Question

A parallel-plate capacitor is connected to a battery. The energy of the capacitor is Uo. The capacitor is then

disconnected from the battery and the plates are slowly pulled apart until the plate separation doubles. The new
energy of the capacitor is U. Find the ratio U/Uo.

Answer 1

The energy stored in a capacitor is given by the formula U = 1/2 * C * V^2, where C is the capacitance of the capacitor and V is the voltage across the plates.

When the plate separation doubles, the capacitance of the capacitor is halved. This means that the new energy of the capacitor, U, is equal to 1/2 * (C/2) * (V/2)^2 = 1/8 * C * V^2 = Uo/8.

The ratio U/Uo is therefore equal to Uo/8/Uo = 1/8, or 0.125.