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  In the circuit shown below, the key K is closed at\[t=0.\]the current through the battery is ?       AIEEE  Solved  Paper-2010

A) \[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]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) \[\frac{V}{{{R}_{2}}}\]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 \[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\]at\[t=\infty \]

Correct Answer: C

Solution :

at \[t=0\]  \[I=\frac{V}{{{R}_{2}}}\] at \[t=\infty \] \[I=\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]