Question

The instantaneous values of alternating current and voltages in a circuit are given as
$I=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)\text{A}$
$V=\frac{1}{\sqrt{2}}\sin (100\pi t+\frac{\pi }{3})\text{V}$
The average power (in watts) consumed in the circuit is

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

Answer 1

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

Given that,
$I=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)\text{A}$
$\Rightarrow I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{1}{2}\text{A}$

$V=\frac{1}{\sqrt{2}}\sin (100\pi t+\frac{\pi }{3})\text{V}$
$\Rightarrow V_{rms}=\frac{V_0}{\sqrt{2}}=\frac{1}{2}\text{V}$
Average power consumed in $\text{ac}$ circuit is given by

$P=V_{rms}{I}_{rms}\cos \varphi$

$P=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\cos \left(\frac{\pi }{3}\right)=\left(\frac{1}{8}\right)$