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

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

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

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

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

answer is D.

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Detailed Solution

Current through the battery

i = $\frac{V}{R_{1}} (1 - e^{\frac{R_{1} t}{L}}) + \frac{V}{R^{2}}$

at t = 0 i = $\frac{V}{R_{2}}$

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

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