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In the circuit shown, the key \( K \) is closed at \( t=0 \). The current through the battery is
(A) \( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} \) at \( t=0 \) and \( \frac{V}{R_{2}} \) at \( t=\infty \).
(B) \( \frac{V R_{1}+R_{2}}{\sqrt{R_{1}^{2}+R_{2}^{2}}} \) at \( t=0 \) and \( \frac{V}{R_{2}} \) at \( t=\infty \).
(C) \( \frac{V}{R_{2}} \) att \( =0 \) and \( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} \) at \( t=\infty \).
(D) \( \frac{V}{R_{2}} \) att \( =0 \) and \( \frac{V R_{1}+R_{2}}{\sqrt{R_{1}^{2}+R_{2}^{2}}} \) at \( t=\infty \).
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