Q. A group of electric lamps having a total power rating of 1000 $watt$ is supplied by an ac voltage $E = 200\sin{(310t + 60{^\circ})}$. Then the $r.m.s.\ $value of the circuit current is
A) 10 $A$
B) $10\sqrt{2}\ A$
C) 20 $A$
D) $20\sqrt{2}\ A$
Explanation
(b) $P = \frac{1}{2}V_{0}i_{0}\cos\phi \Rightarrow 1000 = \frac{1}{2} \times 200 \times i_{0}\cos{60{^\circ}}$
$\Rightarrow i_{0} = 20\ A\ \Rightarrow i_{rms} = \frac{i_{0}}{\sqrt{2}} = \frac{20}{\sqrt{2}} = 10\sqrt{2}A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.