Question

How does the energy stored in a capacitor change if (a) the potential difference is
doubled, and (b) the charge on each plate is doubled, as the capacitor remains connected to a battery?

Does the stored energy go up by a factor of 4 for both A and B?

Answer 1

a. Energy = 0.5*C*V^2

V doubled:
Energy = 0.5*C*(2V)^2 = 0.5*C*4V^2
So the energy is increased by a factor of 4.

b. Yes.

Answer 2

Yes