Q. In an AC circuit the instantaneous values of emf and current are $e = 200\sin{300\ t}\ volt$ and $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i = 2\sin\left( 300t + \frac{\pi}{3} \right)$amp. The average power consumed in watt is
A) 200
B) 100
C) 50
D) 400
Explanation
(b) The average power consumed in an AC circuit is given by
$P = \frac{V_{0}I_{0}}{2}\cos\phi$
Where $\phi$ is phase angle and $V_{0}\ and\ I_{0}$ the peak value of voltage and current.
Given, $V_{0} = 200V,\ I_{0} = 2\ A,\ \phi = \frac{\pi}{3}$.
$P = \frac{200 \times 2}{2}\cos\frac{\pi}{3}$
$= \frac{200 \times 2}{2} \times \frac{1}{2} = 100\ W$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.