Question

The power factor of an AC circuit having resistance $\left(R\right)$ and inductance $\left(L\right)$ connected in series and an angular velocity $\omega$ is

• A. $R/\omega L$
• B. $R/{(R^2+{\omega }^2{L}^2)}^{1/2}$
• C. $\omega L/R$
• D. $R/{(R^2-{\omega }^2{L}^2)}^{1/2}$

Answer 1

The correct option is B $R/{(R^2+{\omega }^2{L}^2)}^{1/2}$

$\text{Reactance due to inductor}=\omega L$
$Z=\sqrt{R^2+{\omega L}^2}$
$\text{Power factor:}\cos \varphi =\frac{R}{Z}$
$\cos \varphi =\frac{R}{\sqrt{R^2+{\omega L}^2}}$