First slide

KVL

Question

In the circuit shown, switch S is closed at t = 0. Let i₁ and i₂ be the currents at any finite time t, then the ratio $\frac{i_{1}}{i_{2}} .$

Moderate

A

is constant
B

Increases with time
C

decreases with time
D

first increases and then decreases

Solution

From the given situation, $i_{1} = \frac{V}{2 R} (e^{\frac{- t}{6 RC}}) and i_{2} = \frac{V}{R} e^{\frac{- t}{RC}}$
$\frac{i_{1}}{i_{2}} = \frac{1}{2} {(e)}^{\frac{5 t}{6 RC}},$ which increases with time

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