Question

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

The correct option is B $\frac{1}{\sqrt{5}}$

Power factor, $cos\varphi =\frac{1}{\sqrt{2}}=\frac{R}{\sqrt{R^2+{\omega }^2{L}^2}}$
Squaring both sides
$\frac{1}{2}=\frac{R^2}{R^2+{\omega }^2{L}^2}$
$2R^2=R^2+{\omega }^2{L}^2$
$R=\omega L$
When $\omega$ is doubled
Power factor
$cos\varphi =\frac{R}{\sqrt{R^2+4{\omega }^2{L}^2}}=\frac{R}{\sqrt{R^2+4R^2}}=\frac{1}{\sqrt{5}}$