Question

The power factor of an $R-L$ circuit is $ \frac{ 1}{ \sqrt 2} $ . If the frequency of AC is doubled, what will be the power factor?

• A. $ \frac{ 1}{ \sqrt 3 } $
• B. $ \frac{ 1}{ \sqrt 5 } $
• C. $ \frac{ 1}{ \sqrt 7 } $
• D. $ \frac{ 1}{ \sqrt {11}} $

Answer 1

Answer: (B)

Power factor
$\cos \phi = \frac{ 1}{ \sqrt 2} = \frac{ R}{ \sqrt{ R^2 + \omega^2 \, L^2 }} $
This gives, $ \omega L = R$
when $\omega$ is doubled, we find
$ \cos \phi' = \frac{ R}{ \sqrt{ R^2 + 4 \omega^2 \, L^2 }} $
= $ \frac{ R}{ \sqrt{ R^2 + 4 R^2}} = \frac{ 1}{ \sqrt 5 } $