= Source-fed parallel resistor-inductor switching
{title2=$\tau=L/(R_1\parallel R_2)$}
An ideal <voltage source> $V_0$ and series <resistor> $R_1$ feed parallel branches $L$ and $R_2$. <Thévenin's theorem> gives $R_{\rm th}=R_1R_2/(R_1+R_2)$ and $V_{\rm th}=V_0R_2/(R_1+R_2)$. Starting with zero <inductor> current, $i_L=(V_0/R_1)(1-e^{-t/\tau})$ and $i_2=V_0e^{-t/\tau}/(R_1+R_2)$. Switch-on heat in $R_2$ is $LV_0^2/[2R_1(R_1+R_2)]$. Disconnecting the source leaves the stored <magnetic energy> $Li_L^2/2$ to dissipate through $R_2$, with <time constant> $L/R_2$.
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