Charging and Discharging an RC Circuit

A capacitor starts empty, with no charge and no voltage across its plates. The instant you close the switch, it offers no opposition at all, so it behaves like a plain wire, and the current is set only by the resistor and the battery: I = V/R. As charge piles onto the plates, the capacitor develops its own voltage that pushes back against the battery. That shrinks the net voltage available to drive current through the resistor, so the current falls. Eventually the capacitor's voltage matches the battery's voltage almost exactly, the net driving voltage is nearly zero, current stops, and the capacitor acts like a broken gap. Voltage across the capacitor climbs from 0 toward V in a curve that rises fast at first then flattens out; current falls from its max value the same way.

Discharging runs this in reverse. Flip the switch to disconnect the battery and connect the charged capacitor straight to the resistor, and in that first instant the capacitor's full voltage drives a current, just like a battery would. As charge drains off the plates, the capacitor's voltage drops, the driving voltage shrinks, and the current dies away toward zero along the same kind of curve.

This sits right after steady current and resistor circuits, where current never changes over time. The RC circuit is the first place current itself becomes a function of time, which sets up exponential decay and the idea of a time constant, tau = RC, that controls how fast charging or discharging happens. Tripling the resistance triples tau, so the same capacitor charges three times slower, even though it still ends up at the same final voltage and charge.