First slide

Time -Varying current in L-R circuit

Question

In the network shown, time constant of the circuit is $ς$ when switches $S_{1}$ and $S_{2}$ are open. When $S_{1}$ and $S_{2}$ are closed, time constant of the circuit will be

Moderate

A

$\frac{4 ς}{3}$
B

$\frac{2 ς}{3}$
C

$\frac{3 ς}{2}$
D

$\frac{3 ς}{4}$

Solution

$ς = \frac{L}{R}$
when $S_{1}$ and $S_{2}$ are closed, $R_{e} = \frac{R \times R}{R + R} = \frac{R}{2}$ and $L_{e} = \frac{2 L \times L}{2 L + L} = \frac{2 L}{3}$
$∴ ς^{1} = \frac{2 L / 3}{R / 2} = \frac{4}{3} ς$

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