Q. Power dissipated in an $LCR$ series circuit connected to an a.c. source of $emf\ E$ is
A) $E^{2}R/\left\lbrack R^{2} + \left( L\omega - \frac{1}{C\omega} \right)^{2} \right\rbrack$
B) $\frac{E^{2}\sqrt{R^{2} + \left( L\omega - \frac{1}{C\omega} \right)^{2}}}{R}$
C) $\frac{E^{2}\left\lbrack R^{2} + \left( L\omega - \frac{1}{C\omega} \right)^{2} \right\rbrack}{R}$
D) $\frac{E^{2}R}{\sqrt{R^{2} + \left( L\omega - \frac{1}{C\omega} \right)^{2}}}$
Explanation
(a) $P = E_{rms}\ i_{rms}\cos\phi = \frac{E^{2}R}{Z^{2}} = \frac{E^{2}R}{\left\lbrack R^{2} + \left( \omega L - \frac{1}{\omega C} \right)^{2} \right\rbrack}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.