Question

In an AC circuit the instantaneous values of emf and current are $e=200 \sin 300\, t$ volt and $i=2 \sin \left(300 t+\frac{\pi}{3}\right) a m p$ the average power consumed in watts is

• A. 200
• B. 100
• C. 50
• D. 400

Answer 1

Answer: (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, $V_{0}=200 V , I_{0}=2 A, \phi=\frac{\pi}{3}$.
$P =\frac{200 \times 2}{2} \cos \frac{\pi}{3}$
$=\frac{200 \times 2}{2} \times \frac{1}{2}=100 W$