Daily Practice Problems

Class 12 Physics

Electrostatic Potential and Capacitance

Class 12 Physics

Electrostatic Potential and Capacitance

**Questions 1:**

Three capacitors of capacitances 3µF, 9µF and 18 µF are connected once in series and then in parallel. The ratio of equivalent capacitances C_{s}/C_{p} will be:

(a) 1: 15

(b) 15: 1

(c) 1: 1

(d) 1: 3

**Question 2:**

A parallel plate air capacitor is given a charge of 3 µC. A sheet of dielectric constant 3 is inserted so that it completely fills the gap between the plates. The induced charge on each face of the sheet is numerically:

(a) 2 µC

(b) 3 µC

(c) 0

(d) 9 µC

**Question 3:**

The capacitance of an isolated conducting sphere of radius r is proportional to:

(a) r²

(b) 1/r

(c) 1/r^{2}

(d) r

**Question 4:**

An equipotential surface is a surface ------------

- on which the potential has positive value at every point.
- on which the potential has the same value at every point.
- on which the potential has the zero value at every point.
- on which the potential has negative value at every point.

**Question 5:**

A capacitor stores 10 μC charge when connected across a battery. When a gap between the plates is filled with a dielectric, a charge of 20 μC flows from through the battery. Find the dielectric constant of the dielectric

- k =2
- k=4
- k=3
- k=1

**Question 6:**

Distinguish between electric potential and potential energy.

**Question 7:**

A ball of mass 5 g and charge 10^{-7} C moves from point A whose potential is 500 V to a point B whose potential is zero. What is the velocity of the ball at point A, if at point B, it is 25 cm per second?

**Question 8:**

On moving a charge of 2C from a point A where potential is +12V to a point B where potential is -12V, the work done is-

**Question 9:**

N small drops of same size are charges to V volt each. They collapse to form a bigger drop. Calculate the capacity & potential of the bigger drop.

**Question 10:**

On inserting the dielectric between the plates of a capacitor, its capacitance is found to increase 5 times. What is the relative permittivity of the dielectric?

**Question 11:**

An air is filled parallel plate capacitor is to be constructed which can store 12μC of charge when operated at 1200 V. What can be the minimum area of capacitor? The dielectric strength of air is 3×10^{7} V/m.

**Question 12:**

A capacitor of capacitance C_{1} = 1 μF withstands with maximum voltage V_{1} = 6 kV. While another capacitor of capacitance C_{2} = 2 μF withstands the maximum voltage V_{2} = 4 kV. What maximum voltage will the system of these two capacitors withstand if they are connected in series?

**Question 13:**

Derive an expression for the energy stored in the capacitor?

**Question 14:**

(a) A comb run through one’s dry hair attracts small bits of paper. Why? What happens if the hair is wet or if it is a rainy day? (Remember, a paper does not conduct electricity.)

(b) Ordinary rubber is an insulator. But special rubber tyres of aircraft are made slightly conducting. Why is this necessary?

**Question 15:**

(a) Calculate the potential at a point P due to a charge of 4 × 10^{–7}C located 9 cm away.

(b) Hence obtain the work done in bringing a charge of 2 × 10^{–9} C from infinity to the point P. Does the answer depend on the path along which the charge is brought?

**Question 16:**

What do you mean by Polarization?

**Question 17:**

A molecule of a substance has a permanent electric dipole moment of magnitude 10^{–29} C m. A mole of this substance is polarised (at low temperature) by applying a strong electrostatic field of magnitude 10^{6} V m^{–1}. The direction of the field is suddenly changed by an angle of 60º. Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. For simplicity, assume 100% polarisation of the sample.

**Question 18:**

The electric potential at a point, distance 0.9 m, from a point charge is +50V. Find the magnitude and nature of the charge.

**Question 19:**

Why the charge on the earth cannot be neutralised?

**Question 20:**

In a parallel plate capacitor, how is the capacitor affected, when without changing the charge:

- The distance between the plates is doubled
- The area of the plate is halved.

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