Question

In an AC circuit, the instantaneous values of emf and current are $e=200sin 314 t$ volt and $I=sin \left(314 t + \frac{\pi }{3}\right) \, $ A $.$ The average power consumed in watt is

• A. 200
• B. 100
• C. 50
• D. 25

Answer 1

Answer: (C)

$V_{r m s}=\frac{200}{\sqrt{2}}, \, I_{r m s}=\frac{1}{\sqrt{2}}$
$\therefore \, \, P=V_{r m s}I_{r m s}cos \phi =\frac{200}{\sqrt{2}}\frac{1}{\sqrt{2}}cos ⁡ \frac{\pi }{3}=50 \, W$