Instrument electronics in plain words

The pickups produce the signal, the selector decides which ones you hear, and the volume and tone pots control the level and how the high frequencies behave. From the output jack, the signal goes through the cable to the amp.

Crackling when you turn a knob, dropouts or a loss of volume can come from contacts, wiring or worn parts. Hum can also come from outside interference, not necessarily from a fault.

On active circuits we check the battery too. When the jack switches the power on, unplug the cable after playing. Before replacing pickups, it's worth a check with a cable and amp you know work: the cause may be much simpler.