Inductive transient ($\tau =L/R$)

Following a change in applied electromotive force, a series inductor and resistor obey $L\dot{I}+RI=\mathcal{E}(t)$. For a constant applied electromotive force, the difference from the final electric current decays as $e^{-tR/L}$. Neglecting self-inductance is justified only when the forcing varies slowly compared with the time constant $L/R$, or when considering a steady state.