Q. In an ac circuit, $V$ and $I$ are given by $V = 100\sin{\ (100\ t)}\ volts,\ I = 100\sin{\left( 100t + \frac{\pi}{3} \right)mA}.$ The power dissipated in circuit is
A) $10^{4}\ watt$
B) 10 $watt$
C) $2.5\ watt$
D) 5 $watt$
Explanation
(c) $P = V_{r.m.s.} \times i_{r.m.s.} \times \cos\phi = \frac{100}{\sqrt{2}} \times \frac{{100 \times 10}^{- 3}}{\sqrt{2}} \times \cos\frac{\pi}{3}$
$= \frac{10^{4} \times 10^{- 3}}{2} \times \frac{1}{2} = \frac{10}{4} = 2.5\ watt$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.