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Q.

The resistance of an R-L circuit is 10 $Ω$ .An e.m.f E0 applied across the circuit at $ω$ =20 rad/s. If the current in the circuit is $\frac{I_{0}}{\sqrt{2}}$ ,what is the value of L

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a

1H

b

2H

c

3H

d

0.5H

answer is D.

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Detailed Solution

$\begin{array}{l} I = \frac{E_{0}}{\sqrt{R^{2} + ω^{2} L^{2}}} = \frac{E_{0}}{R \sqrt{1 + {(\frac{ω L}{R})}^{2}}} = \frac{I_{0}}{\sqrt{1 + {(\frac{ω L}{R})}^{2}}} \\ 1 + {(\frac{ω L}{R})}^{2} = 2 \Rightarrow {(\frac{ω L}{R})}^{2} = 1 \\ \Rightarrow L = \frac{R}{ω} = \frac{10}{20} = 0.5 H \end{array}$

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