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

Moderate

A

$\frac{V (R_{1} + R_{2})}{R_{1} R_{2}} at t = 0 and \frac{V}{R_{2}} at t = \infty$
B

$\frac{{VR}_{1} R_{2}}{\sqrt{{R_{1}}^{2} + {R_{2}}^{2}}} at t = 0 and \frac{V}{R_{2}} at t = \infty$
C

$\frac{V}{R_{2}} at t = 0 and \frac{V (R_{1} + R_{2})}{R_{1} R_{2}} at t = \infty$
D

$\frac{V}{R_{2}} at t = 0 and \frac{{VR}_{1} R_{2}}{\sqrt{{R_{1}}^{2} + {R_{2}}^{2}}} at t = \infty$

Solution

At t = 0 At t → $\infty$
$I = \frac{V}{R_{2}} \Rightarrow I = \frac{V (R_{1} + R_{2})}{R_{1} R_{2}}$

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