A parallel-plate capacitor has an initial charge q, a plate separation distance d, and a plate area A. How much work must you do (in terms of q, d and A) to increase the separation distance to 3d if:

(i) the capacitor is isolated?

(ii) the capacitor is connected to a battery?

(iii) The work you do is positive in both cases. Explain why in one situation the energy stored in the capacitor increases and in the other it decreases.

(iv) How do your answers to (i), (ii) and (iii) change if the space between the plates is filled with a gas of dielectric constant k = 2? Neglect the work done to push around the gas.