RC circuit

An RC circuit contains electrical resistance and capacitance. For a series resistor $R$ charging a capacitor $C$ from a constant voltage $V$, Kirchhoff's voltage law and $i=Cd{v}_C/dt$ give $RCd{v}_C/dt+v_C=V$.

With an initially uncharged capacitor, $v_C(t)=V(1-e^{-t/(RC)})$. The time constant $\tau =RC$ is the time to reach $1-e^{-1}$ of the final voltage. With the source removed, the same model predicts exponential discharge. Measuring this response provides a simple way to determine an unknown capacitance or to construct a smoothing low-pass filter.