Physics - EMI/AC Question with Solution | TestHub

$L_1$ and $L_2$ are in parallel, so the voltage across them is equal at every instant: $L_1\frac{d{I}_1}{dt}=L_2\frac{d{I}_2}{dt}$. Both currents start from zero, so $L_1{I}_1=L_2{I}_2$ at all times and the current ratio stays fixed (A correct).

After a long time the inductors act as wires: $I_1+I_2=\frac{V}{R}$; with $\frac{I_1}{I_2}=\frac{L_2}{L_1}$ this gives $I_1=\frac{V}{R}\cdot \frac{L_2}{L_1+L_2}$ (B correct) and $I_2=\frac{V}{R}\cdot \frac{L_1}{L_1+L_2}$ (C correct).

At $t=0$ the inductors oppose any change in current, so the current through R is 0, not $\frac{V}{R}$ (D wrong). Answer: (A, B, C).