# Capacitors: JEE Advance (Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

## JEE: Capacitors: JEE Advance (Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

The document Capacitors: JEE Advance (Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE is a part of the JEE Course DC Pandey Solutions for JEE Physics.
All you need of JEE at this link: JEE
``` Page 1

For JEE Advanced
Objective Questions
Single Correct Option
Q 1.  Two very large thin conducting plates having same cross-sectional area are placed as shown in
figure. They are carrying charges Q and 3Q respectively. The variation of electric field as a
function at x(for x = 0 to x = 3d) will be best represented by

(a)     (b)
(c)     (d)
Q 2.  The electric field on two sides of a thin sheet of charge is shown in the figure. The charge density
on the sheet is

(a) 2 ?
0
(b) 4 ?
0
(c) 10 ?
0
(d) zero
Q 3.  In the circuit shown in figure the capacitors are initially uncharged. The current through resistor
PQ just after closing the switch is

(a) 2 A from P to Q    (b) 2A from Q to P
(c) 6A from P to Q    (d) zero
Page 2

For JEE Advanced
Objective Questions
Single Correct Option
Q 1.  Two very large thin conducting plates having same cross-sectional area are placed as shown in
figure. They are carrying charges Q and 3Q respectively. The variation of electric field as a
function at x(for x = 0 to x = 3d) will be best represented by

(a)     (b)
(c)     (d)
Q 2.  The electric field on two sides of a thin sheet of charge is shown in the figure. The charge density
on the sheet is

(a) 2 ?
0
(b) 4 ?
0
(c) 10 ?
0
(d) zero
Q 3.  In the circuit shown in figure the capacitors are initially uncharged. The current through resistor
PQ just after closing the switch is

(a) 2 A from P to Q    (b) 2A from Q to P
(c) 6A from P to Q    (d) zero
Q 4.  A graph between current and time during charging of a capacitor by a battery in series with a
resistor is shown. The graphs are drawn for two circuits. R
l
,R
2
,C
1
,C
2
and V
1
, V
2
are the values of
resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of
resistance, capacitance, EMF) are different in the two circuits. What may be the correct option(s)?

(a)V
1
= V
2
, R
1
> R
2
, C
1
> C
2
(b)V
1
> V
2
, R
1
> R
2
, C
1
= C
2

(c) V
1
< V
2
, R
1
< R
2
, C
1
= C
2
(d) V
1
< V
2
, R
1
= R
2
, C
1
< C
2

Q 5.  A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A
resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the
battery by the time capacitor is 50% charged is
(a)
2
3
EC
8
(b)
2
EC
6
(c)
2
EC
12
(d)
2
EC
24

Q 6.  For the circuit shown in the figure, determine the charge on capacitor in steady state?

(a) 4 ?C  (b) 6 ?C  (c) 1 ?C  (d) Zero
Q 7.  For the circuit shown in the figure, find the charge stored on capacitor in steady state

(a)
0
RC
E
RR ?
(b)
0
0
RC
(E E )
R
?  (c) zero  (d)
0
0
RC
(E E )
RR
?
?

Q 8.  Two similar parallel plate capacitors each of capacity C
0
are connected in series. The combination
is connected with a voltage source of V
o
. Now separation between the plates of one capacitor is
increased by a distance d and the separation between the plates of another capacitor is decreased
by the distance d/2 The distance between the plates of each capacitor was d before the change in
separation. Then, select the correct choice.
(a) The new capacity of the system will increase
(b) The new capacity of the system will decrease
(c) The new capacity of the system will remain same
(d) data insufficient
Q 9.  The switch shown in the figure is closed at t = 0. The charge on the capacitor as a function of time
is given by
Page 3

For JEE Advanced
Objective Questions
Single Correct Option
Q 1.  Two very large thin conducting plates having same cross-sectional area are placed as shown in
figure. They are carrying charges Q and 3Q respectively. The variation of electric field as a
function at x(for x = 0 to x = 3d) will be best represented by

(a)     (b)
(c)     (d)
Q 2.  The electric field on two sides of a thin sheet of charge is shown in the figure. The charge density
on the sheet is

(a) 2 ?
0
(b) 4 ?
0
(c) 10 ?
0
(d) zero
Q 3.  In the circuit shown in figure the capacitors are initially uncharged. The current through resistor
PQ just after closing the switch is

(a) 2 A from P to Q    (b) 2A from Q to P
(c) 6A from P to Q    (d) zero
Q 4.  A graph between current and time during charging of a capacitor by a battery in series with a
resistor is shown. The graphs are drawn for two circuits. R
l
,R
2
,C
1
,C
2
and V
1
, V
2
are the values of
resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of
resistance, capacitance, EMF) are different in the two circuits. What may be the correct option(s)?

(a)V
1
= V
2
, R
1
> R
2
, C
1
> C
2
(b)V
1
> V
2
, R
1
> R
2
, C
1
= C
2

(c) V
1
< V
2
, R
1
< R
2
, C
1
= C
2
(d) V
1
< V
2
, R
1
= R
2
, C
1
< C
2

Q 5.  A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A
resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the
battery by the time capacitor is 50% charged is
(a)
2
3
EC
8
(b)
2
EC
6
(c)
2
EC
12
(d)
2
EC
24

Q 6.  For the circuit shown in the figure, determine the charge on capacitor in steady state?

(a) 4 ?C  (b) 6 ?C  (c) 1 ?C  (d) Zero
Q 7.  For the circuit shown in the figure, find the charge stored on capacitor in steady state

(a)
0
RC
E
RR ?
(b)
0
0
RC
(E E )
R
?  (c) zero  (d)
0
0
RC
(E E )
RR
?
?

Q 8.  Two similar parallel plate capacitors each of capacity C
0
are connected in series. The combination
is connected with a voltage source of V
o
. Now separation between the plates of one capacitor is
increased by a distance d and the separation between the plates of another capacitor is decreased
by the distance d/2 The distance between the plates of each capacitor was d before the change in
separation. Then, select the correct choice.
(a) The new capacity of the system will increase
(b) The new capacity of the system will decrease
(c) The new capacity of the system will remain same
(d) data insufficient
Q 9.  The switch shown in the figure is closed at t = 0. The charge on the capacitor as a function of time
is given by

(a) CV(1 - e
-t/RC
) (b) 3CV(1 - e
-t/RC
) (c) CV(1 - e
-3t/RC
)  (d) CV(1 - e
-t/3RC
)
Q 10.  A 2 ?F capacitor C
1
is charged to a voltage 100 V and a 4 ?F capacitor C
2
is charged to a voltage
50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel
connection?
(a) 1.7 J   (b) 0.17 J  (c) 1.7 × 10
-2
J   (d) 1.7 × 10
-3
J
Q 11.  The figure shows a graph of the current in a discharging circuit of a capacitor through a resistor of
resistance 10 ?

(a) The initial potential difference across the capacitor is 100 V
(b) The capacitance of the capacitor is
1
F
10ln 2

(c) The total heat produced in the circuit will be
500
J
ln 2

(d) All of the above
Q 12.  Four capacitors are connected in series with a battery of emf 10 V as shown in the figure. The
points P is earthed. The potential of point A is equal in magnitude to potential of point B but
opposite in sign if

(a)

C
1
+ C
2
+ C
3
= C
4
(b)
1 2 3 4
1 1 1 1
C C C C
? ? ?

(c)
1 2 3
4 222
1 2 3
C C C
C
CCC
?
??

(d) C
4
= (C
1
C
2
C
3
)
1/3

Q 13.  A capacitor of capacity C is charged to a potential difference V and another capacitor of capacity
2C is charged to a potential difference 4 V. The charging batteries are disconnected and the two
capacitors are connected with reverse polarity (i.e., positive plate of first capacitor is connected to
negative plate of second

capacitor). The heat produced during the redistribution of charge between
the capacitors will be
(a)
2
125CV
3
(b)
2
50CV
3
(c) 2CV
2
(d)
2
25CV
3

Q 14.  A capacitor of capacitance 2 ?F

is charged to a potential difference of 5 V. Now the charging
battery is disconnected and the capacitor is connected in parallel to a resistor of 5 ? and another
Page 4

For JEE Advanced
Objective Questions
Single Correct Option
Q 1.  Two very large thin conducting plates having same cross-sectional area are placed as shown in
figure. They are carrying charges Q and 3Q respectively. The variation of electric field as a
function at x(for x = 0 to x = 3d) will be best represented by

(a)     (b)
(c)     (d)
Q 2.  The electric field on two sides of a thin sheet of charge is shown in the figure. The charge density
on the sheet is

(a) 2 ?
0
(b) 4 ?
0
(c) 10 ?
0
(d) zero
Q 3.  In the circuit shown in figure the capacitors are initially uncharged. The current through resistor
PQ just after closing the switch is

(a) 2 A from P to Q    (b) 2A from Q to P
(c) 6A from P to Q    (d) zero
Q 4.  A graph between current and time during charging of a capacitor by a battery in series with a
resistor is shown. The graphs are drawn for two circuits. R
l
,R
2
,C
1
,C
2
and V
1
, V
2
are the values of
resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of
resistance, capacitance, EMF) are different in the two circuits. What may be the correct option(s)?

(a)V
1
= V
2
, R
1
> R
2
, C
1
> C
2
(b)V
1
> V
2
, R
1
> R
2
, C
1
= C
2

(c) V
1
< V
2
, R
1
< R
2
, C
1
= C
2
(d) V
1
< V
2
, R
1
= R
2
, C
1
< C
2

Q 5.  A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A
resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the
battery by the time capacitor is 50% charged is
(a)
2
3
EC
8
(b)
2
EC
6
(c)
2
EC
12
(d)
2
EC
24

Q 6.  For the circuit shown in the figure, determine the charge on capacitor in steady state?

(a) 4 ?C  (b) 6 ?C  (c) 1 ?C  (d) Zero
Q 7.  For the circuit shown in the figure, find the charge stored on capacitor in steady state

(a)
0
RC
E
RR ?
(b)
0
0
RC
(E E )
R
?  (c) zero  (d)
0
0
RC
(E E )
RR
?
?

Q 8.  Two similar parallel plate capacitors each of capacity C
0
are connected in series. The combination
is connected with a voltage source of V
o
. Now separation between the plates of one capacitor is
increased by a distance d and the separation between the plates of another capacitor is decreased
by the distance d/2 The distance between the plates of each capacitor was d before the change in
separation. Then, select the correct choice.
(a) The new capacity of the system will increase
(b) The new capacity of the system will decrease
(c) The new capacity of the system will remain same
(d) data insufficient
Q 9.  The switch shown in the figure is closed at t = 0. The charge on the capacitor as a function of time
is given by

(a) CV(1 - e
-t/RC
) (b) 3CV(1 - e
-t/RC
) (c) CV(1 - e
-3t/RC
)  (d) CV(1 - e
-t/3RC
)
Q 10.  A 2 ?F capacitor C
1
is charged to a voltage 100 V and a 4 ?F capacitor C
2
is charged to a voltage
50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel
connection?
(a) 1.7 J   (b) 0.17 J  (c) 1.7 × 10
-2
J   (d) 1.7 × 10
-3
J
Q 11.  The figure shows a graph of the current in a discharging circuit of a capacitor through a resistor of
resistance 10 ?

(a) The initial potential difference across the capacitor is 100 V
(b) The capacitance of the capacitor is
1
F
10ln 2

(c) The total heat produced in the circuit will be
500
J
ln 2

(d) All of the above
Q 12.  Four capacitors are connected in series with a battery of emf 10 V as shown in the figure. The
points P is earthed. The potential of point A is equal in magnitude to potential of point B but
opposite in sign if

(a)

C
1
+ C
2
+ C
3
= C
4
(b)
1 2 3 4
1 1 1 1
C C C C
? ? ?

(c)
1 2 3
4 222
1 2 3
C C C
C
CCC
?
??

(d) C
4
= (C
1
C
2
C
3
)
1/3

Q 13.  A capacitor of capacity C is charged to a potential difference V and another capacitor of capacity
2C is charged to a potential difference 4 V. The charging batteries are disconnected and the two
capacitors are connected with reverse polarity (i.e., positive plate of first capacitor is connected to
negative plate of second

capacitor). The heat produced during the redistribution of charge between
the capacitors will be
(a)
2
125CV
3
(b)
2
50CV
3
(c) 2CV
2
(d)
2
25CV
3

Q 14.  A capacitor of capacitance 2 ?F

is charged to a potential difference of 5 V. Now the charging
battery is disconnected and the capacitor is connected in parallel to a resistor of 5 ? and another
unknown resistor of resistance R as shown in figure. If the total heat produced in 5 ?

resistance is
10 ?J, then the unknown resistance R is equal

to

(a) 10 ?  (b) 15 ?  (c) (10/3) ?  (d) 7.5 ?
Q 15.  In the circuit shown in figure switch S is thrown to position 1 at t = 0. When the current in the
resistor is 1 A it is then shifted to position 2. The total heat generated in the circuit after shifting to
position 2 is

(a)

zero   (b) 625 ?J  (c) 100 ?J  (d) None of the above
Q 16.  The flow of charge through switch if it is closed is

(a) zero  (b) q/4   (c) 2q/3  (d) q/3
Q 17.  Consider the arrangement of three plates X, Y and Z each of the area A and separation d. The
energy stored when the plates are fully charged is

(a) ?
0
AV
2
/2d  (b) ?
0
AV
2
/d  (c) 2 ?
0
AV
2
/d  (d) 3 ?
0
AV
2
/d
Q 18.  Consider a capacitor - charging circuit. Let Q
1
be the charge given to the capacitor in time interval
of 20 ms and Q
2
be the charge given in the next time interval of 20 ms. Let charge be
deposited in a time interval t
1
and the next charge is deposited in the next time interval t
2
.
Then
(a) Q
1
> Q
2
> t
1
> t
2
(b) Q
1
> Q
2
, t
1
< t
2
(c) Q
1
< Q
2
, t
1
> t
2
(d) Q
1
< Q
2
, t
1
< t
2

Q 19.  The current in 1 ? resistance and charge stored in the capacitor are
Page 5

For JEE Advanced
Objective Questions
Single Correct Option
Q 1.  Two very large thin conducting plates having same cross-sectional area are placed as shown in
figure. They are carrying charges Q and 3Q respectively. The variation of electric field as a
function at x(for x = 0 to x = 3d) will be best represented by

(a)     (b)
(c)     (d)
Q 2.  The electric field on two sides of a thin sheet of charge is shown in the figure. The charge density
on the sheet is

(a) 2 ?
0
(b) 4 ?
0
(c) 10 ?
0
(d) zero
Q 3.  In the circuit shown in figure the capacitors are initially uncharged. The current through resistor
PQ just after closing the switch is

(a) 2 A from P to Q    (b) 2A from Q to P
(c) 6A from P to Q    (d) zero
Q 4.  A graph between current and time during charging of a capacitor by a battery in series with a
resistor is shown. The graphs are drawn for two circuits. R
l
,R
2
,C
1
,C
2
and V
1
, V
2
are the values of
resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of
resistance, capacitance, EMF) are different in the two circuits. What may be the correct option(s)?

(a)V
1
= V
2
, R
1
> R
2
, C
1
> C
2
(b)V
1
> V
2
, R
1
> R
2
, C
1
= C
2

(c) V
1
< V
2
, R
1
< R
2
, C
1
= C
2
(d) V
1
< V
2
, R
1
= R
2
, C
1
< C
2

Q 5.  A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A
resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the
battery by the time capacitor is 50% charged is
(a)
2
3
EC
8
(b)
2
EC
6
(c)
2
EC
12
(d)
2
EC
24

Q 6.  For the circuit shown in the figure, determine the charge on capacitor in steady state?

(a) 4 ?C  (b) 6 ?C  (c) 1 ?C  (d) Zero
Q 7.  For the circuit shown in the figure, find the charge stored on capacitor in steady state

(a)
0
RC
E
RR ?
(b)
0
0
RC
(E E )
R
?  (c) zero  (d)
0
0
RC
(E E )
RR
?
?

Q 8.  Two similar parallel plate capacitors each of capacity C
0
are connected in series. The combination
is connected with a voltage source of V
o
. Now separation between the plates of one capacitor is
increased by a distance d and the separation between the plates of another capacitor is decreased
by the distance d/2 The distance between the plates of each capacitor was d before the change in
separation. Then, select the correct choice.
(a) The new capacity of the system will increase
(b) The new capacity of the system will decrease
(c) The new capacity of the system will remain same
(d) data insufficient
Q 9.  The switch shown in the figure is closed at t = 0. The charge on the capacitor as a function of time
is given by

(a) CV(1 - e
-t/RC
) (b) 3CV(1 - e
-t/RC
) (c) CV(1 - e
-3t/RC
)  (d) CV(1 - e
-t/3RC
)
Q 10.  A 2 ?F capacitor C
1
is charged to a voltage 100 V and a 4 ?F capacitor C
2
is charged to a voltage
50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel
connection?
(a) 1.7 J   (b) 0.17 J  (c) 1.7 × 10
-2
J   (d) 1.7 × 10
-3
J
Q 11.  The figure shows a graph of the current in a discharging circuit of a capacitor through a resistor of
resistance 10 ?

(a) The initial potential difference across the capacitor is 100 V
(b) The capacitance of the capacitor is
1
F
10ln 2

(c) The total heat produced in the circuit will be
500
J
ln 2

(d) All of the above
Q 12.  Four capacitors are connected in series with a battery of emf 10 V as shown in the figure. The
points P is earthed. The potential of point A is equal in magnitude to potential of point B but
opposite in sign if

(a)

C
1
+ C
2
+ C
3
= C
4
(b)
1 2 3 4
1 1 1 1
C C C C
? ? ?

(c)
1 2 3
4 222
1 2 3
C C C
C
CCC
?
??

(d) C
4
= (C
1
C
2
C
3
)
1/3

Q 13.  A capacitor of capacity C is charged to a potential difference V and another capacitor of capacity
2C is charged to a potential difference 4 V. The charging batteries are disconnected and the two
capacitors are connected with reverse polarity (i.e., positive plate of first capacitor is connected to
negative plate of second

capacitor). The heat produced during the redistribution of charge between
the capacitors will be
(a)
2
125CV
3
(b)
2
50CV
3
(c) 2CV
2
(d)
2
25CV
3

Q 14.  A capacitor of capacitance 2 ?F

is charged to a potential difference of 5 V. Now the charging
battery is disconnected and the capacitor is connected in parallel to a resistor of 5 ? and another
unknown resistor of resistance R as shown in figure. If the total heat produced in 5 ?

resistance is
10 ?J, then the unknown resistance R is equal

to

(a) 10 ?  (b) 15 ?  (c) (10/3) ?  (d) 7.5 ?
Q 15.  In the circuit shown in figure switch S is thrown to position 1 at t = 0. When the current in the
resistor is 1 A it is then shifted to position 2. The total heat generated in the circuit after shifting to
position 2 is

(a)

zero   (b) 625 ?J  (c) 100 ?J  (d) None of the above
Q 16.  The flow of charge through switch if it is closed is

(a) zero  (b) q/4   (c) 2q/3  (d) q/3
Q 17.  Consider the arrangement of three plates X, Y and Z each of the area A and separation d. The
energy stored when the plates are fully charged is

(a) ?
0
AV
2
/2d  (b) ?
0
AV
2
/d  (c) 2 ?
0
AV
2
/d  (d) 3 ?
0
AV
2
/d
Q 18.  Consider a capacitor - charging circuit. Let Q
1
be the charge given to the capacitor in time interval
of 20 ms and Q
2
be the charge given in the next time interval of 20 ms. Let charge be
deposited in a time interval t
1
and the next charge is deposited in the next time interval t
2
.
Then
(a) Q
1
> Q
2
> t
1
> t
2
(b) Q
1
> Q
2
, t
1
< t
2
(c) Q
1
< Q
2
, t
1
> t
2
(d) Q
1
< Q
2
, t
1
< t
2

Q 19.  The current in 1 ? resistance and charge stored in the capacitor are

(a) 4A, 6 ?C  (b) 7A, 12 ?C  (c) 4A, 12 ?C  (d) 7A, 6 ?C
Q 20.  A capacitor C is connected to two equal resistances as shown in the figure. Consider the following
statements

(i) At the time of charging of capacitor time constant of the circuit is 2 CR
(ii) At the time of discharging of the capacitor the time constant of the circuit is CR
(iii) At the time of discharging of the capacitor the time constant of the circuit is 2CR
(iv) At the time of charging of capacitor the time constant of the circuit is CR
(a) Statements (i) and (ii) only are correct  (b) Statements (ii) and (iii) only are correct
(c) Statements (iii) and (iv) only are correct  (d) Statements (i) and (iii) only are correct
Q 21.  Two capacitors C
1
= 1 ?F and C
2
= 3 ?F each is charged to a potential difference of 100 V but
with opposite polarity as shown in the figure. When the switch S is closed, the new potential
difference between the points a and b is

(a) 200 V   (b) 100 V  (c) 50 V   (d) 25 V
Q 22.  Four capacitors are connected as shown in figure to a 30 V battery. The potential difference
between points a and b is

(a) 5 V   (b) 9 V   (c) 10 V  (d) 13 V
Q 23.  Four identical capacitors are connected in series with a 12 V battery as shown in figure. The
potentials of points A and B are
```
 Use Code STAYHOME200 and get INR 200 additional OFF

## DC Pandey Solutions for JEE Physics

210 docs

### Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;