capacitor is a power cell used to generate electricity in the motor of ceiling fan

If a capacitor will not charge, it is open, i.e. damaged.

The capacitor is called a bypass capacitor , it provides a low impedence path for AC emitter current to groun.

mica

No, that's a "choke", or if there are two coils, it's a transformer.

A capacitor is two "plates" (in reality they are usually just foil) that are connected to two wires. Often (typically) there is an electrolytic between the plates.

There is more to a capacitor, but that's the basics.