive charge and
21 qq
(b)
1
q
and
2
q
are positive charges and
21.qq
(c)
1
q
and
2
q
are negative charges and
21 qq
E
q2
q1
x
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(d)
1
q
and
2
q
are negative charges and
21.qq
18. Charge q is distributed uniformly on an arc of radius R
subtending an angle /2 at its centre. Another charge –q is
placed at the centre of the arc. The electric dipole moment of
the system is
-q
+q
+
+
+
+
+
+
(a)
qR22
(b)
qR2
(c)
qR
(d)
qR2
19. Two thin different dielectrics are inserted between a parallel
plate capacitor. Then electric field verses separation graph is (k1 <
k2)
+
+
+
+
+
+
+
k1
k2
–
–
–
–
–
–
–
–
Q
–Q
a
E
(a)
a
E
(b)
a
E
(c)
a
E
(d)
20. A uniform rod of length l and mass m charged with a
charge q is hanging from one of its ends as shown in
figure. At t = 0 a horizontal electric field E is switched on
in the horizontal direction perpendicular to the rod. Find
the minimum value of E so that the rod rotates upto
horizontal level.
E
+
+
+
+
+
(a)
q
mg2
(b)
q
mg
(c)
q
mg
2
(d) none
ONE OR MORE THAN ONE CHOICE CORRECT
1. Which statement(s) is/are correct?
(a) Electric field at the equatorial point on a dipole will be anti parallel to the dipole moment.
(b) Electric field lines begin from (+q) charge and terminate in (–q) charge.
(c) Electric field lines intersect at only one point
(d) Charge is always associated with mass
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2. A particle of mass m and charge q is fastened to one end of a
string of length l. The other end of the string is fixed to the
point O. The whole system lies on a frictionless horizontal
plane. Initially, the mass is at rest at A. A uniform electric field
in the direction shown is then switched on. Then
(a) the speed of the particle when it reaches B is
m
qEl2
(b) the speed of the particle when it reaches B is
m
qE l
A
B
O
60°
E
l
(c) the tension in the string when particles reaches at B is 2qE
(d) the tension in the string when the particle reaches at B is zero
3. A capacitor C is charged to a potential V by a battery. The emf of the battery is V. It is then disconnected
from the battery and again connected with its polarity reversed to the battery.
(a) the work done by the battery is 2CV2
(b) The total charge that passes through battery is 2 CV.
(c) The initial energy of the capacitor is greater than the final energy of the capacitor
(d) The heat generated in the circuit is 2CV2
4. Three identical metallic plates are placed at a separation of d1 and d2
as shown in figure. A charge Q is given to middle plate which is free
to move, then
(a) it will slide towards left if d2 > d1
(b) it will slide towards right if d2 < d1
(c) it will remain in equilibrium if d1 = d2
(d) it will remain in equilibrium in all the cases
d1
d2
Q
5. Three capacitors each having capacitance C = 2F are
connected to battery of emf 30 V as shown in the figure.
When the switch is closed.
(a) the amount of charge flow through the battery is 20 C
(b) heat generated in the circuit is 0.6 mJ
(c) work done by the battery is 0.6 mJ
(d) the charge flow through the switch is 60 C
S
C
C
C
30V
6. Three charged particles are in equilibrium under their electrostatic force only. Then choose the correct statements
(a) the particles must be collinear
(b) all charges cannot have same magnitude
(c) all charges cannot have same nature
(d) the equilibrium is unstable
7. Charges Q1 and Q2 are inside and outside respectively of a closed surface S. Let E be the field at any point on S and
be the flux of E over S. Then choose the correct statements
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(a) if Q1 changes, both and E and will change
(b) if Q2 changes, E will change but will not change
(c) if Q1 = 0 and Q2 = 0, then E 0 but = 0
(d) if Q1 = 0 and Q2 = 0, then E = 0 and = 0
8. Two point charges +q and –q are held fixed at (–d, 0) and (d, 0) respectively of a (x, y) co-ordinate system,
then:
(a) The electric field
E
at all points on the x-axis has the same direction.
(b)
E
at all points on the y-axis is parallel to x-axis
(c) Work has to be done in bringing a test charge from infinity to the origin
(d) The dipole moment is 2qd directed along – ve x-axis.
9. 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 the process of inserting the slab, then
(a)
d
AV
Q0
(b)
d
KAV
Q0
(c)
Kd
V
E
(d)
Kd
AV
W1
1
2
2
0
10. An elliptical cavity is carved within a perfect conductor. A positive
charge q is placed at the centre of the cavity. The points A and B
are on the cavity surface as shown in the figure. Then
(a) electric field near A in the cavity = electric field near B in the
cavity.
(b) charge density at A = charge density at B
(c) potential at A = potential at B
(d) total electric field flux through the surface of the cavity is
q/0.
A
q
B
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EXERCISE –III
MATCH THE FOLLOWING
Note: Each statement in column – I has one or more than one match in column –II.
1. A parallel plate capacitor with air between its plates is charged using a battery and then disconnected from
the battery.
Column – I
Column -II
I. Potential difference between the plates
will decrease if
A. Separation between the plates is increased
to K/2 times the initial value and space
between the plates after the separation has
increased, is completely filled with a
dielectric (here K is the dielectric constant)
II. Electric field strength between the plates
will reduce if
B. Separation between the plates is increased
III. Electric energy stored in the capacitor
will decrease if
C. A dielectric with K > 1 is filled between the
plates of capacitor.
IV. Electric energy density will decrease if
D. Separation between the plates is reduced
E. Area of the plates is increased
REASONING TYPE
Directions: Read the following questions and choose
(A) If both the statements are true and statement-2 is the correct explanation of statement-1.
(B) If both the statements are true but statement-2 is not the correct explanation of statement-1.
(C) If statement-1 is True and statement-2 is False.
(D) If statement-1 is False and statement-2 is True.
1. Statement-1: A positively charged particle always moves along an electric line of force.
Statement-2: Force on a charged particle is tangential to electric line of force.
(a) (A) (b) (B) (c) (C) (d) (D)
2. Statement-1: If the electric field intensity
E
is zero at a point, then electric potential should be necessarily
zero at that point (assuming potential is zero at infinity)
Statement-2: Electric field is zero at a point exactly midway between two equal and similar charge.
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(a) (A) (b) (B) (c) (C) (d) (D)
3. Statement-1: Electric field is discontinuous across the surface of a charged conductor.
Statement-2: Electric potential is constant on the surface of conductor.
(a) (A) (b) (B) (c) (C) (d) (D)
4. Statement-1: Work done by the electrostatic field on charge moving on circular or elliptical path will be zero.
Statement-2: electrostatic field is a conservative field.
(a) (A) (b) (B) (c) (C) (d) (D)
5. Statement-1: Electric lines of forces are perpendicular to equipotential surface.
Statement-2: Work done by electric field on moving a positive charge on equipotential surface is always zero.
(a) (A) (b) (B) (c) (C) (d) (D)
LINKED COMPREHENSION TYPE
The capacitors in the figure are initially uncharged and are connected as shown.
a
b
S
28 V
6
F
8
F
5
F
13
F
1. What is the potential difference Vab ?
(a) 4.2 V (b) 5.2 V
(c) 6.2 V (d) 7.2 V
2. Now the key S is closed. What is the potential of point a?
(a) 9.2 V (b) 9.4 V
(c) 9.6 V (d) 7.8 V
3. How much charge flowed through the switch when it was closed?
(a) 3.36 C (b) 33.6 C
(c) 336 C (d) 0.336 C
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SUBJECTIVE PROBLEMS
1. Two charges 500 C each are at a distance r from each other. A third charge q is placed on the line joining
the above two charges such that all the three charges are in equilibrium. What is the magnitude (in C) of
charge q ?
2. Two uniformly charged large plane sheets
1
S
and
2
S
having charge densities 1 and 2
21
are placed
at a distance d parallel to each other. A charge q0 is moved along a line of length
daa
at an angle 450
with the normal to
1
S
. Calculate the work done (in Joule) by the electric field. (take 1 - 2 = 4
2
and q0 =
0, a = 1 unit )
3. A particle having a charge 1.6 10–19 C enters midway between the plates of a parallel plate condenser. The
initial velocity of the particle is parallel to the plane of the plates. A potential difference of 300 V is applied to
the capacitor plates. If the length of the plates be 10 cm and the plates are separated by a distance of 2 cm,
calculate the greatest initial velocity (in km/s)for which the particle will not be able to come out of the
capacitor plates. The mass of the charged particle is 12 10–24 kg.
4. Two spherical bobs of same mass and radius having equal charges are suspended from the same point by
strings of same length. The bobs are immersed in a liquid of relative permittivity r and density 0. Find the
density of the bob (kg/m3) for which the angle of divergence of the strings to be the same in the air and in
the liquid? (Take 0 = 200 kg/m3, r = 5)
5. A thread carrying a uniform charge = 10–7c/m has the
configuration shown in figure. Assuming the curvature radius R
=
2
m to be considerably less than the length of the thread,
find the magnitude of the electric field strength at the point O.
(in N/C)
O
R
6. Find the energy stored (in J) in the electric field produced by a metal sphere of radius 1m containing a charge
of 100 C.
7. An isolated conductor initially free from charge is charged by repeated contacts with a plate which after
each contact is replenished to a charge 100 C from an electrophorus. If 20 C is the charge on the
conductor after the first operation, find the maximum charge (in C) which can be given to the conductor.
8. A parallel plate capacitor has a capacity C = 200 F. The gap between the plates is completely filled with a
glass plate of dielectric constant K = 6. The system is connected across a d.c voltage source E = 100 V. Find
the amount of mechanical work done in removing the dielectric plate, battery still connected.
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9 What amount of heat will be generated in the circuit shown in
figure after the switch Sw is shifted from position 1 to position
2?
Given C = 1F, C0 = 4F and = 12V
C0
C
C
1
2
Sw
10. Three concentric, conducting spherical shells A, B and C have radii a = 10 cm, b = 20 cm and c = 30 cm
respectively. The innermost shell A is earthed and charge q2 = 4 C and q3 = 3C are given to shells B
and C respectively. Calculate energy (in mJ) stored in the system.
ANSWERS
EXERCISE – I
IIT JEE & NEET-SINGLE CHOICE CORRECT
1. (c)
2. (b)
3. (d)
4. (b)
5. (a)
6. (a)
7. (a)
8. (c)
9. (d)
10. (b)
11. (c)
12. (c)
13. (b)
14. (c)
15. (b)
16. (c)
17. (d)
18. (c)
19. (b)
20. (d)
21. (b)
22. (a)
23. (d)
24. (b)
25. (d)
EXERCISE – II
IIT-JEE-SINGLE CHOICE CORRECT
1. (a)
2. (a)
3. (b)
4. (b)
5. (b)
6. (a)
7. (a)
8. (a)
9. (d)
10. (d)
11. (d)
12. (a)
13. (d)
14. (c)
15. (d)
16. (a)
17. (a)
18. (a)
19. (b)
20. (b)
ONE OR MORE THAN CHOICE CORRECT
1. (a,b,d)
2. (b,c)
3. (a,b,d)
4. (a,b,c)
5.(a,c,d)
6. (a,b,c,d)
7. (a,b,d)
8. (b, d)
9. (a,c,d)
10. (c,d)
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EXERCISE – III
MATCH THE FOLLOWING
1. I – A, C, D, E; II – A, C, E; III – A, D, C, E; IV – A, C, E
ASSERTION AND REASON
1. (d)
2. (d)
3. (b)
4. (a)
5. (a)
PASSAGE BASED PROBLEMS
1. (a)
2. (c)
3. (b)
EXERCISE – IV
1. 125
2. 2
3. 10
4. 250
5. 900
6. 45 J
7. 25
8. 5 J
9. 96 J
10. 450
Q.1 The capacitance of a metallic sphere will be 1F, if its radius is nearly-
(1) 9 km (2) 10 m
(3) 1.11 m (4) 1.11 cm
Q.2 The energy of a charged conductor is given by the expression-
(1)
C2
q2
(2)
C
q2
(3) 2qC (4)
2
2
C2
q
Q.3 No current flows between two charged bodies connected together when they have the same-
(1) capacitance or Q/V ratio
(2) charge
(3) resistance
(4) potential or Q/C ratio
Q.4 Two spherical conductors A and B of radii R and 2R respectively are each given a charge Q. When they are
connected by a metallic wire. The charge will-
(1) flow from A to B
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 1
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(2) flow from B to A
(3) remain stationary on conductor
(4) none of these
Q.5 The potential energy of a charged conductor of charge (q) and potential (V) is given by-
(1)
2
1
qV (2)
2
1
q2V
(3)
2
1
V
q
(4)
2
1
qV2
Q.6 A conductor of capacitance 0.5F has been charged to 100 volts. It is now connected to uncharged
conductor of capacitance 0.2F. The loss in potential energy is nearly -
(1) 7 × 10–4 J (2) 3.5 × 10–4 J
(3) 14 × 10–4 J (4) 7 × 10–3 J
Q.7 Two spherical conductors of capacitance 3.0F and 5.0F are charged to potentials of 300 volt and 500 volt.
The two are connected resulting in redistribution of charges. Then the final potential is -
(1) 300 volt (2) 500 volt
(3) 425 volt (4) 400 volt
Q.8 N drops of mercury of equal radii and possessing equal charges combine to form a big spherical drop. Then
the capacitance of the bigger drop compared to each individual drop is-
(1) N times (2) N2/3 times
(3) N1/3 times (4) N5/3 times
Q.9 The capacity of a parallel plate condenser is C. Its capacity when the separation between the plates is halved
will be-
(1) 4C (2) 2C (3) C/2 (4) C/4
Q.10 A parallel plate condenser has a capacitance 50F in air and 110 F, when immersed in an oil. The dielectric
constant K of the oil is-
(1) 0.45 (2) 0.55 (3) 1.10 (4) 2.20
Q.11 The capacity of a parallel plate condenser is 5F. When glass plate is placed between the plates of the
conductor, its potential becomes 1/8th of the original value. The value of dielectric constant will be -
(1) 1.6 (2) 5 (3) 8 (4) 40
Q.12 If the p.d. across the ends of a capacitor 4F is 1.0 kilovolt. Then its electrical potential energy will be-
(1) 4 × 10–3erg (2) 2 erg
(3) 2 joule (4) 4 joule
Q.13 A 6F capacitor charged from 10 volts to 20 volts. Increase in energy will be -
(1) 18 × 10–4 J (2) 9 × 10–4 J
(3) 4.5 × 10–4 J (4) 9 × 10–9 J
Q.14 The energy of a charged capacitor resides in -
(1) the electric field only
(2) the magnetic field only
(3) both the electric and magnetic field
(4) neither in electric nor magnetic field
Q.15 The capacity and the energy stored in a parallel plate condenser with air between its plates are respectively
C0 and W0. If the air is replaced by glass (dielectric constant = 5) between the plates, the capacity of the
plates and the energy stored in it will respectively be -
(1) 5C0 , 5W0 (2) 5C0 ,
5
W0
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(3)
5
C0
, 5W0 (4)
5
C0
,
5
W0
Q.16 By inserting a plate of dielectric material between the plates of a parallel plate capacitor, the energy is
increased five times. The dielectric constant of the material is -
(1) 1/25 (2) 1/5 (3) 5 (4) 25
Q.17 A capacitor of capacity C has charge Q and 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
Q.18 A glass slab is put with in the plates of a charged parallel plate condenser. Which of the following
quantities does not change?
(1) energy of the condenser
(2) capacity
(3) intensity of electric field
(4) charge
Q.19 A parallel plate capacitor is connected to a battery and inserted a dielectric plate between the place of plates
then which quantity increase-
(1) potential difference
(2) electric field
(3) stored energy
(4) E. M . F of battery
Q.20 A parallel plate capacitor is connected to a battery and decreased the distance between the plates then
which quantity is same on the parallel plate capacitor-
(1) potential difference
(2) capacitance
(3) intensity of electric field
(4) stored energy
Q.21 A parallel plate capacitor is charged by a battery after charging the capacitor , battery is disconnected. And if
a dielectric plate is inserted between the place of plates. Then which one of the following statements is not
correct-
(1) increase in the stored energy
(2) decrease in the potential difference
(3) decrease in the electric field
(4) increase in the capacitance
Q.22 A parallel plate capacitor has a capacity C. The separation between plates is doubled and a dielectric
medium is inserted between plates. The new capacity is 3C. The dielectric constant of medium is-
(1) 1.5 (2) 3.0 (3) 6.0 (4) 12.0
Q.23 A parallel plate capacitor is charged by a battery after charging the capacitor, battery is disconnected and
decrease the distance between the plates then which following statement is correct ?
(1) electric field is not constant
(2) potential difference is increased
(3) decrease the capacitance
(4) decrease the stored energy
Q.24 The capacitance of a parallel plate condenser does not depend upon-
(1) the distance between the plates
(2) area of the plates
(3) medium between the plates
(4) metal of the plates
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Q.25 A metallic plate of thickness (t) and face area of one side (A) is inserted between the plates of a parallel
plate air capacitor with a separation (d) and face are (A). Then the equivalent capacitance is -
(1)
d
A
0
(2)
)td(
A
0
(3)
)td(
A
0
(4)
)td(
A
0
Q.26 An air capacitor of 1F is immersed in a transformer oil of dielectric constant 3. The capacitance of the oil
capacitor is-
(1) 1F (2)
3
1
F
(3) 3F (4) 2F
Q.27 Two metal plates form a parallel plate condenser. The distance between the plates in d. Now a metal plate
of thickness d/2 and of same area is inserted completely between the plates, the capacitance -
(1) remains unchanged
(2) is doubled
(3) is halved
(4) reduced to one fourth
Q.28 The capacity of a parallel plate capacitor with air as medium is 2F. After inserting a sheet of mica a equal air
thickness , it becomes 5F. The dielectric constant of mica is -
(1) 0.1 (2) 0.4
(3) 2.5 (4) 10
Q.29 A parallel plate capacitor has rectangular plates of 400 cm2 and are separated by a distance of
2 mm with air as medium. What charge will appear on the plates. If a 200 volt potential difference
is applied across the condenser?
(1)3.54 × 10–6 C (2) 3.54 × 10–8 C
(3) 3.54 × 10–10 C (4) 1770.8 × 10–13 C
Q.30 A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is-
(1) increased proportional to 2.
(2) decreased proportional to 1/2
(3) increased proportional to 2
(4) decreased proportional to 1/2
Q.31 A parallel plate capacitor consists of two plates of 2m × 1m. The space between the plates is of 1mm and
filled with a dielectric of relative permittivity of 7. A potential difference of 300 V is applied across the plates.
Find the potential gradient -
(1) 6 × 105 N/C (2) 3 × 105 N/C
(3) 18 × 105 N/C (4) 12 × 105 N/C
Q.32 Two conductors insulated from each other, charged by transferring electrons from one conductor to the
other. After 25 × 1012 electrons have been transferred. The potential difference between the conductors is
found to be 16V. The capacitance of the system is-
(1) 25F (2) .25F
(3) 25 nF (4) 25 PF
Q.33 The energy density in a parallel plate capacitor is given as 2.2 × 10–10 J/m3. The value of the electric field in
the region between the plates is-
(1) 7 NC–1 (2) 3.6 NC–1
(3) 72 NC–1 (4) 8.4 NC–1
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Q.34 If a 10F capacitor is to have an energy content of 1 Joule. It must be placed across a p.d. of (in volts)-
(1) 900 (2) 450 × 108 (3) 200 (4) 450
Q.35 A capacitor of capacitance
3
1
F is connected to a battery of 300 volt and charged. Then the energy stored in
capacitor is-
(1) 3 × 10–2 joule (2) 1.5 × 10–2 joule
(3) 6 × 102 joule (4) 12 × 102 joule
Q.36 The two parallel plates of a condenser have been connected to a battery of 300V and the charge collected at
each plate is 1C. The energy supplied by battery is -
(1) 6 × 10–4 J (2) 3 × 10–4 J
(3) 1.5 × 10–4 J (4) 4.5 × 10–4 J
Q.37 The plates of a parallel plate capacitor are charged with a battery so that the plates of the capacitor have
acquired the P.D. equal to e.m.f of the battery. The ratio of the work done by the battery and the energy
stored in capacitor is-
(1) 2 : 1 (2) 1 : 1 (3) 1 : 2 (4) 1 : 4
Q.38 A parallel plate condenser has plates of area 200 cm2 and separation 0.05cm has been filled with a dielectric
having K = 8 and then charged to 300volts. The final energy of condenser is -
(1) 1.6 × 10–5 J (2) 2.0 × 10–6 J
(3) 12.8 × 10–5 J (4) 64 × 10–5 J
Q.39 Three capacitors of capacity C1 , C2 , C3 are connected in series. Their total capacity will be-
(1) C1 + C2 + C3 (2)
)CCC(
1
321
(3)
1
3
1
2
1
1CCC
(4) none of these
Q.40 Three capacitors each of capacitance 1F are connected in parallel. To this combination a fourth capacitor of
capacitance 1F connected in series. The resultant capacitance of the system is-
(1) 4F (2) 2 F
(3) 4/3 F (4) 3/4 F
Q.41 Two capacitances of capacity C1 and C2 are connected in series and potential difference V is applied across it.
Then the potential difference across C1 will be-
(1) V
1
2
C
C
(2) V
1
21C
CC
(3) V
21
2CC
C
(4) V
21
1CC
C
Q.42 Two condensers of capacities 1F and 2F are connected in series and system charged to
120 volts. Then the P.D on 1F capacitor (in volts) will be-
(1) 40 (2) 60 (3) 80 (4) 120
Q.43 Two condensers of capacity 0.3F and 0.6F respectively are connected in series. The combination is
connected across a potential of 6 volts. The ratio of energies stored by the condensers will be -
(1) 1/2 (2) 2 (3) 1/4 (4) 4
Q.44 Three capacitors Ca < Cb < Cc are connected in series. Their resultant capacitance will be-
(1) equivalent capacitance greater than Cc
(2) equivalent capacitance less than Cc but greater than Ca
(3) equivalent capacitance less than Ca
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(4) equivalent capacitance is infinite
Q.45 The equivalent capacity in the system of capacitance will be-
1.5µF
3µF
3µF
1.5µF
(1) 1F (2) 2F (3) 1.5 F (4) 3F
Q.46 Three capacitors of capacitance 3F , 9F and 18F are connected once in series and another time in
parallel. The ratio of equivalent capacitance in the two cases
p
s
C
C
will be -
(1) 1 : 15 (2) 15 : 1
(3) 1 : 1 (4) 1 : 3
Q.47 Three equal capacitors, each with capacitance C are connected as shown in figure. Then the equivalent
capacitance between A and B is -
C
C
C
B
A
(1) C (2) 3C
(3) C/3 (4) 3C/2
Q.48 Three capacitors are connected to D.C. source of 100 volts as shown in the adjoining figure. If the charge
accumulated on plates of C1 , C2 and C3 are qa , qb, qc , qd , qe , qf respectively then -
2µF
3µF
4µF
a
b
c
d
e
f
100V
(1) qb + qd + qf = 100/9 Coulomb
(2) qb + qd + qf = 0
(3) qa + qc + qe = 50 Coulomb
(4) qb = qd = qf
Q.49 A capacitor C1 = 4F is connected in series with another capacitor C2 = 1F. The combination is connected
across a d.c. source of voltage 200V. The ratio of potential across C1 and C2 is -
(1) 1 : 4 (2) 4 : 1 (3) 1 : 2 (4) 2 : 1
Q.50 Two condensers of 20 and 30 microfarads are connected in series across a 200 volt D.C. supply. Find the
charge on each condenser ?
(1) 2400 C (2) 4200C
(3) 2600C (4) 3000C
Q.51 The three condensers of capacitances 10, 20 and 30F are first connected in series and then connected in
parallel. The ratio of the resultant capacitance in the two cases is -
(1) 1 : 11 (2) 11 : 1
(3) 1 : 6 (4) 6 : 1
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Q.52 Five equal capacitors, each with capacitance (C) are connected as shown in the adjoining fig. Then the
equivalent capacitance between A and B is -
C
C
C
B
A
C
C
(1) C (2) 5C (3) C/5 (4) 3C
Q.53 The total capacity of the system of capacitors shown in adjoining figure between the points A and B is -
2µF
2µF
2µF
1µF
1µF
A
B
(1) 1F (2) 2F (3) 3F (4) 4F
Q.54 The equivalent capacitance between the points A and B in the given diagram is -
2µF
2µF
2µF
2µF
B
A
(1) 8F (2) 6F (3)
3
8
F (4)
8
3
F
Q.55 Five capacitors of 10F capacitor each are connected to a D.C. potential of 100 volts as shown in the
adjoining figure. The equivalent capacitance between the points A and B will be equal to-
10µF
10µF
10µF
10µF
10µF
A
B
100V
(1) 40F (2) 20 F
(3) 30 F (4) 10 F
Q.56 Three capacitors of capacity 10F , 5F and 5F are connected in parallel. The total capacity will be-
(1) 10F (2) 5F
(3) 20 F (4) none of the above
Q.57 Two capacitors connected in parallel having the capacities C1 and C2 are given 'q' charge, which is
distributed among them. The ratio of the charge on C1 and C2 will be -
(1)
2
1
C
C
(2)
1
2
C
C
(3) C1C2 (4)
21CC
1
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Q.58 In an adjoining figure are shown three capacitors C1 , C2 and C3 joined to battery. The correct condition will
be-
V1
C1
Q1
V2
C2
Q2
V3
C3
Q3
V
(1) Q1 = Q2 = Q3 and V1 = V2 = V3 = V
(2) Q2 = Q2 + Q3 and V = V1 + V2 + V3
(3) Q1 = Q2 + Q3 and V = V1 + V2
(4) Q2 = Q3 and V2 = V3
(Symbols have their usual meanings)
Q.59 Two capacitors of equal capacity are first connected in parallel and then in series. The ratio of the total capacities
in the two cases will be -
(1) 2 : 1 (2) 1 : 2 (3) 4 : 1 (4) 1 : 4
Q.60 A 4F condenser is connected in parallel to another condenser of 8F. Both the condensers are then
connected in series with a 12F condenser and charged to 20 volts. The charge on the plate of 4F
condenser is-
(1) 3.3 C (2) 40C
(3) 80 C (4) 240 C
Q.61 If three capacitors each of capacity 1F are connected in such a way that the resultant capacity is 1.5F
then-
(1) all the three are connected in series
(2) all the three are connected in parallel
(3) two of them are in parallel and then connected in series to the third
(4) two of them are in series and then connected in parallel to the third
Q.62 Two capacitor each of 1F capacitance are connected in parallel and are then charged by 200 volts D.C.
supply. The total energy of their charges (in joule is)-
(1) 0.01 (2) 0.02
(3) 0.04 (4) 0.06
Q.63 Four capacitors are connected as shown in the fig. The equivalent capacitance between the points P and Q
is-
1µF
1µF
1µF
1µF
P
Q
(1) 4F (2) 1/4 F
(3) 3/4 F (4) 4/3 F
Q.64 The total capacity of the system of capacitors shown in the adjoining figure between the points A and B will
be-
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3µF
2µF
6µF
1µF
A
B
(1) 1F (2) 2F
(3) 3F (4) 4F
Q.65 Two dielectric slabs of constant K1 and K2 have been filled in between the plates of a capacitor as shown
below. What will be the capacitance of the capacitor -
d/2
d/2
K1
K2
(1)
d
A2 0
(K1 + K2) (2)
d
A2 0
21
21 KK
KK
(3)
A2
d
0
(4)
d
A2 0
21
21 KK
KK
Q.66 A parallel plate capacitor with air as medium between the plates has a capacitance of 10F. The area of
capacitor is divided into two equal halves and filled with two media having dielectric constant K1 = 2 and K2
= 4. The capacitance of the system will now be-
(1) 10F (2) 20 F (3) 30 F (4) 40 F
Q.67 Separation between the plates of a parallel plate capacitor is d and the area of each plate is A. When a slab
of material of dielectric constant K and thickness t (t < d) is introduced between the plates , its capacitance
becomes-
(1)
K
1
1td
A
0
(2)
K
1
1td
A
0
(3)
K
1
1td
A
0
(4)
K
1
1td
A
0
Q.68 If area of each plate is A and plates are separated from each other by a distance d then Ceq. between A and
B is -
A
B
(1)
d
A3 0
(2)
d3
A
0
(3)
d2
A3 0
(4)
d3
A2 0
Q.69 The capacitance of a capacitor, filled with two dielectrics of same dimensions but of dielectric constants K1
and K2 respectively as shown will be -
K1
K2
d
(1)
d2
A
0
(K1 + K2) (2)
d
A
0
(K1 + K2)
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(3)
21
21
0KK
KK
d2
A
(4)
21
21
0KK
KK
d
A
Q.70 The capacitance of a parallel plate capacitor is 2.5F when it is half filled with a dielectric as shown in the
figure, Its capacitance becomes 5F , the dielectric constant of the dielectric is-
Air
Medium
(1) 7.5 (2) 3.0 (3) 0.33 (4) 4.0
Q.71 The capacitance of a spherical condenser is 1F. If the spacing between the two spheres is 1mm, then the
radius of the outer sphere is-
(1) 30cm (2) 6 m (3) 5 cm (4) 3m
Q.72 The capacitance (C) for an isolated conducting sphere of radius (a) is given by 40.a. If the sphere is
enclosed with an earthed concentric sphere. The ratio of the radii of the sphere being (n/n–1) then the
capacitance of such a sphere will be increased by a factor -
(1) n (2) n/(n–1)
(3) (n–1)/n (4) a.n
Q.73 A1 is a spherical conductor of radius (r) placed concentrically inside a thin spherical hollow conductor A2 of
radius (R). A1 is earthed and A2 is given a charge +Q then the charge on A1 is -
(1) –Q (2) Qr/R
(3) –rQ/R (4) –Q (R–r)/R
Q.74 Two spherical conductors A1 and A2 of radii (r1) and (r2) (r2 > r1 ) are placed concentrically in air. A1 is given a
charge +Q while A2 in earthed. Then the capacitance of the system is -
(1) 40
12
21 rr
r.r
(2) 40 (r1 + r2)
(3) 40 . r2 (4) 40
12
2
2rr
r
Q.75 A capacitor of capacitance 100µF is charged by connecting it to a battery of emf 12V and internal resistance
2. The time taken before 99% of the maximum charge is stored on the capacitor-
(1) 0.92 ms (2) 0.4 ms
(3) 0.8 ms (4) 0.1 ms
Q.76 A capacitor of capacitance 0.1 µF is charged to certain potential and allow to discharge through a resistance
of 10 MHow long will it take for the potential to fall to one half of its original value-
(1) 0.1s (2) 0.2346 s
(3) 1.386 s (4) 0.693 s
Q.77 A 500F capacitor is charged at a steady rate of 100C/sec. The potential difference across the capacitor
will be 10V after an interval of-
(1) 5 sec. (2) 20 sec. (3) 25 sec. (4) 50 sec.
Q.78 A C. R series circuit is connected to a battery of e.m.f E. The time required by the capacitor to acquire
maximum charge, depends upon -
(1) R only
(2) C only
(3) RC
(4) applied potential difference
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Q.79 Calculate the charge on the plates of the capacitor C in the given circuit -
E
r
R1
R2
A
B
C
(1) C ×
rR
ER
2
2
(2) C ×
rR
ER
1
1
(3) C ×
21
21 RR
R.RE
(4) C ×
rR
RE
2
1
Q.80 In the adjoining circuit diagram E = 5 volt,
r = 1 ohm , R2 = 4 ohm, R1 = R3 = 1 ohm and
C = 3F. Then the numerical value of the charge on each plate of the capacitor is –
R2
R1
R3
E,r
C
C
C
C
(1) 24C (2) 12C
(3) 6C (4) 3C
Q.81 Two condensers of capacities 2C and C are joined in parallel and charged upto potential V. The battery is
removed and the condenser of capacity C is filled completely with a medium of dielectric constant K . The
p.d. across the capacitors will now be -
(1)
2K
V3
(2)
K
V3
(3)
2K
V
(4)
K
V
Q.82 0.2F capacitor is charged to 600V by a battery. On removing the battery. It is connected with another
parallel plate condenser (1.0F). The potential decreases to-
(1) 100 volts (2) 120 volts
(3) 300 volts (4) 600 volts
Q.83 A 0.01F capacitor is charged to a potential of 500v. It is then connected to an instrument of input
capacitance 1.0F. The p.d across the instrument in V is now-
(1) 1.00 (2) 4.95 (3) 5.00 (4) 50.0
Q.84 A condenser of capacitance 10F has been charged to 100V. It is now connected to another uncharged
condenser. The common potential becomes 40V. The capacitance of another condenser is -
(1) 5F (2) 10F (3) 15F (4) 20F
Q.85 A capacitor having capacitance C is charged to a voltage V. It is then removed and connected in parallel with
another identical capacitor which is uncharged. The new charge on each capacitor is now-
(1) CV (2) CV/2 (3) 2CV (4) CV/4
Q.86 Two capacitors of capacities C1 and C2 are charged to voltages V1 and V2 respectively. There will be no
exchange of energy in connecting them in parallel. If-
(1) C1 = C2 (2) C1V1 = C2V2
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(3) V1 = V2 (4)
1
1
V
C
=
2
2
V
C
Q.1 A parallel plate capacitor is charged and kept connected with the battery. If now a dielectric slab is inserted
between the plates to fill the entire space between the plates then what will be the change in the charge,
potential difference and electric field intensity between the plates respectively -
(1) increases , constant, increases
(2) increases, constant , constant
(3) increases , constant , decreases
(4) constant, decreases , decreases.
Q.2 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 of the previous one as -
(1) Q > Q0 (2) V > V0
(3) E > E0 (4) U U0
Q.3 A battery charges a parallel plate capacitor of thickness (d) so that an energy [U0] is stored in the system. A
slab of dielectric constant (K) and thickness (d) is then introduced between the plates of the capacitor. The
new energy of the system is given by -
(1) KU0 (2) K2 U0
(3)
K
U0
(4) U0/K2
Q.4 Two spheres of radii R1 and R2 have equal charge are joint together with a copper wire. If the potential on
each sphere after they are separated to each other is V, then initial charge on any sphere was (k =
0
4
1
) –
(1)
k
V
(R1+ R2) (2)
k2
V
(R1 + R2)
(3)
k
V
(R1 + R2) (4)
21
21 RR
)RR(
k
V
Q.5 Calculate the reading of voltmeter between X and Y then (VX – VY ) is equal to -
1F
1F
X
2F
3F
6F
20V
A
B
V
Y
(1) 10 V (2) 13.33V
(3) 3.33 V (4) 10.33 V
Q.6 The capacitance of two capacitors was compared with the aid of an electrometer. The capacitors were
charged to potential of
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V1 = 300V and V2 = 100V and were connected in parallel. The potential difference between the plates
measured by the electrometer was 250V. The capacitance ratio is -
(1) 3 : 1 (2) 1 : 3
(3) 1 : 2.5 (4) 2.5 : 1
Q.7 Three capacitors 2, 3 and 4F are connected in series with 6V battery. When the current stops, the charge
on the 3F capacitor is
(1) 5.5 C (2) 4.4 C
(3) 3.3 C (4) 2.2 C
Q.8 There are two metallic plates of a parallel plate capacitor. One plate is given a charge +q while the other is
earthed as shown . Points P , P1 and P2 are taken as shown in adjoining figure. Then the electric intensity is
not zero at -
+
+
+
+
+
+
–
–
–
–
–
–
P1
P
P2
(1) P only (2) P1 only
(3) P2 only (4) P , P1 and P2
Q.9 The resultant capacitance between (A) and (B) in the following figure is -
3µF
3µF
3µF
2µF
A
B
3µF
3µF
3µF
3µF
2µF
(1)1F (2) 3F
(3) 2F (4) 1.5F
Q.10 The diameter of the plate of a parallel plate condenser is 6 cm. If its capacity is equal to a sphere of
diameter 200 cm, the separation between the plates of the condenser is -
(1) 4.5 × 10–4m (2) 2.25 × 10–4m
(3) 6.75 × 10–4 m (4) 9 × 10–4 m
Q.11 Four metallic plates of each with a surface area of one side (A) , are placed at a distance (d) from each other.
The alternate plate are connected to point (A) and (B) as shown in the fig. The capacitance of the system is
A
B
(1)
d
A
0
(2)
d
A2 0
(3)
d
A3 0
(4)
d
A4 0
Q.12 A sheet of aluminium foil of negligible thickness is placed between the plates of a capacitor of capacitance C
as shown in the figure then capacitance of capacitor becomes
d/2
d/2
Foil
(1) 2C (2) C (3) C/2 (4) zero
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Q.13 In above problem if foil is connected to any one plate of capacitor by means of conducting wire then
capacitance of capacitor becomes -
(1) 2C (2) C (3) C/2 (4) zero
Q.14 For circuit, the equivalent capacitance between P and Q is -
Q
P
C
C
C
C
C
C
(1) 6C (2) 4C (3) 3C/2 (4) 3C/4
Q.15 The figure shows a circuit consisting of four capacitors. The effective capacitance between A and B is –
1µF
2µF
1µF
1µF
A
B
(1)
6
5
F (2)
6
7
F (3)
3
8
F (4) 1F
Q.16 The p.d. across the capacitance of 2F in the figure along with is -
3µF
+
6µF
3µF
2µF
–
70V
(1) 10V (2) 60V (3) 28 V (4) 56V
Q.17 A circuit is shown in the figure below. Find out the charge of the condenser having capacity 5F-
2µF
+
–
6V
3µF
5µF
4µF
(1) 4.5 µC (2) 6.0 µC (3) 9.0 µC (4) 30 µC
Q.18 In the circuit shown in the following fig. The p.d across 3F capacitor is -
20V
5µF
3µF
4V
(1) 4 V (2) 6 V (3) 10 V (4) 16 V
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Q.19 Three capacitors of capacitors C1 , C2 , C3 are connected as shown in the figure. The points A , B and C are at
potential V1 , V2 and V3 respectively. Then the potential at O will be –
C1
C3
C2
A
B
C
O
(1)
2
VVV 321
(2)
321
133221 VVV
VVVVVV
(3)
321
332211 CCC
CVCVCV
(4) zero
Q.20 Three capacitors A , B and C are connected to a battery of 25volt as shown in the figure. The ratio of charges on
capacitors A , B and C will be -
A
25V
12µF
C
B
8µF
5µF
(1) 5 : 2 : 3 (2) 5 : 3 : 2
(3) 2 : 5: 3 (4) 2 : 3 : 5
Q.21 Four equal capacitors , each with a capacitance (C) are connected to a battery of E.M.F 10volts as shown in
the adjoining figure. The mid point of the capacitor system is connected to earth. Then the potentials of B
and D are respectively-
C
D
A
B
Earthed
(1) +10 volt , zero volt (2) +5 volt , –5 volt
(3) –5 volt, +5 volt (4) zero volt, 10 volt
Q.22 A circuit has a section AB as shown in the fig. With E = 10V , C1 = 1.0F, C2 = 2.0F and the potential
difference VA – VB = 5V. The voltage across C1 is -
E
–
+
A
B
C1
C2
(1) zero (2) 5V (3) 10V (4) 15V
Q.23 The potential difference between points (A) and (B) of the circuit is-
C2
C4
C3
C1
B
A
E
(1) (C2 – C1 ) E (2) (C4 – C3) E
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(3)
)CCCC(
E)CCCC(
4321
4132
(4)
)CC)(CC(
E)CCCC(
4321
4132
Q.24 A 1F capacitor is connected in the circuit shown below. The e.m.f of the cell is 2 volts and internal resistance is
0.5 ohm. The resistors R1 and R2 have values 4 ohm and 1 ohm respectively. The charge on the capacitor must be-
R1
E=2V, r = 0.5
1µF
R2
(1) 2C (2) 1C (3) 1.33C (4) zero
Q.25 In the figure shown, the capacity of the condenser C is 2F. The current in 2 resistor is-
6V
2µF
+
–
(1) 9 A (2) 0.9 A (3)
9
1
A (4)
9.0
1
A
Q.26 In the circuit shown here C1 = 6F, C2 = 3F and battery B = 20V. The Switch S1 is first closed. It is then
opened and afterwards S2 is closed. What is the charge finally on C2 ?
C2
3µF
C1
6µF
B=20V
S2
S1
(1) 120C (2) 80C (3) 40C (4) 20C
Q.27 As in figure shown, if a capacitor C is charged by connecting it with resistance R, then energy is given by the
battery will be -
C
V
R
(1)
2
CV
2
1
(2) More than
2
CV
2
1
(3) Less than
2
CV
2
1
(4) Zero
Q.28 A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V0. The
charging battery is disconnected and the plates are pulled apart to three times the initial separation. The
work required to separate the plates is -
(1)
d
AV32
00
(2)
d2
AV2
00
(3)
d3
AV2
00
(4)
d
AV2
00
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Q.29 A capacitor of capacity C1 is charged to the potential of V0. On disconnecting with the battery, it is connected
with a capacitor of capacity C2 as shown in the adjoining figure. The ratio of energies before and after the
connection of switch S will be -
S
C1V0
C2
(1) (C1 + C2)/C1 (2) C1/(C1 + C2)
(3) C1C2 (4) C1/C2
Q.30 Condenser A has a capacity of 15F when it is filled with a medium of dielectric constant 15. Another
condenser B has a capacity of 1F with air between the plates. Both are charged separately by a battery of
100 V. After charging, both are connected in parallel without the battery and the dielectric medium being
removed. The common potential now is -
(1) 400 V (2) 800 V
(3) 1200 V (4) 1600V
Q.31 A parallel plate capacitor is charged to a P.d. of 50 V. it is discharged through a resistance. After 1s, the P.d.
between plates becomes 40 V. Then -
(1) Fraction of stored energy after 1s is 16/25
(2) P.d. between the plates after 2 s will be 32 V
(3) P.d. between the plates after 2 s.will be 20 V
(4) Fraction of stored energy after 1 s. is 4/5
Q.32 Three identical capacitors are given a charge Q each and they are then allowed to discharge through
resistance R1, R2 and R3. Their charges, as a function of time shown in the graph below. The smallest of the
three resistance is -
R3
R2
R1
Q
t
(1) R3 (2) R2
(3) R1 (4) Cannot be predicted
Q.33 A glass slab is put with in the plates of a charged parallel plate condenser. Which of the following quantities
does not change ?
(1) energy of the condenser (2) capacity
(3) intensity of electric field (4) charge
Q.34 A parallel plate capacitor is connected to a battery and inserted a dielectric plate between the place of plates
then which quantity increase-
(1) potential difference (2) electric field
(3) stored energy (4) e.m.f. of battery
Q.35 A parallel plate capacitor is charged by a battery after charging the capacitor, battery is disconnected and
decrease the distance between the plates then which of the following statement is correct-
(1) electric field is not constant
(2) potential difference is increased
(3) decrease the capacitance
(4) decrease the stored energy
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Q.36 A parallel plate capacitor has rectangular plates of 400 cm2 and are separated by a distance of 2mm with air
as medium. What charge will appear on the plates. If a 200 volt potential difference is applied across the
condenser. ?
(1) 3.54 × 10–6 C (2) 3.54 × 10–8 C
(3) 3.54 × 10–10 C (4) 1770.8 × 10–13 C
Q.37 Seven capacitors each of capacitance 2F are to be so connected to have total capacity
11
10
µFWhich will be
the necessary figure as shown-
(1)
(2)
(3)
(4)
Q.38 An infinite number of identical capacitors each of capacitance 1F are connected as in adjoining figure.
Then the equivalent capacitance between A and B is-
8 capacitor
16 capacitor
A
B
(1) 1µF (2) 2µF (3)
2
1
µF (4)
Q.39 An air capacitor, a capacitor with a dielectric and a capacitor with a conducting slab (thickness one half the
separation introducing between the plates of parallel plate air capacitor in both case) has capacity C1, C2 and
C3 respectively then-
(1) C1 > C2 > C3 (2) C2 > C3 > C1
(3) C3 > C2 > C1 (4) C3 > C1 > C2
Q.40 Two spheres of radii 1 cm and 2 cm have been charged with 1.5 × 10–8 and 0.3 × 10–7 coulomb of positive
charge. When they are connected with a wire, charge-
(1) will flow from the first to the second
(2) will flow from the second to the first
(3) will not flow at all
(4) may flow either from first to second, or from the second to first, depending upon the length of the
connecting wire
Q.41 A number of capacitors, each of capacitance 1µF and each one of which gets punctured if a potential
difference just exceeding 500 volt is applied are provided. Then an arrangement suitable for giving a
capacitor of capacitance 3µF across which 2000 volt may be applied requires at least -
(1) 4 component capacitors
(2) 12 component capacitors
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(3) 48 component capacitors
(4) 16 component capacitors
Q.42 A circuit has a section AB as shown in the figure with E = 10V, C1 = 1.0µF, C2 = 2.0 µF and the potential
difference VA – VB = 5V. The voltage across C1 is-
–
+
C1
C2
B
A
E
(1) zero (2) 5V (3) 10V (4) 15V
Q.1 The effective capacity of the network between terminals A and B is-
A
6µF
6µF
6µF
6µF
B
20µF
(1) 6 µF (2) 20 µF (3) 3 µF (4) 10 µF
Q.2 The energy and capacity of a charged parallel plate capacitor are U and C respectively. Now a dielectric slab
of r = 6 is inserted in it then energy and capacity becomes (Assuming charge on plates remains constant)
(1) 6U, 6C (2) U, C (3)
6
U
, 6C (4) U, 6C
Q.3 A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor
of same capacity is connected in parallel with it. Then energy stored in each capacitor is-
(1) U/2 (2) U/4 (3) 4U (4) 2U
Q.4 Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given
by-
(1)
2
2
0d
V
2
1
(2)
2
2
0d
V
2
1
(3)
2
CV
2
1
(4)
C2
Q2
Q.5 A capacitor of capacity C1 charged upto V and then connected to an uncharged capacitor of capacity C2.
Then final potential difference across each will be-
(1)
21
2CC
VC
(2)
21
1CC
VC
(3)
1
2
C
C
1
.V (4)
V.
C
C
1
1
2
Q.6 Three capacitors each of capacity 4 µF are to be connected in such a way that the effective capacitance of 6
µF. This can be done by-
(1) connecting all of them in series
(2) connecting them in parallel
(3) connecting two in series and one in parallel
(4) connecting two in parallel and one in series
Q.7 A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a
battery as shown in the figure. The ratio of the charges on C2 and C4 is-
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C2
V
C3
C1
C4
(1)
4
7
(2)
3
22
(3)
22
3
(4)
7
4
Q.8 A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging
battery the distance between the plates of the capacitor is increased using an insulating handle. As a result
the potential difference between the plates-
(1) Decreases (2) Does not change
(3) Becomes zero (4) Increases
Q.9 Two condensers, one of capacity C and the other of capacity
2
C
, are connected to a V-volt battery, as shown.
The work done in charging fully both the condensers is-
V
C
C/2
(1)
2
1
CV2 (2) 2 CV2
(3)
4
1
CV2 (4)
4
3
CV2
Q.10 If the distance between the plates of a parallel plate condenser is halved and the dielectric is doubled, then
its capacity will-
(1) remain the same (2) increase by 2 times
(3) increase by 4 times (4) increase by 6 times
Q.11 What is the area of the plate of a 3F parallel plate capacitor, if the separation between the plates is 5 mm ?
(1) 1.694 × 109 m2 (2) 4.569 × 109 m2
(3) 9.281 × 109 m2 (4) 12.918 × 109 m2
Q.12 The dimensions of RC is equal to-
(1) time
(2) inverse time
(3) square of inverse time
(4) square of time
Q.13 Minimum number of 8µF and 250 V capacitors used to make a combination of 16 µF and
1000 V are -
(1) 32 (2) 16 (3) 8 (4) 4
Q.14 Three capacitors of capacitance 3µF, 10µF and 15µF are connected in series to a voltage source of 100 V.
The charge on 15µF is-
(1) 50 µC (2) 160 µC
(3) 200 µC (4) 280 µC
Q.15 Two materials of dielectric constant k1 and k2 are filled between two parallel plates of a capacitor as shown
in figure. The capacity of the capacitor is-
k1
k2
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(1)
d2
)kk(A 210
(2)
21
21
0kk
kk
d
A2
(3)
21
21
0kk
kk
d
A
(4)
21
21
0kk
kk
d2
A
Q.16 A conducting sphere of radius 10 cm is charged with 10 µC. Another uncharged sphere of radius 20 cm is
allowed to touch it for some time. After that if the sphere are separated, then surface density of charged on
the spheres will be in the ratio of-
(1) 1 : 4 (2) 1 : 3 (3) 2 : 1 (4) 1 : 1
Q.17 In the given figure, the capacitors C1, C3, C4, C5 have a capacitance 4µF each. If the capacitor C2 has a
capacitance 10µF, then effective capacitance between A and B will be-
A
C4
B
C3
C2
c
d
a
b
C5
C1
(1) 2µF (2) 4µF (3) 6µF (4) 8µF
Q.18 A 40 µF capacitor in a defibrillator is charged to 3000 V. The energy stored in the capacitor is sent through
the patient during a pulse of duration 2 ms. The power delivered to the patient is-
(1) 45 kW (2) 90 kW
(3) 180 kW (4) 360 kW
Q.19 Five capacitors, each of capacitance value C are connected as shown in the figure. The ratio of capacitance
between P and R, and the capacitance between P and Q is-
C
C
C
C
C
Q
T
R
S
P
(1) 3 : 1 (2) 5 : 2 (3) 2 : 3 (4) 1 : 1
Q.20 Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance
and breakdown voltage of the combination will be-
(1) 3C, 3V (2)
3
C
,
3
V
(3) 3C,
3
V
(4)
3
C
, 3V
Q.21 A parallel plate condenser has a uniform electric field E (V/m) in the space between the plates. If the
distance between the plates is d (m) and area of each plate is A (m2) the energy (joules) stored in the
condenser is :
(1)
2
1
0E2 Ad (2) E2Ad/0
(3)
2
1
0E2 (4) 0EAd
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Q.1 Two capacitors of 1F and 2F are connected in series and this combination is charged upto a potential
difference of 120V. What will be the potential difference across 1 µF capacitor ?
(1) 40 V (2) 60 V
(3) 80 V (4) 120 V
Q.2 The capacity of a parallel plate air capacitor is 10F. As shown in the figure this capacitor is divided into two
equal parts, these parts are filled by media of dielectric constants K1 = 2 and K2 = 4, capacity of this
arrangement will be -
A/2
d
A/2
a
b
K1
K2
(1) 20 F (2) 30 F (3) 10 F (4) 40 F
Q.3 Parallel combination of two capacitors, each of value 10 F is charged by 200 volt d.c. Total energy of the
charges in joules will be -
(1) 0.1 (2) 0.2 (3) 0.4 (4) 0.6
Q.4 Three capacitors, each of value 1F are such combined that the resultant capacity is 1.5 F. Then
(1) All three capacitors are connected in parallel.
(2) All three capacitors are connected in series.
(3) Third capacitor is in series with parallel combination of others two.
(4) Third capacitor is in parallel with series combination of others two.
Q.5 As shown in figure, two identical capacitors of values C1 and C2 are connected with a battery. Space between
the plates of C1 is filled with air and that of between plates of C2 is filled with an insulator, then -
C2
Q2
r
C1
Q1
0
+
–
(1) Q1 > Q2 (2) Q1 < Q2
(3) Q1 = Q2 (4) None of the above
Q.6 Charge and the energy stored of a capacitor of value C are respectively Q and W. If its charge is increased to
2Q, then the stored energy will be -
(1) 2 W (2) W/2 (3) 4 W (4) W/4
Q.7 A capacitor of capacity C is charged to a potential V. Then it is taken out and connected in parallel with an
uncharged identical capacitor. Then charge on each capacitor will be -
(1) CV (2) CV/2 (3) CV/8 (4) CV/4
Q.8 Two capacitors of value 0.3 F and 0.6F are connected in series with a source of 6 volt, then the ratio of
energy stored in each capacitor will be -
(1)
2
1
(2) 2 (3)
4
1
(4) 4
Q.9 A parallel plate capacitor is connected with a battery whose potential is constant. If the plates capacitor are
shifted apart then the intensity of electric field -
(1) Decrease and charge on plates also decreases.
(2) Remains constant but charge on plates decreases.
(3) Remains constant but charge on plates increases.
(4) Increase but charge on plates decreases.
Q.10 Half of the space between parallel plate capacitor is filled with a medium of dielectric constant K parallel to
the plates. If initially the capacity is C, then the new capacity will be -
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(1) 2KC/(1+K) (2) C(K+1)/2
(3) CK/(1+K) (4) KC
Q.11 The distance between the plates of a circular parallel capacitor of diameter 40 mm, whose capacity is equal
to that of a metallic sphere of radius 1m will be -
(1) 0.01 mm (2) 0.1 mm
(3) 1.0 mm (4) 10 mm
Q.12 When a slab of dielectric medium is placed between plates of a parallel plate capacitor high is connected
with a battery, then the charge on plates in comparison with earlier charge -
(1) Is less
(2) Is same
(3) Is more
(4) Depends on the nature of the material inserted
Q.13 Two identical parallel plate capacitors are connected in series and then joined with a battery of 100 V. A
sheet of dielectric constant 4.0 is inserted between the plates of second capacitor. The potential difference
across the capacitors will be respectively -
(1) 50V, 50V (2) 80V, 20V
(3) 20V, 80V (4) 75V, 25V
Q.14 If a capacitor, with air as dielectric, is so charged that the potential difference across the plates becomes
100V. If now the space between plates is filled with a medium of dielectric constant 10, then the potential
difference across the plates will be -
(1) 1000 V (2) 100 V (3) 10 V (4) zero
Q.15 A capacitor of value 4F charged at 50V is connected with another capacitor of value 2F charged at 100V,
in such a way that plates of similar charges are connected together. Before joining and after joining the total
energy in multiple 10–2 J will be -
(1) 1.5 and 1.33 (2) 1.33 and 1.5
(3) 3.0 and 2.67 (4) 2.67 and 3.0
Q.16 64 small drops of water, whose charge and radius are same, are joined to make a big drop. The capacity of
big drop is following times that of small drop -
(1) 4 (2) 8 (3) 16 (4) 64
Q.17 The radii of a spherical capacitor are 0.5 m and 0.6 m. If the empty space is completely filled by a medium of
dielectric constant 6, then the capacity of the capacitor will be –
(1) 3.3 × 10–10 F (2) 2 × 10–9 F
(3) 2 F (4) 18 F
Q.18 The distance between plates of a parallel plate capacitor is 'd'. Another thick metal plate of thickness d/2
and area same as that of plates is so plated between the plates, that it does not touch the plates. The
capacity of the resultant capacitor –
(1) remains same (2) becomes double
(3) becomes half (4) becomes one fourth
Q.19 When air is replaced by a dielectric medium from the space between the plates of a charged parallel plate
capacitor, then the intensity of electric field -
(1) Decreases (2) Remain same
(3) Becomes zero (4) Increases
Q.20 In a parallel plate capacitor, sheets of thickness t1 and t2 with dielectric constant of K1 and K2 respectively are
placed. Capacity of this condenser will be -
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(1) 0A/
2
2
1
1K
t
K
t
(2) 0A/
2
2
1
1t
K
t
K
(3) 0A/
1
2
2
1K
t
K
t
(4) 0A/
2
1
1
2t
K
t
K
Q.21 When a capacitor of value 200F charged to 200V is discharged separately through resistance of 2 and 8
, then heat produced in joule will respectively be -
(1) 4 and 16 (2) 16 and 4
(3) 4 and 8 (4) 4 and 4
Q.22 A series combination of two capacitors of value 0.1 F and 1F is connected with a source of voltage 500
volt. The p.d. in volt across the capacitor of value 0.1 F will be-
(1) 50 (2) 500
(3) 45.5 (4) 454.5
Q.23 The magnitude of storing capacity of a PPC does not depend on -
(1) area of the plate
(2) medium between the plates
(3) distance between the plates
(4) metal of the plate
Q.24 An uncharged capacitor is connected with a battery on charging the capacitor fully -
(1) The total energy given is stored in capacitor.
(2) Half of the energy given is stored in capacitor.
(3) The energy stored depends only on capacity of capacitor.
(4) The energy stored depends on the time taken to charge the capacitor.
Q.25 Three capacitors of value 6, 3 and 9F are joined according to the circuit and then the combination is
connected with a battery of 10 volt. The potential difference across the third capacitor plates will be –
9F
6F
3F
10V
+
–
(1) 4 V (2) 5 V (3) 6 V (4) 2 V
Q.26 Two uncharged capacitors are charged with a battery of E volt. The ratio of charges produced on these
capacitors Q1/Q2 will be-
4F
E
C1
C2
2F
(1) 1 : 2 (2) 2 : 1 (3) 4 :1 (4) 1 : 1
Q.27 A parallel plate capacitor is charged with a battery and afterwards the battery is removed. If now with the
help of insulating handles, the distance between plates is increased, then -
(1) charge on capacitor increases and capacity decreases.
(2) potential difference between plates increases.
(3) capacity of capacitor increases.
(4) value of energy stored in capacitor decreases.
Q.28 Capacity of a capacitor is C and the potential given to it is V. Now if it is connected with a resistance R, then
the energy across the resistance R liberated as the form of heat will be
(1) 1/2 CV2 (2) 1/2 CV
(3) Q/2C (4) QV2 /2
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Q.29 A 3F capacitor is charged to a potential of 300 V and 2F capacitor is charged to 200 V. The capacitor are then
connected in parallel with plates of opposite polarity joined together. What amount of charge will flow, when the
plates are so connected ?
(1) 1300 C (2) 800 C
(3) 600 C (4) 300 C
Q.30 The value of capacitor formed by a thin metallic foil is 2 F. The foil is attached to both sides of paper having
a thickness of 0.015 mm. The dielectric constant of the paper is 2.5 and its breadth is 40 mm. The length of
the foil used is-
(1) 0.34 m (2) 1.33 m
(3) 13.4 mm (4) 33.9 m
Q.31 The value of equivalent capacitance of the combination shown in fig., between the points P and Q is -
2C
2C
C
Q
C
C
2C
P
(1) 3 C (2) 2 C (3) C (4) C/3
Q.32 The equivalent capacitance of the circuit shown, between points A and B will be -
1F
1F
2F
1F
A
B
(1)
3
2
F (2)
3
5
F
(3)
3
8
F (4)
3
7
F
Q.33 The effective capacitance between the points P and Q of the arrangement shown in the fig. is -
1F
2F
2F
P
Q
1F
2F
5F
2F
(1) (1/2) F (2) 1 F
(3) 2 F (4) 1.33 F
Q.34 In the given circuit if point C is connected to the earth and a potential of + 2000 V is given to point A, the
potential at B is -
10F
10F
10F
5F
A
B
C
(1) 1500 V (2) 1000 V
(3) 500 V (4) 400 V
Q.35 A capacitor of capacitance 5 F is connected as shown in the fig. The internal resistance of the cell is 0.5 .
The amount of charge on the capacitor plate is -
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1
1
5F
2
2.5V
+
–
(1) 0 C (2) 5 C
(3) 10 C (4) 25 C
Q.36 Choose the incorrect statement from the following when two identical capacitors are charged individually to
different potentials and connected parallel to each other after disconnecting them from the source-
(1) Net charge equals the sum of initial charges
(2) The net energy stored in the two capacitors is less than the sum of the initial individual
energies.
(3) The net potential difference across them is different from the sum of the individual
initial potential difference.
(4) The net potential difference across them equals the sum of the individual initial
potential differences.
Q.37 The area of the plates of a parallel plate condenser is A and the distance between the plates is 10 mm. There
are two dielectric sheets in it, one of dielectric constant 10 and thickness 6 mm and the other of dielectric
constant 5 and thickness 4 mm. The capacity of the condenser is- (1)
35
12
0A (2)
3
2
0A
(3)
7
5000
0A (4) 1500 0A
Q.38 Two condensers C1 and C2 in a circuit are joined as shown in fig. The potential of point A is V1 and that of B is
V2. The potential of point D will be -
A
D
B
V1
C1
C2
V2
(1)
2
1
(V1 + V2) (2)
21
2112 CC
VCVC
(3)
21
2211 CC
VCVC
(4)
21
2112 CC
VCVC
Q.39 An air capacitor of capacity C = 10 F is connected to a constant voltage battery of 12 V. Now the space
between the plates is filled with a liquid of dielectric constant 5. The additional charge that flows now from
battery to the capacitor is -
(1) 120 C (2) 600 C
(3) 480 C (4) 24 C
Q.40 The capacitance of a parallel plate capacitor is C and distance between the plates is d. If the space between
the plates is filled with a substance of dielectric constant K as shown in the fig. then what will be the new
capacitance of the capacitor -
A
C
d
I-Condition
A/2
d
II-Condition
A/2
d
K
(1)
2
C
(1 + K) (2)
2
C
(K)
(3)
2
C
(4) 2 C
Q.41 If there are three capacitors and a source which has an e.m.f. V then how the three capacitors should be
connected across the source for the stored energy to be maximum -
(1) All the three capacitors should be connected in parallel
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(2) All the three capacitors should be connected in series
(3) The stored energy will be same in all cases
(4) Nothing can be said
Q.42 A capacitor is charged, now the battery is removed and a dielectric plate is entered, then choose the correct
statement -
(1) Charge increases, voltage decreases and electrostatic energy increases
(2) Charge remains constant, voltage increases and electrostatic energy decreases
(3) Charge remains constant and voltage and electrostatic energy both decrease
(4) None of these
Q.43 In the given circuit, the potential difference across 3F capacitor will be -
3F
5F
20V
4V
(1) 16 V (2) 10 V (3) 6 V (4) 4 V
Q.44 A parallel plate capacitor has the space between its plates filled by two slabs of thickness d/2 each and
dielectric constant K1 and K2 . d is the plate separation of the capacitor. The capacitance of the capacitor is -
(1)
21
21
0KK
KK
d
A2
(2)
21
0KK
d
A2
(3)
21
21
0KK
KK
d
A2
(4)
21
21
0KK
KK
A
d2
Q.45 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 volt. The capacitance of second
capacitor is -
(1) 10 F (2) 20 F (3) 30 F (4) 15 F
Q.46 The equivalent capacitance of three capacitors of capacitance C1 , C2 and C3 are connected in parallel is 12
units and product C1 . C2. C3 = 48. When the capacitors C1 and C2 are connected in parallel, the equivalent
capacitance is 6 units. Then the capacitance are -
(1) 2, 3, 7 (2) 1.5, 2.5, 8
(3) 1, 5, 6 (4) 2, 4, 6
Q.47 Two charged spheres having radii a and b are joined with a wire then the ratio of electric field Ea/Eb on their
surface is -
(1) a/b (2) b/a (3) a2/b2 (4) b2/a2
Q.48 Two capacitors A and B are connected in series with a battery as shown in the figure when the switch S is
closed and the two capacitors get charged fully, then -
2F
A
10V
B
S
3F
(1) The p.d. across the plates of A is 4 V and across the plates of B is 6V
(2) The p.d. across the plates of A is 6V and across the plates B is 4V
(3) The ratio of electrical energies stored in A and B is 2 : 3
(4) The ratio of charges on A and B is 3 : 2
Q.49 In a capacitor of capacitance 20 F the distance between the plates is 2mm. If a dielectric slab of width 1 mm
and dielectric constant 2 is inserted between the plates, then the new capacitance will be -
(1) 22 F (2) 26.6 F
(3) 52.2 F (4) 13 F
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Q.50 An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when
it has been compressed by 0.2 m to the potential energy stored in a 10 F capacitor at a potential difference
of 10000 V will be
(1)
4
1
(2) 1 (3)
2
1
(4) 2
Q.51 In the given figure the steady state current is -
2
3
C = 0.2F
4
2.8
6V
(1) zero (2) 0.6 A (3) 0.9 A (4) 1.5 A
Q.52 The charge on capacitors shown in fig. and the potential difference across each will be respectively -
3F
C1
C2
C3
2F
4F
120V
(1) 240 C, 80 C, 160 C and 80 V, 40 V, 40 V (2) 300 C, 75 C, 150 C and 40 V, 80 V, 60 V (3) 220 C,
70 C, 140 C and 60 V, 50 V, 40 V (4) none of these
Q.53 Three capacitor 2F, 3F and 6F are connected in series with 10 volt battery then charge on 3F capacitor
is -
(1) 5C (2) 10C
(3) 11 C (4) 15 C
Q.54 Two capacitors C1 = 2F and C2 = 6F in series, are connected in parallel to a third capacitor
C3 = 4F. This arrangement is then connected to a battery of e.m.f = 2V, as shown in the fig. How much
energy is given by the battery in charging the capacitors -
C1
C2
C3
2V
(1) 22 × 10–6 J (2) 11 × 10–6 J
(3)
3
32
× 10–6 J (4)
3
16
× 10–6 J
Q.55 A solid conducing sphere of radius R1 is surrounded by another concentric hollow conducting sphere of
radius R2. The capacitance of this assembly is proportional to -
(1)
21
12 RR
R–R
(2)
21
12 RR
RR
(3)
21
21 RR
RR
(4)
12
21 R–R
RR
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Q.56 Two conducting spheres of radii R1 and R2 are charged with charges Q1 and Q2 respectively. On bringing them
in contact there is -
(1) No change in the energy of the system
(2) An increase in the energy of the system if Q1R2 Q2R1
(3) Always a decrease in energy of the system
(4) A decrease in energy of the system if Q1R2 Q2R1
Q.57 When the key is pressed at time t = 0 then which of the following statement about the current i in the
resistor AB of the given circuit is true -
K
A
1F
C
i
2V
1000
B
1000
(1) at t = 0, i = 2mA and with time it goes to 1mA
(2) i oscillates between 1 mA and 2 mA
(3) i = 2mA at all t
(4) i = 1 mA at all t
Q.58 Time constant of a series R–C circuit is -
(1) + RC (2) – RC
(3)
C
R
(4)
R
C
Q.59 Two capacitors of capacitances 3F and 6F are charged to a potential of 12V each .They are now connected
to each other with the positive plate of each joined to the negative plate of the other. The potential
difference across each will be -
(1) 3V (2) Zero (3) 6V (4) 4V
Q.60 A capacitor of 0.2 F capacitance is charged to 600 V. On removing the battery, it is connected with a 1.0 F
capacitor in the parallel then the potential of capacitor will become -
(1) 300V (2) 600V
(3) 100V (4) 120V
Q.61 Mean electric energy density between the plates of a charged capacitor is -
Here q = Charge on capacitor
A = Area of the plate of the capacitor
(1) q2/20A2 (2) q/20A2
(3) q2/20A (4) None of these
Q.62 If potential difference across a capacitor is changed from 15 V to 30 V, work done is W. The work done when
potential difference is changed from 30 V to 60 V, will be -
(1) W (2) 4W (3) 3W (4) 2W
Q.63 The combination of capacitors with C1 = 3F, C2 = 4F and C3 = 2F is charged by connecting AB to a battery.
Consider the following statements –
(I) Energy stored in C1 = Energy stored in C2 + Energy stored in C3
(II) Charge on C1=Charge on C2 + Charge on C3
(III) Potential drop across C1 = Potential drop across C2 = Potential drop across C3
Which of these are correct –
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A
C3
C2
C1
B
(1) I and II (2) II only
(3) I and III (4) III only
Q.64 A capacitor is connected to 10 V. The charge on plates is 40 C. If medium between plates is air. The charge
on plates will become 100C if the space between the plates is filled with oil. The dielectric constant of oil is-
(1) 2.5 (2) 4 (3) 6.25 (4) 10
Q.65 The energy density of electric field is proportional to -
(1)
2
E
1
(2) E (3)
E
1
(4) E2
Q.66 If the distance between plates of a capacitor having capacity C and charge Q is increased to double then
work done will be -
(1) Q2/4C (2) Q2/2C (3) Q2/C (4) 2Q2/C
Q.67 A slab of copper of thickness d/2 is introduced between the plates of a parallel plate capacitor where d is the
separation between its two plates. If the capacitance of the capacitor without copper slab is C and with
copper slab is C then
C
C
is -
(1)
2
(2) 2 (3) 1 (4)
2
1
Q.68 Two capacitor each having a capacitance C and break down voltage V are joined in series. The effective
capacitance and maximum working voltage of the combination is-
(1) 2C, 2V (2)
2
C
,
2
V
(3) 2C, V (4)
2
C
, 2V
Q.69 The capacitance of a capacitor is 4 × 10–6 F and its voltage is 100 V. The energy required to discharge it
completely -
(1) 0.025 J (2) 0.05 J
(3) 0.02 J (4) 0.04 J
Q.70 Between the plates of parallel plate capacitors of capacity C two parallel plates of the same metal and area
same as the plates of the original capacitor are placed. If the thickness of each plate is equal to
5
1
th of the
distance between the plates of the original capacitor then the capacity of the new capacitor is -
(1)
C
3
5
(2)
C
5
3
(3)
C
10
3
(4)
C
3
10
Q.71 The charge on any one of the 2F capacitor and lF capacitor will be given respectively (in C) as
2F
2F
1F
2V
(1) 1,2 (2) 2,1 (3) 1,1 (4) 2,2
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Q.72 The electric field between the plates of a parallel plate capacitor when connected to a certain battery is E0. If
the spaced between the plates of the capacitor is filled by introducing a material of dielectric constant K
without disturbing the battery connections, the field between the plates shall be -
(1) KE0 (2) E0
(3)
K
E0
(4) None of the above
Q.73 Two capacitor with capacity C1 and C2 , when connected in series, have a capacitance Cs and when connected
in parallel have a capacitance Cp. Which of the following is true -
(1) Cs = C1 + C2 (2) Cp =
21
21 CC
CC
(3)
p
s
C
C
=
2
1
C
C
(4) CsCp = C1C2
Q.74 A parallel plate capacitor C has a charge q and potential V between the plates. Work required to double the
distance between the plates is -
(1)
2
CV
2
1
(2)
2
CV
4
1
(3)
2
2
V
C
2
1
(4) CV2
Q.75 Two metallic spheres of radii R1 and R2 are connected by a thin wire. If + q1 and +q2 are the charges on the
two spheres then -
(1)
2
2
2
1
2
1
R
R
q
q
(2)
2
1
2
1R
R
q
q
(3)
3
2
3
1
2
1
R
R
q
q
(4)
2
2
2
1
2
2
2
1
2
1
RR
R–R
q
q
Q.76 Two same sphere having radii 10 cm and 20 cm. these have been given total charge 150 C and connected
by a wire. Their common potential will be -
(1) 9 × 106 volt
(2) 4.5 × 106 volt
(3) 1.8 × 106 volt
(4) 1.35 × 109 volt
These questions of two statements each, printed as Assertion and Reason. While answering these
Questions you are required to choose any one of the following four responses.
(A) If both Assertion & Reason are true & the Reason is a correct explanation of the Assertion.
(B) If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
(C) If Assertion is true but the Reason is false.
(D) If Assertion & Reason both are false.
Q.1 Assertion: Farad is too big a unit of capacity.
Reason: Capacity of earth- which is the largest sphere is in microfarad.
(1) A (2) B (3) C (4) D
Q.2 Assertion : Capacity of a parallel plate condenser increases on introducing a conducting or insulating slab
between the plates.
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 5
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Reason : In both the cases, electric field intensity between the plates reduces.
(1) A (2) B (3) C (4) D
Q.3 Assertion : When charges are shared between any two bodies, some charge is lost, and some loss of energy
does occur.
Reason : Some energy disappears in the form of heat, sparking etc.
(1) A (2) B (3) C (4) D
Q.4 Assertion : The whole charge of a body can be transferred to another body.
Reason : Charge can not be transferred partially.
(1) A (2) B (3) C (4) D
Q.5 Assertion : In a series combination of capacitors, charge on each capacitor is same.
Reason : In such a combination, charge can move only along one route.
(1) A (2) B (3) C (4) D
Q.6 Assertion : Increasing the charge on the plates of a capacitor means increasing the capacitance.
Reason : Because Q = CV Q C.
(1) A (2) B (3) C (4) D
Q.7 Assertion : The capacitance of a capacitor depends on the shape, size and geometrical placing of the
conductors and its medium between them.
Reason : When a charge q passes through a battery of emf E from the negative terminal to an positive
terminal, an amount qE of work is done by the battery.
(1) A (2) B (3) C (4) D
Q.8 Assertion : A dielectric slab is inserted between the plates of an isolated charged capacitor. The charge on
the capacitor will remain the same.
Reason : Charge on a isolated system is conserved.
(1) A (2) B (3) C (4) D
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Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. 1 1 4 1 1 1 3 3 2 4 3 3 2 1 2 2 3 4 3 1
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. 1 3 4 4 3 3 2 3 2 2 2 2 1 4 2 2 1 3 4 4
Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. 3 3 2 3 1 1 2 4 1 1 1 1 2 3 4 3 1 3 3 2
Q.No. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
Ans. 4 3 4 2 4 3 3 3 1 2 4 1 3 1 1 4 4 3 1 3
Q.No. 81 82 83 84 85 86
Ans. 1 1 2 3 2 3
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. 2 1 1 2 3 1 1 1 1 2 3 2 1 4 3 2 3 3 3 1
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. 2 3 4 3 2 3 2 4 1 2 1,2 3 4 3 4 2 1 2 3 3
Q.No. 41 42
Ans. 3 3
Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans. 1 3 2 1 2 3 3 4 4 3 1 1 1 3 1
Ques. 16 17 18 19 20 21
Ans. 3 2 2 3 4 1
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. 3 2 3 4 2 3 2 2 1 1 2 3 2 3 1 1 2 2 1 1
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. 4 4 4 2 2 2 2 1 3 4 1 3 2 3 3 4 3 3 3 1
Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. 1 3 2 3 4 4 2 2 2 2 4 1 2 1 4 4 1 1 4 3
Q.No. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76
Ans. 1 2 2 1 4 2 2 4 3 1 4 2 4 1 2 2
Ques. 1 2 3 4 5 6 7 8
Ans. 1 1 4 3 1 4 2 1
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 1 (ANSWERS)
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 2 (ANSWERS)
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 3 (ANSWERS)
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 4 (ANSWERS)
IMPORTANT PRACTICE QUESTION SERIES FOR IIT-JEE EXAM – 5 (ANSWERS)
