Source-fed parallel resistor-inductor switching ($\tau =L/(R_1\parallel R_2)$)

An ideal voltage source $V_0$ and series resistor $R_1$ feed parallel branches $L$ and $R_2$. Thévenin's theorem gives $R_{\mathrm{th}}=R_1{R}_2/(R_1+R_2)$ and $V_{\mathrm{th}}=V_0{R}_2/(R_1+R_2)$. Starting with zero inductor current, $i_L=(V_0/R_1)(1-e^{-t/\tau })$ and $i_2=V_0{e}^{-t/\tau }/(R_1+R_2)$. Switch-on heat in $R_2$ is $L{V}_0^2/[2R_1(R_1+R_2)]$. Disconnecting the source leaves the stored magnetic energy $L{i}_L^2/2$ to dissipate through $R_2$, with time constant $L/R_2$.