Capacitors: JEE Advance (Part - 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

 Page 1


For JEE Advanced 
More than One Correct Options 
 
Q 1.  X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is 
given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure 
 
  (a) The field at B is 
0
Q
2A ?
   
(b) The field at B is 
0
Q
A ?
 
  (c) The field at A, B and C are of the same magnitude 
  (d) The fields at A and C are of the same magnitude, but in opposite directions 
Q 2.  In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements.  
 
(a) Rate of increase of charge is same in both the capacitors 
  (b) Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 
  (c) Time constants of both the capacitors are equal 
  (d) Steady state charge in capacitors C and 2C are in the ratio of 1 : 2 
Q 3.  An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and 
each ammeter is 100 £1. The charge on the capacitor of 100 ?F in steady state is 4 mC. Choose 
correct statements (s) regarding the given circuit. 
 
  (a) Reading of voltmeter V
2
 is 16 V 
  (b) Reading of ammeter A
1
 is zero and A
2
 is 1/25 A 
  (c) Reading of voltmeter V
1
 is 40 V ' 
  (d) EMF of the ideal cell is 66 V 
Q 4.  In the circuit shown, A and B are equal resistances. When S is closed, the capacitor C charges 
from the cell of emf ? and reaches a steady state 
Page 2


For JEE Advanced 
More than One Correct Options 
 
Q 1.  X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is 
given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure 
 
  (a) The field at B is 
0
Q
2A ?
   
(b) The field at B is 
0
Q
A ?
 
  (c) The field at A, B and C are of the same magnitude 
  (d) The fields at A and C are of the same magnitude, but in opposite directions 
Q 2.  In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements.  
 
(a) Rate of increase of charge is same in both the capacitors 
  (b) Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 
  (c) Time constants of both the capacitors are equal 
  (d) Steady state charge in capacitors C and 2C are in the ratio of 1 : 2 
Q 3.  An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and 
each ammeter is 100 £1. The charge on the capacitor of 100 ?F in steady state is 4 mC. Choose 
correct statements (s) regarding the given circuit. 
 
  (a) Reading of voltmeter V
2
 is 16 V 
  (b) Reading of ammeter A
1
 is zero and A
2
 is 1/25 A 
  (c) Reading of voltmeter V
1
 is 40 V ' 
  (d) EMF of the ideal cell is 66 V 
Q 4.  In the circuit shown, A and B are equal resistances. When S is closed, the capacitor C charges 
from the cell of emf ? and reaches a steady state 
 
  (a) During charging, more heat is produced in A then in B 
  (b) In steady state, heat is produced at the same rate in A and B 
  (c) In the steady state, energy stored in C is 
2
1
C
4
? 
  (d) In the steady state energy stored in C is 
2
1
C
8
? 
Q 5.  A parallel plate capacitor is charged from a cell and then isolated from it. The separation between 
the plates is now increased  
  (a) The force of attraction between the plates will decrease  
  (b) The field in the region between the plates will not change  
  (c) The energy stored in the capacitor will increase 
  (d) The potential difference between the plates will decrease 
Q 6.  In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is 
closed 
 
  (a) positive charge will flow out of the positive terminal of the cell 
  (b) positive charge will enter the positive terminal of the cell 
  (c) the amount of the charge flowing through the cell will be 
1
CE
3
 
  (d) the amount of charge flowing through the cell is (4/3) CE 
Q 7.  Two capacitors of 2 ?F and 3 ?F
 
are charged to 150 V and 120 V respectively. The plates of 
capacitor are connected as shown in the figure. An uncharged capacitor
 
of capacity falls to 
the free end of the wire. Then 
  
  (a) charge on 1.5 ?F capacitor is 180 ?C (b) charge on 2 ?F
 
capacitor is 120 ?C 
  (c) positive charge flows through A from right to left 
  (d) positive charge flows through A from left to right 
Page 3


For JEE Advanced 
More than One Correct Options 
 
Q 1.  X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is 
given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure 
 
  (a) The field at B is 
0
Q
2A ?
   
(b) The field at B is 
0
Q
A ?
 
  (c) The field at A, B and C are of the same magnitude 
  (d) The fields at A and C are of the same magnitude, but in opposite directions 
Q 2.  In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements.  
 
(a) Rate of increase of charge is same in both the capacitors 
  (b) Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 
  (c) Time constants of both the capacitors are equal 
  (d) Steady state charge in capacitors C and 2C are in the ratio of 1 : 2 
Q 3.  An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and 
each ammeter is 100 £1. The charge on the capacitor of 100 ?F in steady state is 4 mC. Choose 
correct statements (s) regarding the given circuit. 
 
  (a) Reading of voltmeter V
2
 is 16 V 
  (b) Reading of ammeter A
1
 is zero and A
2
 is 1/25 A 
  (c) Reading of voltmeter V
1
 is 40 V ' 
  (d) EMF of the ideal cell is 66 V 
Q 4.  In the circuit shown, A and B are equal resistances. When S is closed, the capacitor C charges 
from the cell of emf ? and reaches a steady state 
 
  (a) During charging, more heat is produced in A then in B 
  (b) In steady state, heat is produced at the same rate in A and B 
  (c) In the steady state, energy stored in C is 
2
1
C
4
? 
  (d) In the steady state energy stored in C is 
2
1
C
8
? 
Q 5.  A parallel plate capacitor is charged from a cell and then isolated from it. The separation between 
the plates is now increased  
  (a) The force of attraction between the plates will decrease  
  (b) The field in the region between the plates will not change  
  (c) The energy stored in the capacitor will increase 
  (d) The potential difference between the plates will decrease 
Q 6.  In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is 
closed 
 
  (a) positive charge will flow out of the positive terminal of the cell 
  (b) positive charge will enter the positive terminal of the cell 
  (c) the amount of the charge flowing through the cell will be 
1
CE
3
 
  (d) the amount of charge flowing through the cell is (4/3) CE 
Q 7.  Two capacitors of 2 ?F and 3 ?F
 
are charged to 150 V and 120 V respectively. The plates of 
capacitor are connected as shown in the figure. An uncharged capacitor
 
of capacity falls to 
the free end of the wire. Then 
  
  (a) charge on 1.5 ?F capacitor is 180 ?C (b) charge on 2 ?F
 
capacitor is 120 ?C 
  (c) positive charge flows through A from right to left 
  (d) positive charge flows through A from left to right 
Q 8.  A parallel plate capacitor is charged and then the battery is disconnected. When the plates of the 
capacitor are brought closer, then 
  (a) energy stored in the capacitor decreases 
  (b) the potential difference between the plates decreases 
  (c) the capacitance increases   (d) the electric field between the plates decreases 
Q 9.  A capacitor of 2 F (practically not possible to have a capacity of 2 F) is charged by a battery of 6 
V. The battery is removed and circuit is made as shown. Switch is closed at time t = 0. Choose the 
correct options 
 
  (a) At time t - 0 current in the circuit is 2 A 
  (b) At time t = (6 ln 2) second potential difference across capacitor is 3 V 
  (c) At time t = (6 ln 2) second, potential difference across 1 ? resistance is 1 V 
  (d) At time t = (6 ln 2) second potential difference across 2? resistance is 2 V 
Q 10.  Given that potential difference across 1 ?F
 
capacitor is 10 V. Then  
 
  (a) potential difference across 4 ?F
 
capacitor is 40 V 
  (b) potential difference across 4 ?F
 
capacitor is 2.5 V 
  (c) potential difference across 3 ?F
 
capacitor is 5 V 
  (d) value of E is 70 V 
Answers 
  More than One Correct Options 
1. (a,c,d)2. (b,c,d) 3. (b,c) 4. (a,b,d) 5.(b,c) 6.(a,d) 7. (a,b,d) 8.(a,b,c) 9. (a,b,c,d) 10. (b) 
Solutions 
1.  
    
Page 4


For JEE Advanced 
More than One Correct Options 
 
Q 1.  X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is 
given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure 
 
  (a) The field at B is 
0
Q
2A ?
   
(b) The field at B is 
0
Q
A ?
 
  (c) The field at A, B and C are of the same magnitude 
  (d) The fields at A and C are of the same magnitude, but in opposite directions 
Q 2.  In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements.  
 
(a) Rate of increase of charge is same in both the capacitors 
  (b) Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 
  (c) Time constants of both the capacitors are equal 
  (d) Steady state charge in capacitors C and 2C are in the ratio of 1 : 2 
Q 3.  An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and 
each ammeter is 100 £1. The charge on the capacitor of 100 ?F in steady state is 4 mC. Choose 
correct statements (s) regarding the given circuit. 
 
  (a) Reading of voltmeter V
2
 is 16 V 
  (b) Reading of ammeter A
1
 is zero and A
2
 is 1/25 A 
  (c) Reading of voltmeter V
1
 is 40 V ' 
  (d) EMF of the ideal cell is 66 V 
Q 4.  In the circuit shown, A and B are equal resistances. When S is closed, the capacitor C charges 
from the cell of emf ? and reaches a steady state 
 
  (a) During charging, more heat is produced in A then in B 
  (b) In steady state, heat is produced at the same rate in A and B 
  (c) In the steady state, energy stored in C is 
2
1
C
4
? 
  (d) In the steady state energy stored in C is 
2
1
C
8
? 
Q 5.  A parallel plate capacitor is charged from a cell and then isolated from it. The separation between 
the plates is now increased  
  (a) The force of attraction between the plates will decrease  
  (b) The field in the region between the plates will not change  
  (c) The energy stored in the capacitor will increase 
  (d) The potential difference between the plates will decrease 
Q 6.  In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is 
closed 
 
  (a) positive charge will flow out of the positive terminal of the cell 
  (b) positive charge will enter the positive terminal of the cell 
  (c) the amount of the charge flowing through the cell will be 
1
CE
3
 
  (d) the amount of charge flowing through the cell is (4/3) CE 
Q 7.  Two capacitors of 2 ?F and 3 ?F
 
are charged to 150 V and 120 V respectively. The plates of 
capacitor are connected as shown in the figure. An uncharged capacitor
 
of capacity falls to 
the free end of the wire. Then 
  
  (a) charge on 1.5 ?F capacitor is 180 ?C (b) charge on 2 ?F
 
capacitor is 120 ?C 
  (c) positive charge flows through A from right to left 
  (d) positive charge flows through A from left to right 
Q 8.  A parallel plate capacitor is charged and then the battery is disconnected. When the plates of the 
capacitor are brought closer, then 
  (a) energy stored in the capacitor decreases 
  (b) the potential difference between the plates decreases 
  (c) the capacitance increases   (d) the electric field between the plates decreases 
Q 9.  A capacitor of 2 F (practically not possible to have a capacity of 2 F) is charged by a battery of 6 
V. The battery is removed and circuit is made as shown. Switch is closed at time t = 0. Choose the 
correct options 
 
  (a) At time t - 0 current in the circuit is 2 A 
  (b) At time t = (6 ln 2) second potential difference across capacitor is 3 V 
  (c) At time t = (6 ln 2) second, potential difference across 1 ? resistance is 1 V 
  (d) At time t = (6 ln 2) second potential difference across 2? resistance is 2 V 
Q 10.  Given that potential difference across 1 ?F
 
capacitor is 10 V. Then  
 
  (a) potential difference across 4 ?F
 
capacitor is 40 V 
  (b) potential difference across 4 ?F
 
capacitor is 2.5 V 
  (c) potential difference across 3 ?F
 
capacitor is 5 V 
  (d) value of E is 70 V 
Answers 
  More than One Correct Options 
1. (a,c,d)2. (b,c,d) 3. (b,c) 4. (a,b,d) 5.(b,c) 6.(a,d) 7. (a,b,d) 8.(a,b,c) 9. (a,b,c,d) 10. (b) 
Solutions 
1.  
    
   E
A
=E
1
 + E
4
 (towards left) 
    
    
2.  In steady state 
   q
C
 = EC and q
2C
 = 2EC 
   ?
C
 = 2CR of both circuits. At time t 
   
3.  In steady state current through capacitor wire is zero. Current flows through 200 ?, 900 ?
 
and A
2
. 
    
This is also potential drop across 900 ? resistance and 100 ? ammeter A
2
 (Total resistance = 
1000 ?). 
  Now, this 1000 ? and 200 ? are in series. Therefore, 
    
    
    
4.  Current through A is the main current passing through the battery. So, this current is more than the 
current passing through B. Hence during charging more heat is produced in A. In steady state 
   i
C
 = 0 and i
A
 = i
B
 
  Hence heat is produced at the same rate in A and B. Further in steady state 
   
5.  
  q remains unchanged. Hence F remains unchanged. 
    
  q remains unchanged. Hence E also remains unchanged. 
    
  C will decrease. Hence U will increase. 
   V = Ed or V ? d  
  d is increasing. Hence V will increase. 
Page 5


For JEE Advanced 
More than One Correct Options 
 
Q 1.  X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is 
given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure 
 
  (a) The field at B is 
0
Q
2A ?
   
(b) The field at B is 
0
Q
A ?
 
  (c) The field at A, B and C are of the same magnitude 
  (d) The fields at A and C are of the same magnitude, but in opposite directions 
Q 2.  In the circuit shown in the figure, switch S is closed at time t = 0. Select the correct statements.  
 
(a) Rate of increase of charge is same in both the capacitors 
  (b) Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2 
  (c) Time constants of both the capacitors are equal 
  (d) Steady state charge in capacitors C and 2C are in the ratio of 1 : 2 
Q 3.  An electrical circuit is shown in the given figure. The resistance of each voltmeter is infinite and 
each ammeter is 100 £1. The charge on the capacitor of 100 ?F in steady state is 4 mC. Choose 
correct statements (s) regarding the given circuit. 
 
  (a) Reading of voltmeter V
2
 is 16 V 
  (b) Reading of ammeter A
1
 is zero and A
2
 is 1/25 A 
  (c) Reading of voltmeter V
1
 is 40 V ' 
  (d) EMF of the ideal cell is 66 V 
Q 4.  In the circuit shown, A and B are equal resistances. When S is closed, the capacitor C charges 
from the cell of emf ? and reaches a steady state 
 
  (a) During charging, more heat is produced in A then in B 
  (b) In steady state, heat is produced at the same rate in A and B 
  (c) In the steady state, energy stored in C is 
2
1
C
4
? 
  (d) In the steady state energy stored in C is 
2
1
C
8
? 
Q 5.  A parallel plate capacitor is charged from a cell and then isolated from it. The separation between 
the plates is now increased  
  (a) The force of attraction between the plates will decrease  
  (b) The field in the region between the plates will not change  
  (c) The energy stored in the capacitor will increase 
  (d) The potential difference between the plates will decrease 
Q 6.  In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is 
closed 
 
  (a) positive charge will flow out of the positive terminal of the cell 
  (b) positive charge will enter the positive terminal of the cell 
  (c) the amount of the charge flowing through the cell will be 
1
CE
3
 
  (d) the amount of charge flowing through the cell is (4/3) CE 
Q 7.  Two capacitors of 2 ?F and 3 ?F
 
are charged to 150 V and 120 V respectively. The plates of 
capacitor are connected as shown in the figure. An uncharged capacitor
 
of capacity falls to 
the free end of the wire. Then 
  
  (a) charge on 1.5 ?F capacitor is 180 ?C (b) charge on 2 ?F
 
capacitor is 120 ?C 
  (c) positive charge flows through A from right to left 
  (d) positive charge flows through A from left to right 
Q 8.  A parallel plate capacitor is charged and then the battery is disconnected. When the plates of the 
capacitor are brought closer, then 
  (a) energy stored in the capacitor decreases 
  (b) the potential difference between the plates decreases 
  (c) the capacitance increases   (d) the electric field between the plates decreases 
Q 9.  A capacitor of 2 F (practically not possible to have a capacity of 2 F) is charged by a battery of 6 
V. The battery is removed and circuit is made as shown. Switch is closed at time t = 0. Choose the 
correct options 
 
  (a) At time t - 0 current in the circuit is 2 A 
  (b) At time t = (6 ln 2) second potential difference across capacitor is 3 V 
  (c) At time t = (6 ln 2) second, potential difference across 1 ? resistance is 1 V 
  (d) At time t = (6 ln 2) second potential difference across 2? resistance is 2 V 
Q 10.  Given that potential difference across 1 ?F
 
capacitor is 10 V. Then  
 
  (a) potential difference across 4 ?F
 
capacitor is 40 V 
  (b) potential difference across 4 ?F
 
capacitor is 2.5 V 
  (c) potential difference across 3 ?F
 
capacitor is 5 V 
  (d) value of E is 70 V 
Answers 
  More than One Correct Options 
1. (a,c,d)2. (b,c,d) 3. (b,c) 4. (a,b,d) 5.(b,c) 6.(a,d) 7. (a,b,d) 8.(a,b,c) 9. (a,b,c,d) 10. (b) 
Solutions 
1.  
    
   E
A
=E
1
 + E
4
 (towards left) 
    
    
2.  In steady state 
   q
C
 = EC and q
2C
 = 2EC 
   ?
C
 = 2CR of both circuits. At time t 
   
3.  In steady state current through capacitor wire is zero. Current flows through 200 ?, 900 ?
 
and A
2
. 
    
This is also potential drop across 900 ? resistance and 100 ? ammeter A
2
 (Total resistance = 
1000 ?). 
  Now, this 1000 ? and 200 ? are in series. Therefore, 
    
    
    
4.  Current through A is the main current passing through the battery. So, this current is more than the 
current passing through B. Hence during charging more heat is produced in A. In steady state 
   i
C
 = 0 and i
A
 = i
B
 
  Hence heat is produced at the same rate in A and B. Further in steady state 
   
5.  
  q remains unchanged. Hence F remains unchanged. 
    
  q remains unchanged. Hence E also remains unchanged. 
    
  C will decrease. Hence U will increase. 
   V = Ed or V ? d  
  d is increasing. Hence V will increase. 
6.  
    
   C
f
 = 2C q
f
 = 2EC 
   ?q = q
f
 - q
i
 
    
7.  Let (+q) ?C charge flows in the closed loop in clockwise direction. Then final charges on different 
capacitors are as shown in figure. 
    
  Now applying Kirchhoff s loop law 
    
  Solving the above equation, we get 
   q = 180 ?C 
8.  It the battery is disconnected, then q = constant  
    
  d is decreased. Hence C will increase. 
    
   C in increasing. Hence U will decrease. 
    
  C is increasing. Hence V will decrease. 
9.  (a) At t = 0, emf of the circuit = PD across the capacitor = 6 V. 
   
  Half-life of the circuit 
   = (ln 2) ?
C
 
(ln 2) CR = (6 ln 2) s.  
  In half-life time all values get halved. For example 
    
   
10.  
  In series (as q = constant)