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