Question

When a voltage $v_{s}=200\sqrt{2}sin\left(\omega t + 15 ^\circ \right)$ is applied to an AC circuit, the current in the circuit is found to be $i=2sin\left(\omega t + \pi / 4\right)$ then average power consumed in the circuit is

• A. $200 \, $ watt
• B. $400\sqrt{2}$ watt
• C. $100\sqrt{6}$ watt
• D. $200\sqrt{2}$ watt

Answer 1

Answer: (C)

Correction $150 \rightarrow 15^\circ $
$P_{av}=v_{rms}I_{rms}cosϕ$
$=\frac{200 \sqrt{2}}{\sqrt{2}}\frac{2}{\sqrt{2}}\cdot cos\left(30 ^\circ \right)=200\sqrt{2}cos\left(15\right)$
$=200\sqrt{2}\left[\frac{1}{\sqrt{2}} \left(\frac{\sqrt{3}}{2} + \frac{1}{2}\right)\right]$
$=200\left[\frac{\sqrt{3} + 1}{2}\right]=100\left(\sqrt{3} + 1\right)$