A parallel-plate capacitor has an initial charge \(q\) and a plate separation distance \(d\). How much work must you do, in terms of \(q, d\), and plate area \(A\), to increase the separation distance to \(3 d\) if \((a)\) the capacitor is isolated and (b) the capacitor is connected to a battery? (c) The work you do is positive in both cases. Explain why in one situation the electric potential energy increases and in the other it decreases.