A parallel-plate capacitor is connected to a battery. The energy of the capacitor is U0. The capacitor remains connected to the battery while the plates are slowly pulled apart until the plate separation doubles. The new energy of the capacitor is U. Find the ratio U/U0.

U/U₀ = 1/2

Explanation:

The energy stored in the capacitor initially is U₀ = 1/2C₀V². When the separation distance doubles, the new energy stored is U = 1/2CV².

Since the capacitance of a parallel plate capacitor is C = εA/d. So, C ∝ 1/d

So, C/C₀ = d₀/d = 1/2. Since d = 2d₀ that is, the separation distance doubles

U/U₀ = 1/2CV²/1/2C₀V² = C/C₀ = d₀/d = 1/2

So, U/U₀ = 1/2