Question

The instantaneous values of alternating current and voltages in a circuit are given as
i $=\frac{1}{\sqrt{2}}$sin(100 $\pi t$) 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

The correct option is C $\frac{1}{8}$

P $=V_{rms}$ $I{}_{rms}$ cos $\varphi$
$=\left(\frac{1}{2}\right)$ $\left(\frac{1}{2}\right)$cos$\left(\frac{\pi }{3}\right)$=$\frac{1}{8}$