Question

The instantaneous values of alternating current and voltage in a circuit are given as

$i=\frac{1}{\sqrt{2}}\text{sin}\left(100\pi t\right)\text{ampere}$

$e=\frac{1}{\sqrt{2}}\text{sin}(100\pi t+\frac{\pi }{3})\text{volt}$

The average power in watts consumed in the circuit is

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

Answer 1

The correct option is D

$\frac{1}{8}$

${\text{P}}_{\text{av}}=\frac{1}{2}{i}_0{e}_0\text{cos}\frac{\pi }{3}$

$=\frac{1}{2}\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\times \frac{1}{2}=\frac{1}{8}\text{W}$