# MCQs for Physics Class 12 with Answers Chapter 2 Electrostatic Potential and Capacitance

Students of class 12 Physics should refer to MCQ Questions Class 12 Physics Electrostatic Potential and Capacitance with answers provided here which is an important chapter in Class 12 Physics NCERT textbook. These MCQ for Class 12 Physics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 12 Physics. The following MCQs can help you to practice and get better marks in the upcoming class 12 Physics examination

## Chapter 2 Electrostatic Potential and Capacitance MCQ with Answers Class 12 Physics

MCQ Questions Class 12 Physics Electrostatic Potential and Capacitance provided below have been prepared by expert teachers of grade 12. These objective questions with solutions are expected to come in the upcoming Standard 12 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B

C

Question. The electrostatic potential on the surface of a charged conducting sphere is 100 V. Two statements are made in this regard:
S1 : At any point inside the sphere, electric intensity is zero.
S2 : At any point inside the sphere, the electrostatic potential is 100 V.
Which of the following is a correct statement?
(a) S1 is true but S2 is false.
(b) Both S1 and S2 are false.
(c) S1 is true, S2 is also true and S1 is the cause of S2.
(d) S1 is true, S2 is also true but the statements are independent.

C

Question. The capacitance of a capacitor becomes 7/6 times its original value if a dielectric slab of thickness t = 2/3 d is introduced in between the plates, where d is the separation between the plates. The dielectric constant of the slab is
(a) 14/11
(b) 11/14
(c) 7/11
(d) 11/7

A

Question. The variation potential V with r and electric field E with r for a point charge is correctly shown in the graphs.

B

Question. A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d1 and dielectric constant k1 and the other has thickness d2 and dielectric constant k2 as shown in figure. This arrangement can be thought as a dielectric slab of thickness d (= d1+d2) and effective dielectric constant k. The k is

C

Question. In the case of a charged metallic sphere, potential (V) changes with respect to distance (r) from the centre as

B

Question. Three capacitors of capacitance 1mF, 2 mF and 3 mF are connected in series and a p.d. of 11 V is applied across the combination. Then, the p.d. across the plates of 1 mF capacitor is
(a) 2 V
(b) 4 V
(c) 1 V
(d) 6 V

D

Question. A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are

B

Question. Four point charges – Q, – q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

B

Question. A parallel plate capacitor is charged to a certain voltage. Now, if the dielectric material (with dielectric constant k) is removed then the
(a) capacitance increases by a factor of k
(b) electric field reduces by a factor k
(c) voltage across the capacitor decreases by a factor k
(d) None of these

D

Question. A sphere of radius R has uniform volume charge density. The electric potential at a points (r <R) is
(a) due to the charge inside a sphere of radius r only
(b) due to the entire charge of the sphere
(c) due to the charge in the spherical sheel of inner and outer radii r and R, only
(d) independent of r

A

Question. Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is
(a) 16 times
(b) 8 times
(c) 4 times
(d) 2 times

D

Question. The capacitance of a metallic sphere is 1mF , then it’s radius is nearly
(a) 1.11 m
(b) 10 m
(c) 9 km
(d) 1.11 cm

C

Question. The electric potential due to a small electric dipole at a large distance r from the centre of the dipole is proportional to
(a) r
(b) 1/r
(c) 1/r2
(d) 1/r3

C

Question. An electron of mass m and charge e is accelerated from rest through a potential difference V in vacuum. Its final speed will be

A

Question. Force between two plates of a capacitor is

B

Question. An alpha particle is accelerated through a potential difference of 106 volt. Its kinetic energy will be
(a) 1 MeV
(b) 2 MeV
(c) 4 MeV
(d) 8 MeV

B

Question. Two capacitors of capacitances C1 and C2 are connected in parallel across a battery. If Q1 and Q2 respectively be the charges on the capacitors, then Q1/Q2 will be equal to

B

Question. A system of two parallel plates, each of area A, are separated by distances d1 and d2. The space between them is filled with dielectrics of permittivities e1 and e2. The permittivity of free space is e0. The equivalent capacitance of the system is

A

Question. A large insulated sphere of radius r charged with Q units of electricity is placed in contact with a small insulated
uncharged sphere of radius r´ and is then separated. The charge on smaller sphere will now be

D

Question. The capacitance of the capacitor of plate areas A1 and A2 (A1 < A2) at a distance d, as shown in figure is

D

Question. The magnitude of the electric field E in the annular region of a charged cylindrical capacitor
(a) is same throughout
(b) is higher near the outer cylinder than near the inner cylinder
(c) varies as 1/r, where r is the distance from the axis
(d) varies as 1/r2, where r is the distance from the axis

C

Question. A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes
(a) √2C
(b) 2 C
(c) C/√2
(d) C/2

D

Question. A parallel plate condenser has a uniform electric field E(V/ m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is A(m2) the energy (joules) stored in the condenser is

D

Question. Which of the following figure shows the correct equipotential surfaces of a system of two positive charges?

C

Question. The positive terminal of 12 V battery is connected to the ground. Then the negative terminal will be at
(a) – 6 V
(b) + 12 V
(c) zero
(d) – 12 V

D

Question. A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of the sphere is
(a) zero
(b) 10 V
(c) 4 V
(d) 10/3 V

B

Question. The electric potential at the surface of an atomic nucleus (Z = 50) of radius of 9 × 10–15 m is
(a) 80 V
(b) 8 × 106 V
(c) 9 V
(d) 9 × 105 V

B

Question. Three point charges +q , + 2q and – 4q where q = 0.1 μC, are placed at the vertices of an equilateral triangle of side 10 cm as shown in figure. The potential energy of the system is

(a) 3 × 10–3 J
(b) –3 × 10–3 J
(c) 9 × 10–3 J
(d) –9 × 10–3 J

D

Question. A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitors is
(a) 3 U/2
(b) U
(c) U/4
(d) U/2

C

Question. Two capacitors when connected in series have a capacitance of 3 μF, and when connected in parallel have a capacitance of 16 μF. Their individual capacities are
(a) 1 μF, 2 μF
(b) 6 μF, 2 μF
(c) 12 μF, 4 μF
(d) 3 μF, 16 μF

C

Question. Two capacitors C1 and C2 in a circuit are joined as shown in figure. The potentials of points A and B are V1 and V2 respectively; then the potential of point D will be

C

Question. A parallel plate capacitor with air between the plates is charged to a potential difference of 500V and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes 75V. The dielectric constant of plastic is
(a) 10/3
(b) 5
(c) 20/3
(d) 10

C

Question. Calculate the area of the plates of a one farad parallel plate capacitor if separation between plates is 1 mm and plates are in vacuum
(a) 18 × 108 m2
(b) 0.3 × 108 m2
(c) 1.3 × 108 m2
(d) 1.13 × 108 m2

D

Question. The potential at a point x (measured in m m) due to some charges situated on the x-axis is given by V(x) = 20/(x2 – 4) volt The electric field E at x = 4 m m is given by
(a) (10/9) volt/ m m and in the +ve x direction
(b) (5/3) volt/ m m and in the –ve x direction
(c) (5/3) volt/ m m and in the +ve x direction
(d) (10/9) volt/ m m and in the –ve x direction

A

Question. Identical charges – q each are placed at 8 corners of a cube of each side b. Electrostatic potential energy of a charge + q which is placed at the centre of cube will be

C

Question. A charge +q is fixed at each of the points x = x0, x = 3x0, x = 5x0, …. upto ¥ on X-axis and charge –q is fixed on each of the points x = 2x0, x = 4x0, x = 6x0, …. upto ¥ . Here x0 is a positive constant. Take the potential at a point due to a charge Q at a distance r from it to be Q/4π∈0r Then the potential at the origin due to above system of charges will be

D

Question. If we increase ‘d’ of a parallel plate condenser to ‘2d’ and fill wax to the whole empty space between its two plate, then capacitance increase from 1pF to 2pF. What is the dielectric constant of wax?
(a) 2
(b) 4
(c) 4
(d) 8

B

Question. Two spherical conductors A and B of radii a and b (b > a) are placed concentrically in air. B is given charge +Q and A is earthed. The equivalent capacitance of the system is

D

Question. The capacitance of a parallel plate capacitor is Ca (Fig. a). A dielectric of dielectric constant K is inserted as shown in fig (b) and (c). If Cb and Cc denote the capacitances in fig (b) and (c), then

(a) both Cb, Cc > Ca
(b) Cc > Ca while Cb > Ca
(c) both Cb, Cc < Ca
(d) Ca = Cb = Cc

A

Question. In the circuit shown, which of the following statements is true if V1 (potential across C1) is 30 V and V2 (potential across C2) is 20 V?
V1 = 30V V2 = 20V

(a) With S1 closed, V1 = 15 V, V2 = 25 V
(b) With S3 closed, V1 = V2 = 25 V
(c) With S1 and S2 closed, V1 = V2 = 0
(d) With S1 and S3 closed, V1 = 30 V, V2 = 20 V

D

Question. A parallel plate capacitor is located horizontally such that one of the plates is submerged in a liquid while the other is above the liquid surface. When plates are charged the level of liquid
(a) rises
(b) falls
(c) remains unchanged
(d) may rise or fall depending on the amount of charge

A

Question. Two small conductors A and B are given charges q1 and q2 respectively. Now they are placed inside a hollow metallic conductor C carrying a charge Q. If all the three conductors A, B and C are connected by a conducting wire
as shown, the charges on A, B and C will be respectively

D

Question. Between the plates of a parallel plate capacitor dielectric plate is introduced just to fill the space between the plates. The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to plates. The plot of the potential difference V across the plates and the length of the dielectric plate drawn out is

B

Question. Three capacitors C1, C2 and C3 are connected to a battery as shown. With symbols having their usual meanings, the correct conditions are

(a) Q1 = Q2 = Q3 and V1 = V2 = V
(b) V1 = V2 = V3 = V
(c) Q1 = Q2 + Q3 and V = V1 = V2
(d) Q2 = Q3 and V2 = V3

C

Question. 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) C1 = C2
(b) C1 < C2
(c) C1 > C2
(d) C1 and C2 cannot be compared

C

Question. If a charge – 150 nC is given to a concentric spherical shell and a charge +50 nC is placed at its centre then the charge on inner and outer surface of the shell is
(a) –50 nC, –100 nC
(b) +50 nC, –200 nC
(c) –50 nC, –200 nC
(d) 50 nC, 100 nC

A

Question. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be
(a) 1/2
(b) 1
(c) 2
(d) 1/4

A

Question. Four point charges q, q, q and – 3q are placed at the vertices of a regular tetrahedron of side L. The work done by electric force in taking all the charges to the centre of the tetrahedron is (where K = 1/4π∈0)
(a) 6kq2/L
(b) -6kq2/L
(c) 12kq2/L
(d) zero

B

Question. Two identical particles each of mass m and having charges – q and +q are revolving in a circle of radius r under the influence of electric attraction. Kinetic energy of each particle is ( K = 1/4π∈0 )
(a) kq2/4r
(b) kq2/2r
(c) kq2/8r
(d) kq2/r

C

Question. Figure shows three circular arcs, each of radius R and total charge as indicated. The net electric potential at the centre of curvature is

A

Question. If the potential of a capacitor having capacity 6 μF is increased from 10 V to 20 V, then increase in its energy will be
(a) 4 × 10–4 J
(b) 4 × 10–4 J
(c) 9 × 10–4 J
(d) 12 × 10–6 J

C

Question. In the given circuit with steady current, the potential drop across the capacitor must be

(a) 2V/3
(a) V/3
(a) V/2
(a) V

B

Question. A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. the capacitor is given some charge. As one goes from 0 to 3d
(a) the magnitude of the electric field remains the same
(b) the direction of the electric field remains the same
(c) the electric potential decreases continuously
(d) the electric potential increases at first, then decreases and again increases

C

Question. In the given circuit if point C is connected to the earth and a potential of +2000V is given to the point A, the potential at B is

(a) 1500V
(b) 1000 V
(c) 500 V
(d) 400 V

C

Question. As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge – Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is
(a) zero

A

Question. Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4π∈0) k, where k is

(a) 8q1
(b) 6q1
(c) 8q2
(d) 6q2

C

#### Fill in the Blanks

Question. The magnitude of electric field is given by the change in the magnitude of potential per unit _______________ normal to the equipotential surface at the point.

displacement

Question. Equipotential surfaces due to long linear change distribution will be _______________ in shape.

cylindrical

Question. The potential energy of two unlike charges (q1q2 < 0) is _______________.

negative

Question. It is safer to be inside the car rather than standing outside under a tree during lightening is based on _______________ concept.

electrostatic shielding

Question. Two capacitors each of capacitance 2 μF are connected in series. Equivalent capacitance will be ________________.

1 μF

Question. The potential energy of two like charged (q1q2 > 0) is _______________

Question. The dielectric constant of a substance is a factor (>1) by which the capacitance _______________ from its vacuum value, when the dielectric is inserted fully between the plates of a capacitor.

increases

Question. Electric field is in the direction in which the potential ________________ steepest.

decreases

Question. The maximum electric field that a dielectric medium can withstand without break-down of its insulting property is called its _______________.