Question

Choose the correct answer for the following questions.

1) A plate capacitor is charged up and is then disconnected from the voltage source. If we reduce the distance between the plates, then...

a) ...the potential difference increases.

b) ...the potential difference is constant.

c) ...the potential difference is reduced.

2) If the potential difference between the plates of a capacitor is constant, then...

a) ...the energy of the capacitor is not dependent on its capacitance.

b) ...the energy of the capacitor depends linearly on its capacitance.

c) ...the energy of the capacitor and its capacitance has a quadratic relationship.

Answer 1

1) The potential difference across the plates is given by

Q=CV

implies that V = Q/C--------------(1)

Capacitance is given by

C = ε_oA/d, it is determined only by the geometry of the capacitor, not by the charge or the potential.

Since the area is same, if the distance is decreased, the capacitance C will increase, and hence from eq. (1)

Potential difference V decreases. c part

2) The energy of a capacitor is given by

U = (1/2)CV² = (1/2)Q²/C because Q=CV

we see that U and C have a linear relation with each other.