In the circuit shown below, the key K is closed at t = 0. The current through the battery is

Question

( A ) $\frac{V}{R^2}$ at $t=0$ and $\large\frac{VR_1R_2}{\sqrt{R_1^2+R_2^2}}$ at $t=\infty$
( B ) $\frac{V(R_1+R_2)}{R_1^2+R_2^2}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
( C ) $\frac{VR_1R_2}{\sqrt{R_1^2+R_2^2}}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
( D ) $\frac{V}{R^2}$ at $t=0$ and $\large\frac{VR_1R_2}{R_1+R_2}$ at $t=\infty$