Q. In an AC circuit the emf(e) and the current (i) at any instant are given respectively by $\ \ \ \ \ \ \ \ \ e = E_{0}\sin{\omega t}$ $i = I_{0}\sin{(\omega t - \phi)}$ The average power in the circuit over one cycle of AC is
A) $\frac{E_{0}I_{0}}{2}$
B) $\frac{E_{0}I_{0}}{2}\sin\phi$
C) $\frac{E_{0}I_{0}}{2}\cos\phi$
D) $E_{0}I_{0}$
Explanation
(c) Power = Rate of work done in one complete cycle.
or $P_{av} = \frac{W}{T}$
or $P_{av} = \frac{(E_{0}I_{0}\cos{\phi)T/2}}{T}$
or $P_{av} = \frac{E_{0}I_{0}\cos\phi}{2}$
Where $\cos\phi$ is called the power factor of an AC circuit.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.