The plates of a parallel-plate capacitor are separated by distance d, and each p

Question

The plates of a parallel-plate capacitor are separated by distance d, and each plate has area A. The capacitor is charged to a potential difference V and then disconnected from the voltage source. The plates are then pulled apart until the separation is 3d. Find the following. (Use the following as necessary: d, A, V, e0.)
(a) the new capacitance
Cnew =

(b) the new potential difference
Vnew =

(c) the new stored energy
Unew =

(d) How much work was required to change the plate separation from d to 3d?
W =

Explanation / Answer

1) capacitance c = A/d

substitute d = 3d

cnew = A/3d

2)cnew = Q/vnew

since the charge remains same

cnew * vnew = cv

vnew = 3V

3) the stored energy is 1/2 CV2 = 1/2 (A/3d )*(3V)2 = 3/2 AV2/d

4) work done is the change in energy to bring the change

work done = 3/2 AV2/d - 1/2 AV2/d

= AV2/d

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