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My textbook reads, “the power supply does work on the electrons, so their potential energy increases. You recover this energy when you discharge the capacitor.”
I don’t get why this is the case... doesn’t the power supply increase the K.E. of the electrons? Now where does the energy for the capacitor come from and what it ‘form’?
You can model a capacitor as if it were a spring. Squeezing the spring to make it deflect is the same as pushing current into a capacitor to charge it up; both require work to be done. The squeezed spring contains an amount of stored energy equal to the work expended to squeeze it, and in the case of the capacitor the energy stored in it equals the work performed on it by the power supply in charging it up.
While charging the capacitor the electrons are forcefully jammed inside, working against the Coulomb force that is trying to push them out (opposite charges attract, same ones try to separate). As E=F*s you get the stored energy as from the force that is trying to push the electrons out, times the distance that they have been pushed against this force. This energy is saved in potential energy form since at any time, once the circuit is closed, the coulomb force can finally push out the excess electrons, thus increasing their kinetic energy again. It really does resemble a spring a lot, just that the "force trying to push things out" is now electromagnetic instead of the usual spring force.
