Figure shows a circuit contains three identical resistors with resistance $R=9.0\Omega$ each, two identical inductors with inductance $L=2.0\text{mH}$ each, and an ideal battery with emf $ϵ=18\text{V}$. The current '$i$ ' through the battery just after the switch closed is:

At the instant the switch is closed ($t=0$), an inductor behaves as an infinite resistance (open circuit) because it opposes the sudden change in current.Therefore, no current flows through the two branches containing inductors.The current only flows through the single resistor directly connected in the main path (assuming standard circuit configuration where one $R$ is in series with the battery and the others are blocked).
$$i=\frac{ϵ}{R}=\frac{18}{9}=2\text{A}.$$