Question

An air-filled parallel-plate capacitor is charged and then disconnected from the battery. The plates are then pulled apart to twice their original separation. Which of the following statements about this capacitor is true?

A. The capacitance has doubled.
B. The energy stored in the capacitor has doubled.
C. The potential difference across the plates has decreased.
D. The electric field between the plates has increased.

Answer 1

B.

Step-by-step explanation:

From the given information, since the capacitors are disconnected from the battery, the electric field between the plate does not change due to the fact that there is no difference in charge density.

Hence, the potential difference after separating the plates is:

V' = Ed

V = e (2d')

V' = 2V

For the energy stored in the capacitor;

`U' = (1)/(2)QV'`

where;

V' = 2V

`U' = (1)/(2) Q (2V)}`

`U' =2( (1)/(2) Q V)`

U' = 2U

Thus, in the capacitor, the energy that is being stored is doubled.