Q. The power factor of an AC circuit having resistance R and inductance L (connected in series) and an angular velocity $\omega$ is
A) $R/\omega L$
B) $R/\left( R^{2} + \ \omega^{2}L^{2} \right)^{1/2}$
C) $\omega\ L/R$
D) $R/\left( R^{2} - \ \omega^{2}L^{2} \right)^{1/2}$
Explanation
(b) From the relation, $\tan\phi = \frac{\omega L}{R}$
Power factor $\cos{\phi = \frac{1}{\sqrt{1 + \tan^{2}\phi}}}$
$= \frac{1}{\sqrt{1 + \left( \frac{\omega L}{R} \right)^{2}}}$
$= \frac{R}{\sqrt{R^{2} + \omega^{2}L^{2}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.