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The power factor of an AC circuit having resistance ‘R’ and inductor ‘L’ (connected in series) and an angular frequency ${}^{'}ω^{'}$ is

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$\frac{R}{ω L}$

$\frac{R}{{(R^{2} + ω^{2} L^{2})}^{1 / 2}}$

$\frac{ω L}{R}$

$\frac{R}{{(R^{2} - ω^{2} L^{2})}^{1 / 2}}$

answer is B.

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Detailed Solution

$\tan ϕ = \frac{W L}{R}$

Power factor = $\frac{1}{\sqrt{1 + \tan^{2} ϕ}} = \frac{1}{\sqrt{1 + {(\frac{ω L}{R})}^{2}}}$

$\cos ϕ = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}}$

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