Question

When a voltage $V_s=200\sqrt{2}\sin (\omega t+{15}^{\circ })V$ is applied to an ac circuit, the current in the circuit is found to be $i=2\sin [\omega t+(\pi /4\left)\right]A$. If the average power consumed in the circuit is $x\sqrt{6}W$. Find $x$

Answer 1

Using above attached concept
$V_{max}$ = $200\sqrt{2}$V
$I_{max}$ = 2 A
$\varphi$ = 45 - 15 = 30
$P_{avg}$ = $\frac{1}{2}{V}_{max}{I}_{max}Cos\varphi =\frac{1}{2}\times 200\sqrt{2}\times 2\times Cos30=100\sqrt{6}$
so x= 100