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

A

$$\frac{V R_1 R_2}{\sqrt{R_1^2 + R_2^2}}$$ at $$t = 0$$ and $$\frac{V}{R_2}$$ at $$t = \infty$$

B

$$\frac{V}{R_2}$$ at $$t = 0$$ and $$\frac{V(R_1 + R_2)}{R_1 R_2}$$ at $$t = \infty$$

C

$$\frac{V}{R_2}$$ at $$t = 0$$ and $$\frac{V R_1 R_2}{\sqrt{R_1^2 + R_2^2}}$$ at $$t = \infty$$

D

$$\frac{V(R_1 + R_2)}{R_1 R_2}$$ at $$t = 0$$ and $$\frac{V}{R_2}$$ at $$t = \infty$$