Past exam of the physics 2 paper of the University of Oxford / 2014 / 9 / i / Solution

The source diagram has $2R$ in series with two parallel branches: one containing $R$ then $L$, and the other containing $2R$. Let their common voltage be $u(t)$, measured from the upper node to the lower return. Kirchhoff's current law and the branch laws giveUsing $I_2=u/(2R)$ in the source equation yields $u=V/2-R{I}_1$. Substitution into the coil branch givesThe switch was open for a long time, so $I_1(0^{-})=0$. Inductor current continuity gives $I_1(0^{+})=0$ for a finite applied voltage.