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