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Time Constant

In the circui...

Question

In the circuit shown in figure switch $S$ is closed at time $t = 0$ . Let $i_{1}$ and $i_{2}$ be the currents at any finite time $t$ then the ratio $\frac{i_{1}}{i_{2}}$

Is constant

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Increases with time

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Decreases with time

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First increases and then decreases

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Solution

The correct option is B
Increases with time

$i_{1} = \frac{V}{R} e^{- t / 2 C R}$
and $i_{2} = \frac{V}{R} e^{- t / C R}$
$∴ \frac{i_{1}}{i_{2}} = \frac{V}{R} e^{- t / 2 C R}$

i.e., the desired ratio increases with time.

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