Question

In an $\text{AC}$ circuit, voltage $V$ and current $i$ are given by :
$V=200\sin 100t\text{Volt}$ and
$i=100\sin (100t+\frac{\pi }{3})\text{mA}$.
The power dissipated in the circuit is $\text{W}.$

Answer 1

Given:
$V=200\sin 100t\text{Volts}$

$i=100\sin (100t+\frac{\pi }{3})\text{mA}$

$i=100\times {10}^{-3}\sin (100t+\frac{\pi }{3})\text{A}$

$i=0.1\sin (100t+\frac{\pi }{3})\text{A}$

Here, $\varphi =(100t+\frac{\pi }{3})-100t=\frac{\pi }{3}$

$\therefore$ Power dissipated is,

$P=\frac{V_0{I}_0}{2}\cos \varphi$

$=\frac{200\times 0.1}{2}\times \cos \left(\frac{\pi }{3}\right)=10\times \frac{1}{2}=5\text{W}$

Correct Answer: $5$