= RC circuit
{c}
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 $i=C\,dv_C/dt$ give $RC\,dv_C/dt+v_C=V$.
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>.
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