Electrostatic Potential & Capacitance Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The electric potential V(x) in a region around the origin is given by V(x)
= 4x
2
 volts. The electric charge enclosed in a cube of 1 m side with its
centre at the origin is (in coulomb)
(a) 8e
0
(b) – 4e
0
(c) 0
(d) – 8e
0
2. The capacitance of a parallel plate capacitor is C
a
 (Fig. a). A dielectric
of dielectric constant K is inserted as shown in fig (b) and (c). If C
b
 and
C
c
 denote the capacitances in fig (b) and (c), then
  
Page 2


PART-I (Single Correct MCQs)
1. The electric potential V(x) in a region around the origin is given by V(x)
= 4x
2
 volts. The electric charge enclosed in a cube of 1 m side with its
centre at the origin is (in coulomb)
(a) 8e
0
(b) – 4e
0
(c) 0
(d) – 8e
0
2. The capacitance of a parallel plate capacitor is C
a
 (Fig. a). A dielectric
of dielectric constant K is inserted as shown in fig (b) and (c). If C
b
 and
C
c
 denote the capacitances in fig (b) and (c), then
  
(a) both C
b
, C
c
 > C
a
(b) C
c
 > C
a
 while C
b
 > C
a
(c) both C
b
, C
c
 < C
a
(d) C
a
 = C
b
 = C
c
3. Figure (i) shows two capacitors connected in series and connected by a
battery. The graph (ii) shows the variation of potential as one moves
from left to right on the branch AB containing the capacitors. Then
(a) C
1
 =  C
2
(b) C
1
 <  C
2
(c) C
1
 >  C
2
(d) C
1
 and  C
2
 cannot be compared
4. In a hollow spherical shell, potential (V) changes with respect to
distance (s) from centre as
(a)
(b)
(c)
Page 3


PART-I (Single Correct MCQs)
1. The electric potential V(x) in a region around the origin is given by V(x)
= 4x
2
 volts. The electric charge enclosed in a cube of 1 m side with its
centre at the origin is (in coulomb)
(a) 8e
0
(b) – 4e
0
(c) 0
(d) – 8e
0
2. The capacitance of a parallel plate capacitor is C
a
 (Fig. a). A dielectric
of dielectric constant K is inserted as shown in fig (b) and (c). If C
b
 and
C
c
 denote the capacitances in fig (b) and (c), then
  
(a) both C
b
, C
c
 > C
a
(b) C
c
 > C
a
 while C
b
 > C
a
(c) both C
b
, C
c
 < C
a
(d) C
a
 = C
b
 = C
c
3. Figure (i) shows two capacitors connected in series and connected by a
battery. The graph (ii) shows the variation of potential as one moves
from left to right on the branch AB containing the capacitors. Then
(a) C
1
 =  C
2
(b) C
1
 <  C
2
(c) C
1
 >  C
2
(d) C
1
 and  C
2
 cannot be compared
4. In a hollow spherical shell, potential (V) changes with respect to
distance (s) from centre as
(a)
(b)
(c)
(d)
5. Charges +q and –q are placed at points A
and B respectively  which are a distance 2L
apart, C is the midpoint between A and B.
The work done in moving a charge +Q
along the semicircle CRD is
(a)
(b)
(c)
(d)
6. A, B and C are three points in a uniform
electric field. The electric potential is
(a) maximum at B
(b) maximum at C
(c) same at all the three points A, B and C
(d) maximum at A
7. A unit charge moves on an equipotential surface from a point A to point
B, then
(a) V
A
 – V
B
 = + ve
(b) V
A
 – V
B
 = 0
(c) V
A
 – V
B
 = – ve
(d) it is stationary
8. Identify the false statement.
Page 4


PART-I (Single Correct MCQs)
1. The electric potential V(x) in a region around the origin is given by V(x)
= 4x
2
 volts. The electric charge enclosed in a cube of 1 m side with its
centre at the origin is (in coulomb)
(a) 8e
0
(b) – 4e
0
(c) 0
(d) – 8e
0
2. The capacitance of a parallel plate capacitor is C
a
 (Fig. a). A dielectric
of dielectric constant K is inserted as shown in fig (b) and (c). If C
b
 and
C
c
 denote the capacitances in fig (b) and (c), then
  
(a) both C
b
, C
c
 > C
a
(b) C
c
 > C
a
 while C
b
 > C
a
(c) both C
b
, C
c
 < C
a
(d) C
a
 = C
b
 = C
c
3. Figure (i) shows two capacitors connected in series and connected by a
battery. The graph (ii) shows the variation of potential as one moves
from left to right on the branch AB containing the capacitors. Then
(a) C
1
 =  C
2
(b) C
1
 <  C
2
(c) C
1
 >  C
2
(d) C
1
 and  C
2
 cannot be compared
4. In a hollow spherical shell, potential (V) changes with respect to
distance (s) from centre as
(a)
(b)
(c)
(d)
5. Charges +q and –q are placed at points A
and B respectively  which are a distance 2L
apart, C is the midpoint between A and B.
The work done in moving a charge +Q
along the semicircle CRD is
(a)
(b)
(c)
(d)
6. A, B and C are three points in a uniform
electric field. The electric potential is
(a) maximum at B
(b) maximum at C
(c) same at all the three points A, B and C
(d) maximum at A
7. A unit charge moves on an equipotential surface from a point A to point
B, then
(a) V
A
 – V
B
 = + ve
(b) V
A
 – V
B
 = 0
(c) V
A
 – V
B
 = – ve
(d) it is stationary
8. Identify the false statement.
(a) Inside a charged or neutral conductor, electrostatic field is zero
(b) The electrostatic field at the surface of the charged conductor must be
tangential to the surface at any point
(c) There is no net charge at any point inside the conductor
(d) Electrostatic potential is constant throughout the volume of the
conductor
9. A, B, C, D, E, F are conducting plates each
of area A and any two consecutive plates
separated by a distance d. The net energy
stored in the system after the switch S is
closed is
(a)
(b)
(c)
(d)
10. Two concentric, thin metallic spheres of radii R
1
 and R
2
 (R
1
 > R
2
) bear
charges Q
1
 and Q
2
 respectively. Then the potential at distance r between
R
1
 and R
2
 will be 
(a)
(b)
(c)
(d)
Page 5


PART-I (Single Correct MCQs)
1. The electric potential V(x) in a region around the origin is given by V(x)
= 4x
2
 volts. The electric charge enclosed in a cube of 1 m side with its
centre at the origin is (in coulomb)
(a) 8e
0
(b) – 4e
0
(c) 0
(d) – 8e
0
2. The capacitance of a parallel plate capacitor is C
a
 (Fig. a). A dielectric
of dielectric constant K is inserted as shown in fig (b) and (c). If C
b
 and
C
c
 denote the capacitances in fig (b) and (c), then
  
(a) both C
b
, C
c
 > C
a
(b) C
c
 > C
a
 while C
b
 > C
a
(c) both C
b
, C
c
 < C
a
(d) C
a
 = C
b
 = C
c
3. Figure (i) shows two capacitors connected in series and connected by a
battery. The graph (ii) shows the variation of potential as one moves
from left to right on the branch AB containing the capacitors. Then
(a) C
1
 =  C
2
(b) C
1
 <  C
2
(c) C
1
 >  C
2
(d) C
1
 and  C
2
 cannot be compared
4. In a hollow spherical shell, potential (V) changes with respect to
distance (s) from centre as
(a)
(b)
(c)
(d)
5. Charges +q and –q are placed at points A
and B respectively  which are a distance 2L
apart, C is the midpoint between A and B.
The work done in moving a charge +Q
along the semicircle CRD is
(a)
(b)
(c)
(d)
6. A, B and C are three points in a uniform
electric field. The electric potential is
(a) maximum at B
(b) maximum at C
(c) same at all the three points A, B and C
(d) maximum at A
7. A unit charge moves on an equipotential surface from a point A to point
B, then
(a) V
A
 – V
B
 = + ve
(b) V
A
 – V
B
 = 0
(c) V
A
 – V
B
 = – ve
(d) it is stationary
8. Identify the false statement.
(a) Inside a charged or neutral conductor, electrostatic field is zero
(b) The electrostatic field at the surface of the charged conductor must be
tangential to the surface at any point
(c) There is no net charge at any point inside the conductor
(d) Electrostatic potential is constant throughout the volume of the
conductor
9. A, B, C, D, E, F are conducting plates each
of area A and any two consecutive plates
separated by a distance d. The net energy
stored in the system after the switch S is
closed is
(a)
(b)
(c)
(d)
10. Two concentric, thin metallic spheres of radii R
1
 and R
2
 (R
1
 > R
2
) bear
charges Q
1
 and Q
2
 respectively. Then the potential at distance r between
R
1
 and R
2
 will be 
(a)
(b)
(c)
(d)
11. The space between the plates of a parallel plate capacitor is filled with a
‘dielectric’ whose ‘dielectric constant’ varies with distance as per the
relation:
K(x) = K
o
 + ?x (? = a constant)
The capacitance C, of the capacitor, would be related to its vacuum
capacitance C
o
 for the relation :
(a)
(b)
(c)
(d)
12. For the circuit shown in figure, which of the following statements is
true?
(a) With S
1
 closed V
1
 = 15V, V
2
 = 20V
(b) With S
3
 closed V
1
 = V
2
 = 25 V
(c) With S
1
 and S
2
 closed V
1
 = V
2
 = 0
(d) With S
1
 and S
3
 closed, V
1
 = 30 V, V
2 
= 20 V
13. Two thin wire rings each having a radius R are placed at a distance d
apart with their axes coinciding. The charges on the two rings are +q
and –q. The potential difference between the centres of the two rings is
(a)