The potential energy stored in a capacitor (Section 17-9) can be written as either CV2/2 or Q2/2C. In the first case the energy is proportional to C; in the second case the energy is proportional to 1 C.

(a) Explain how both of these equations can be correct.

(b) When might you use the first equation and when might you use the second equation?

(c) If a paper dielectric is inserted into a parallel-plate capacitor that is attached to a battery (V does not change), by what factor will the energy stored in the capacitor change?

(d) If a quartz dielectric is inserted into a charged parallel-plate capacitor that is isolated from any battery, by what factor will the energy stored in the capacitor change?