RL Circuits

Switching a DC source $V$ onto a series RL circuit:

$i(t) = \frac{V}{R}\left(1 - e^{-tR/L}\right)$

The time constant is $\tau = L/R$. After about 5τ the current settles at $V/R$, limited only by the resistance.

When the source is removed, the inductor tries to keep the current flowing; with no path, its voltage rises until something breaks down (a spark at a switch). A flyback diode across the inductor gives the current a safe path.