The fundamental intuition about capacitors is that they never let electrons through.

They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.

Therefore, they cannot conduct direct current long term.

For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.

The key equation that relates Voltage to electric current in the capacitor is:
So if a voltage Heavyside step function is applied what happens is:More realistically, one may consider the behaviour or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.

$I(t)=CdtdV(t) $

- the capacitor fills up instantly with an infinite current
- the current then stops instantly