Electrostatics- 4 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.15) : There are 15 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A parallel plate capacitor is charged to a potential
difference of 50V. It is discharged through a resistance.
After 1 second, the potential difference between plates
becomes 40V. Then
(a) Fraction of stored energy after 1 second is 16/25
(b) Potential difference between the plates after 2
seconds will be 30V
(c) Potential difference between the plates after 2
seconds will be 20V
(d) Fraction of stored energy after 1 second is 4/5
Q.2 Five identical plates each of area A are joined as shown in
the figure. The distance between the plates is d. The plates
are connected to a potential difference of V volts. The
charge on plates 1 and 4 will be respectively
(a)
00
2
,
22
AV AV
dd
ee
(b)
00
2
,
22
AV AV
dd
ee
(c)
00
2
,
AV AV
dd
e -e
V
+
–
1 2 3 4 5
(d)
00
2
,
AV AV
dd
-e -e
Q.3 Figure given below shows two identical parallel plate capacitors
connected to a battery with switch S closed. The switch is now opened
and the free space between the plates of capacitors is filled with a
dielectric of dielectric constant 3. What will be the ratio of total
electrostatic energy stored in both capacitors before and after the
introduction of the dielectric?
(a) 3 : 1
(b) 5 : 1
(c) 3 : 5
B A V
(d) 5 : 3
Page 2


DIRECTIONS (Q.1-Q.15) : There are 15 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A parallel plate capacitor is charged to a potential
difference of 50V. It is discharged through a resistance.
After 1 second, the potential difference between plates
becomes 40V. Then
(a) Fraction of stored energy after 1 second is 16/25
(b) Potential difference between the plates after 2
seconds will be 30V
(c) Potential difference between the plates after 2
seconds will be 20V
(d) Fraction of stored energy after 1 second is 4/5
Q.2 Five identical plates each of area A are joined as shown in
the figure. The distance between the plates is d. The plates
are connected to a potential difference of V volts. The
charge on plates 1 and 4 will be respectively
(a)
00
2
,
22
AV AV
dd
ee
(b)
00
2
,
22
AV AV
dd
ee
(c)
00
2
,
AV AV
dd
e -e
V
+
–
1 2 3 4 5
(d)
00
2
,
AV AV
dd
-e -e
Q.3 Figure given below shows two identical parallel plate capacitors
connected to a battery with switch S closed. The switch is now opened
and the free space between the plates of capacitors is filled with a
dielectric of dielectric constant 3. What will be the ratio of total
electrostatic energy stored in both capacitors before and after the
introduction of the dielectric?
(a) 3 : 1
(b) 5 : 1
(c) 3 : 5
B A V
(d) 5 : 3
2
DPP/ P 35
Q.4 All six capacitors shown are identical, Each can withstand
maximum 200 volts between its terminals. The maximum
voltage that can be safely applied between A and B is
(a) 1200 V
(b) 400 V
A B
(c) 800 V
(d) 200 V
Q.5 A capacitor of capacity C
1
 is charged upto V volt and then
connected to an uncharged capacitor of capacity C
2
. Then
final potential difference across each will be
(a)
2
12
CV
CC +
(b) 
2
1
1
æö
+
ç÷
èø
C
V
C
 (c) 
1
12
CV
CC +
   (d)   
2
1
1
æö
-
ç÷
èø
C
V
C
Q.6 Two capacitors of capacitances 3mFand 6mFare 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
(a) 6 volt (b) 4 volt
(c) 3 volt (d) zero
Q.7 In the figure a capacitor is filled with dielectrics K
1
, K
2
and K
3
. The resultant capacitance is
(a)
0
1 23
2 1 11 éù e
++
êú
ëû
A
d K KK
(b)
0
1 23
1 11 éù e
++
êú
ëû
A
d K KK
 d/2
 A/2 A/2
 d
1
K
2
K
3
K
(c)
0
1 23
2
[]
e
++
A
K KK
d
(d) None of these
Q.8 The resultant capacitance of given circut is
(a)
3C
(b)
2C
(c)
C
P
Q
2C
2C
2C
C C
C
(d)
3
C
Q.9 Two dielectric slabs of constant K
1 
and K
2 
have been filled
in between the plates of a capacitor as shown below. What
will be the capacitance of the capacitor
(a)
0
12
2
()
A
KK
d
e
+
(b)
0 12
12
2 AKK
d KK
æö e +
ç÷
´
èø
 d
1
K
2
K
(c)
0 12
12
4 A KK
d KK
æö e ´
ç÷
+
èø
(d)
0 12
12
2 A KK
d KK
æö e ´
ç÷
+
èø
Q.10Eight drops of mercury of equal radii possessing equal
charges combine to form a big drop. Then the capacitance
of bigger drop compared to each individual small drop is
(a) 8 times (b) 4 times
(c) 2 times (d) 32 times
Q.11 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
(a)
0
1
1
A
dt
k
e
æö
+-
ç÷
èø
(b)
0
1
1
A
dt
k
e
æö
++
ç÷
èø
(c)
0
1
1
A
dt
k
e
æö
--
ç÷
èø
(d)
0
1
1
A
dt
k
e
æö
-+
ç÷
èø
Q.12 There is an air filled 1pF parallel plate capacitor. When
the plate separation is doubled and the space is filled with
wax, the capacitance increases to 2pF. The dielectric
constant of wax is
(a)2 (b)4 (c)6 (d)8
Q.13 Between the plates of a parallel plate condenser, a plate of
thickness t
1 
and dielectric constant k
1 
is placed. In the rest
of the space, there is another plate of thickness t
2 
and
dielectric constant k
2 
. The potential difference across the
condenser will be
(a)
12
0 12
tt Q
A KK
æö
+
ç÷
e
èø
(b)
0 12
12
Qtt
A KK
æö e
+
ç÷
èø
(c)
12
0 12
KK Q
A tt
æö
+
ç÷
e
èø
(d)
0
11 22
()
Q
Kt Kt
A
e
+
Page 3


DIRECTIONS (Q.1-Q.15) : There are 15 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A parallel plate capacitor is charged to a potential
difference of 50V. It is discharged through a resistance.
After 1 second, the potential difference between plates
becomes 40V. Then
(a) Fraction of stored energy after 1 second is 16/25
(b) Potential difference between the plates after 2
seconds will be 30V
(c) Potential difference between the plates after 2
seconds will be 20V
(d) Fraction of stored energy after 1 second is 4/5
Q.2 Five identical plates each of area A are joined as shown in
the figure. The distance between the plates is d. The plates
are connected to a potential difference of V volts. The
charge on plates 1 and 4 will be respectively
(a)
00
2
,
22
AV AV
dd
ee
(b)
00
2
,
22
AV AV
dd
ee
(c)
00
2
,
AV AV
dd
e -e
V
+
–
1 2 3 4 5
(d)
00
2
,
AV AV
dd
-e -e
Q.3 Figure given below shows two identical parallel plate capacitors
connected to a battery with switch S closed. The switch is now opened
and the free space between the plates of capacitors is filled with a
dielectric of dielectric constant 3. What will be the ratio of total
electrostatic energy stored in both capacitors before and after the
introduction of the dielectric?
(a) 3 : 1
(b) 5 : 1
(c) 3 : 5
B A V
(d) 5 : 3
2
DPP/ P 35
Q.4 All six capacitors shown are identical, Each can withstand
maximum 200 volts between its terminals. The maximum
voltage that can be safely applied between A and B is
(a) 1200 V
(b) 400 V
A B
(c) 800 V
(d) 200 V
Q.5 A capacitor of capacity C
1
 is charged upto V volt and then
connected to an uncharged capacitor of capacity C
2
. Then
final potential difference across each will be
(a)
2
12
CV
CC +
(b) 
2
1
1
æö
+
ç÷
èø
C
V
C
 (c) 
1
12
CV
CC +
   (d)   
2
1
1
æö
-
ç÷
èø
C
V
C
Q.6 Two capacitors of capacitances 3mFand 6mFare 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
(a) 6 volt (b) 4 volt
(c) 3 volt (d) zero
Q.7 In the figure a capacitor is filled with dielectrics K
1
, K
2
and K
3
. The resultant capacitance is
(a)
0
1 23
2 1 11 éù e
++
êú
ëû
A
d K KK
(b)
0
1 23
1 11 éù e
++
êú
ëû
A
d K KK
 d/2
 A/2 A/2
 d
1
K
2
K
3
K
(c)
0
1 23
2
[]
e
++
A
K KK
d
(d) None of these
Q.8 The resultant capacitance of given circut is
(a)
3C
(b)
2C
(c)
C
P
Q
2C
2C
2C
C C
C
(d)
3
C
Q.9 Two dielectric slabs of constant K
1 
and K
2 
have been filled
in between the plates of a capacitor as shown below. What
will be the capacitance of the capacitor
(a)
0
12
2
()
A
KK
d
e
+
(b)
0 12
12
2 AKK
d KK
æö e +
ç÷
´
èø
 d
1
K
2
K
(c)
0 12
12
4 A KK
d KK
æö e ´
ç÷
+
èø
(d)
0 12
12
2 A KK
d KK
æö e ´
ç÷
+
èø
Q.10Eight drops of mercury of equal radii possessing equal
charges combine to form a big drop. Then the capacitance
of bigger drop compared to each individual small drop is
(a) 8 times (b) 4 times
(c) 2 times (d) 32 times
Q.11 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
(a)
0
1
1
A
dt
k
e
æö
+-
ç÷
èø
(b)
0
1
1
A
dt
k
e
æö
++
ç÷
èø
(c)
0
1
1
A
dt
k
e
æö
--
ç÷
èø
(d)
0
1
1
A
dt
k
e
æö
-+
ç÷
èø
Q.12 There is an air filled 1pF parallel plate capacitor. When
the plate separation is doubled and the space is filled with
wax, the capacitance increases to 2pF. The dielectric
constant of wax is
(a)2 (b)4 (c)6 (d)8
Q.13 Between the plates of a parallel plate condenser, a plate of
thickness t
1 
and dielectric constant k
1 
is placed. In the rest
of the space, there is another plate of thickness t
2 
and
dielectric constant k
2 
. The potential difference across the
condenser will be
(a)
12
0 12
tt Q
A KK
æö
+
ç÷
e
èø
(b)
0 12
12
Qtt
A KK
æö e
+
ç÷
èø
(c)
12
0 12
KK Q
A tt
æö
+
ç÷
e
èø
(d)
0
11 22
()
Q
Kt Kt
A
e
+
DPP/ P 35
3
Q.14 A parallel plate capacitor is charged and the charging battery
is then disconnected. If the plates of the capacitor are moved
further apart by means of insulating handles, then
(a) The charge on the capacitor  increases
(b) The voltage across the plates decreases
(c) The capacitance increases
(d) The electrostatic energy stored in the capacitor
increases
Q.15 A parallel plate capacitor of plate area A and plates separation
distance d is charged by applying a potential V
0
 between the
plates. The dielectric constant of the medium between the
plates is K. What is the uniform electric field E between the
plates of the capacitor ?
(a)
0
0
CV
E
KA
=Î (b)
0
V
E
Kd
=
(c)
0
V
E
KA
= (d)
0
0
Kvd
E
A
=
Î
DIRECTIONS (Q.16-Q.18) : In the following questions, more
than one of the answers  given are correct. Select the correct
answers  and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct ( b) 1 and 2 are correct
(c) 2 and 4 are correct ( d) 1 and 3 are correct
Q.16 A parallel plate air condenser is connected with a battery.
Its charge, potenital difference, electric field and energy are
Q
0 
, V
0 
, E
0 
, and U
0 
, respectively . In order to fill the complete
space between the plates a dielectric slab is inserted, the
battery is still connected. Now the corresponding values Q,
V , E and U are in relation with the initially stated as
(1) V > V
0
(2) Q > Q
0
(3) E > E
0
(4) U > U
0
Q.17 The false statement are, on increasing the distance between
the plates of a parallel plate condenser,
(1) The electric field intensity between the plates will
decrease
(2) The electric field intensity between the plates will
increase
(3) The P . D. between the plates will decrease
(4) The electric field intensity between the plates will
remain unchanged
Q.18 The capacitance of a parallel plate condenser depends on
(1) Area of the plates
(2) Medium between the plates
(3) Distance  between the plates
(4) Metal of the plates
DIRECTIONS (Q.19-Q.21) : Read the passage given below and
answer the questions that follows :
Capacitor C
3
 in the circuit is variable capacitor (its capacitance
can be varied). Graph is plotted between potential difference V
1
(across capacitor C
1
) versus C
3
.
Electric potential V
1
 approaches on asymptote of 10 volts as
C
3
 ® ¥.
V
C
1
C
2
C
3  
2
2
4
4
6
6
8
8
10
V
1
C
3
Q.19 The ratio of the capacitance 
1
2
C
C
 will be
(a) 2 / 3 (b) 4 / 3 (c) 3 / 4 (d) 3 / 2
Q.20 The value of C
3
 for which potential difference across C
1
will become 8V, is
(a) 1.5C
1
(b) 2.5C
1
(c) 3.5 C
1
(d) 4.5 C
1
Q.21 The ratio of energy stored in capacitor C
1
 to that of total
energy when C
3
 ® ¥ is
(a) zero (b) 1/3
(c)1 (d) Data insufficient
DIRECTIONS (Q. 22-Q.24) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. Y ou have to select the
correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
Page 4


DIRECTIONS (Q.1-Q.15) : There are 15 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A parallel plate capacitor is charged to a potential
difference of 50V. It is discharged through a resistance.
After 1 second, the potential difference between plates
becomes 40V. Then
(a) Fraction of stored energy after 1 second is 16/25
(b) Potential difference between the plates after 2
seconds will be 30V
(c) Potential difference between the plates after 2
seconds will be 20V
(d) Fraction of stored energy after 1 second is 4/5
Q.2 Five identical plates each of area A are joined as shown in
the figure. The distance between the plates is d. The plates
are connected to a potential difference of V volts. The
charge on plates 1 and 4 will be respectively
(a)
00
2
,
22
AV AV
dd
ee
(b)
00
2
,
22
AV AV
dd
ee
(c)
00
2
,
AV AV
dd
e -e
V
+
–
1 2 3 4 5
(d)
00
2
,
AV AV
dd
-e -e
Q.3 Figure given below shows two identical parallel plate capacitors
connected to a battery with switch S closed. The switch is now opened
and the free space between the plates of capacitors is filled with a
dielectric of dielectric constant 3. What will be the ratio of total
electrostatic energy stored in both capacitors before and after the
introduction of the dielectric?
(a) 3 : 1
(b) 5 : 1
(c) 3 : 5
B A V
(d) 5 : 3
2
DPP/ P 35
Q.4 All six capacitors shown are identical, Each can withstand
maximum 200 volts between its terminals. The maximum
voltage that can be safely applied between A and B is
(a) 1200 V
(b) 400 V
A B
(c) 800 V
(d) 200 V
Q.5 A capacitor of capacity C
1
 is charged upto V volt and then
connected to an uncharged capacitor of capacity C
2
. Then
final potential difference across each will be
(a)
2
12
CV
CC +
(b) 
2
1
1
æö
+
ç÷
èø
C
V
C
 (c) 
1
12
CV
CC +
   (d)   
2
1
1
æö
-
ç÷
èø
C
V
C
Q.6 Two capacitors of capacitances 3mFand 6mFare 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
(a) 6 volt (b) 4 volt
(c) 3 volt (d) zero
Q.7 In the figure a capacitor is filled with dielectrics K
1
, K
2
and K
3
. The resultant capacitance is
(a)
0
1 23
2 1 11 éù e
++
êú
ëû
A
d K KK
(b)
0
1 23
1 11 éù e
++
êú
ëû
A
d K KK
 d/2
 A/2 A/2
 d
1
K
2
K
3
K
(c)
0
1 23
2
[]
e
++
A
K KK
d
(d) None of these
Q.8 The resultant capacitance of given circut is
(a)
3C
(b)
2C
(c)
C
P
Q
2C
2C
2C
C C
C
(d)
3
C
Q.9 Two dielectric slabs of constant K
1 
and K
2 
have been filled
in between the plates of a capacitor as shown below. What
will be the capacitance of the capacitor
(a)
0
12
2
()
A
KK
d
e
+
(b)
0 12
12
2 AKK
d KK
æö e +
ç÷
´
èø
 d
1
K
2
K
(c)
0 12
12
4 A KK
d KK
æö e ´
ç÷
+
èø
(d)
0 12
12
2 A KK
d KK
æö e ´
ç÷
+
èø
Q.10Eight drops of mercury of equal radii possessing equal
charges combine to form a big drop. Then the capacitance
of bigger drop compared to each individual small drop is
(a) 8 times (b) 4 times
(c) 2 times (d) 32 times
Q.11 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
(a)
0
1
1
A
dt
k
e
æö
+-
ç÷
èø
(b)
0
1
1
A
dt
k
e
æö
++
ç÷
èø
(c)
0
1
1
A
dt
k
e
æö
--
ç÷
èø
(d)
0
1
1
A
dt
k
e
æö
-+
ç÷
èø
Q.12 There is an air filled 1pF parallel plate capacitor. When
the plate separation is doubled and the space is filled with
wax, the capacitance increases to 2pF. The dielectric
constant of wax is
(a)2 (b)4 (c)6 (d)8
Q.13 Between the plates of a parallel plate condenser, a plate of
thickness t
1 
and dielectric constant k
1 
is placed. In the rest
of the space, there is another plate of thickness t
2 
and
dielectric constant k
2 
. The potential difference across the
condenser will be
(a)
12
0 12
tt Q
A KK
æö
+
ç÷
e
èø
(b)
0 12
12
Qtt
A KK
æö e
+
ç÷
èø
(c)
12
0 12
KK Q
A tt
æö
+
ç÷
e
èø
(d)
0
11 22
()
Q
Kt Kt
A
e
+
DPP/ P 35
3
Q.14 A parallel plate capacitor is charged and the charging battery
is then disconnected. If the plates of the capacitor are moved
further apart by means of insulating handles, then
(a) The charge on the capacitor  increases
(b) The voltage across the plates decreases
(c) The capacitance increases
(d) The electrostatic energy stored in the capacitor
increases
Q.15 A parallel plate capacitor of plate area A and plates separation
distance d is charged by applying a potential V
0
 between the
plates. The dielectric constant of the medium between the
plates is K. What is the uniform electric field E between the
plates of the capacitor ?
(a)
0
0
CV
E
KA
=Î (b)
0
V
E
Kd
=
(c)
0
V
E
KA
= (d)
0
0
Kvd
E
A
=
Î
DIRECTIONS (Q.16-Q.18) : In the following questions, more
than one of the answers  given are correct. Select the correct
answers  and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct ( b) 1 and 2 are correct
(c) 2 and 4 are correct ( d) 1 and 3 are correct
Q.16 A parallel plate air condenser is connected with a battery.
Its charge, potenital difference, electric field and energy are
Q
0 
, V
0 
, E
0 
, and U
0 
, respectively . In order to fill the complete
space between the plates a dielectric slab is inserted, the
battery is still connected. Now the corresponding values Q,
V , E and U are in relation with the initially stated as
(1) V > V
0
(2) Q > Q
0
(3) E > E
0
(4) U > U
0
Q.17 The false statement are, on increasing the distance between
the plates of a parallel plate condenser,
(1) The electric field intensity between the plates will
decrease
(2) The electric field intensity between the plates will
increase
(3) The P . D. between the plates will decrease
(4) The electric field intensity between the plates will
remain unchanged
Q.18 The capacitance of a parallel plate condenser depends on
(1) Area of the plates
(2) Medium between the plates
(3) Distance  between the plates
(4) Metal of the plates
DIRECTIONS (Q.19-Q.21) : Read the passage given below and
answer the questions that follows :
Capacitor C
3
 in the circuit is variable capacitor (its capacitance
can be varied). Graph is plotted between potential difference V
1
(across capacitor C
1
) versus C
3
.
Electric potential V
1
 approaches on asymptote of 10 volts as
C
3
 ® ¥.
V
C
1
C
2
C
3  
2
2
4
4
6
6
8
8
10
V
1
C
3
Q.19 The ratio of the capacitance 
1
2
C
C
 will be
(a) 2 / 3 (b) 4 / 3 (c) 3 / 4 (d) 3 / 2
Q.20 The value of C
3
 for which potential difference across C
1
will become 8V, is
(a) 1.5C
1
(b) 2.5C
1
(c) 3.5 C
1
(d) 4.5 C
1
Q.21 The ratio of energy stored in capacitor C
1
 to that of total
energy when C
3
 ® ¥ is
(a) zero (b) 1/3
(c)1 (d) Data insufficient
DIRECTIONS (Q. 22-Q.24) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. Y ou have to select the
correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
4
DPP/ P 35
Q.22 Statement-1 : The force with which one plate of a parallel
plate capacitor is attracted towards the other plate is equal
to square of surface density per 
0
2 Î per unit area.
Statement-2 : The electric field due to one charged plate
of the capacitor at the location of the other is equal to
surface density per 2
0
Î .
Q.23Statement-1 : Circuit containing capacitors should be
handled cautiously even when there is no current.
Statement-2 : The capacitors are very delicate and so quickly
break down.
Q.24 Statement-1 : If the distance between parallel plates of a
capacitor is halved and dielectric constant is made three
times, then the capacitance becomes 6 times.
Statement-1 : Capacitance of the capacitor does not
depend upon the nature of the material of plates.