The power factor of an LR ac circuit is $\frac{1}{\sqrt{2}}$ and resistance of the circuit is R. The reactance of a capacitor that should be connected in series in this circuit so that the power factor of the circuit will become one..

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$\sqrt{2} R$

$\frac{\sqrt{3} R}{2}$

$\frac{R}{\sqrt{2}}$

answer is B.

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Detailed Solution

if power factor of a LR circuit is $\frac{1}{\sqrt{2}}$ then phase angle is $45^{0}$ $(\cos ϕ = \frac{R}{Z} a n d \tan ϕ = \frac{X_{L}}{R})$ i.e, $X_{L} = R$

when power factor is unity circuit is in resonance $X_{L} = X_{c}$

but $X_{L} = R s o X_{c} i s a l s o e q u a l t o R$

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