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Impedance

In the given ...

Question

In the given circuit, if current through inductor L is given as $i = i_{0} (1 - e^{\frac{- R t}{2}})$ , then R in ohms is (Write upto two digits after the decimal point.)

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Solution

Here, $R$ is the equivalent resistance across the inductor after short-circuiting the battery.
Therefore,
$R e q = \frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{3}$
Req $= \frac{R_{1} R_{2} + R_{1} R_{3} + R_{2} R_{2}}{R_{1} + R_{2}} = \frac{4 \times 6 + 4 \times 3 + 6 \times 3}{4 + 6} = 5.4 Ω$

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