conceptual

Asked by manu p.prakash | 23rd Feb, 2012, 03:30: PM

Expert Answer:


Energy Stored by Capacitors

Let us consider charging an initially uncharged parallel plate capacitor by transferring a charge from one plate to the other, leaving the former plate with charge and the later with charge . Of course, once we have transferred some charge, an electric field is set up between the plates which opposes any further charge transfer. In order to fully charge the capacitor, we must do work against this field, and this work becomes energy stored in the capacitor. Let us calculate this energy.

Suppose that the capacitor plates carry a charge and that the potential difference between the plates is . The work we do in transferring an infinitesimal amount of charge from the negative to the positive plate is simply

(117)
In order to evaluate the total work done in transferring the total charge from one plate to the other, we can divide this charge into many small increments , find the incremental work done in transferring this incremental charge, using the above formula, and then sum all of these works. The only complication is that the potential difference between the plates is a function of the total transferred charge. In fact, , so
(118)
Integration yields
(119)
Note, again, that the work done in charging the capacitor is the same as the energy stored in the capacitor. Since , we can write this stored energy in one of three equivalent forms:
 

Answered by  | 24th Feb, 2012, 08:29: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.