Question

The instantaneous values of alternating current and voltages in a circuit are given as
$i=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)$ ampere
$e=\frac{1}{\sqrt{2}}\sin (100\pi t+\pi /3)$ volt
The average power in Watts consumed in the circuit is-

• A. $\frac{\sqrt{3}}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{8}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{1}{8}$

We know that,
$P=V_{rms}{I}_{rms}\cos \varphi$
from the given data, we have
$=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\cos \left(\frac{\pi }{3}\right)=\frac{1}{8}$