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Q.

The power factor of a series RL circuit is $\frac{1}{\sqrt{2}}$ . If the frequency of the applied ac is doubled, the power factor becomes

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a

$\frac{1}{\sqrt{11}}$

b

$\frac{1}{\sqrt{7}}$

c

$\frac{1}{\sqrt{3}}$

d

$\frac{1}{\sqrt{5}}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

$cosϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + L^{2} ω^{2}}}$

$\frac{1}{2} = \frac{R^{2}}{R^{2} + {X_{L}}^{2}} X_{L} = R$

${cosϕ}^{'} = \frac{R}{\sqrt{R^{2} + {(2 X_{L})}^{2}}} = \frac{R}{\sqrt{5 R^{2}}}$ = $\frac{1}{\sqrt{5}}$

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