First slide

Power in a.c. circuit

Question

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 become.

Moderate

A

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

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

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

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

Solution

$cosϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + L^{2} ω^{2}}}$
$\frac{1}{2} = \frac{R^{2}}{R^{2} + {Xc}^{2}} X_{c} = R$
${cosϕ}^{1} = \frac{R}{\sqrt{R^{2} + {(2 X_{c})}^{2}}} = \frac{R}{\sqrt{5 R^{2}}}$

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