= Solution
Position A disconnects the <battery> and closes the <resistor>-<inductor> loop. Taking clockwise <electric current> as positive, <Kirchhoff's voltage law> for this <RL circuit> gives
$$
L\frac{dI}{dt}+RI=0.
$$
The <electric current> through an ideal <inductor> remains continuous across a switch with no impulsive <voltage>. Thus $I(0^+)=I_0$, and <separation of variables> gives
$$
\boxed{I(t)=I_0e^{-Rt/L}\quad(0<t<\Delta t).}
$$
If the switch remains at A, the same result holds for every $t>0$. The <time constant> is $L/R$; the stored <magnetic energy> is dissipated by <Joule heating>.
Back to article page
