RC Circuits: Discharging A Capacitor

When a capacitor is fully charged, the potential difference across the capacitor is equal to the voltage source.

If the battery gets disconnected from the circuit, the capacitor discharges.

Using Kirchhoff's loop rule yields an equation. Here, the current is the rate at which the charge is leaving the capacitor. Since the capacitor is losing charge with time, the sign is negative.

Substituting the definition of current yields an equation. This equation is further integrated to get the charge on the capacitor as a function of time.

For a discharging capacitor, the charge on the capacitor decreases exponentially from the initial charge, which is the maximum charge acquired by the capacitor while charging.

The time derivative of the— charge on a capacitor— equation results in the current expression as a function of time.

The negative sign in the expression signifies the opposite direction of the current compared to the capacitor's charging case.

The current decay has an exponential behavior. Its magnitude decreases exponentially and tends to zero as time tends to infinity.