Inductor branch shunted by a resistor ($\tau =L/(2R)$)

An ideal source $V$ feeds a series resistance $2R$, followed by parallel branches $R+L$ and $2R$. The Thévenin equivalent seen by the inductor has voltage $V/2$ and resistance $R+(2R\parallel 2R)=2R$. From zero initial current, the inductor current is $V(1-e^{-t/\tau })/(4R)$, the other branch current is $V(1+e^{-t/\tau })/(8R)$, and the source current is $V(3-e^{-t/\tau })/(8R)$. Kirchhoff's current law holds at every time, and the final stored magnetic energy is $L{V}^2/(32R^2)$.