Question

In an AC circuit, the instantaneous emf and current are given by $e=100\sin 30t,i=20\sin (30t-\frac{\pi }{4})$. In one cycle of AC, the average power consumed by the circuit in watt and the wattless current in amperes are, respectively –

• A. $50,0$
• B. $50,0$
• C. $\frac{1000}{\sqrt{2}},10$
• D. $\frac{50}{\sqrt{2}},0$

Answer 1

The correct option is C $\frac{1000}{\sqrt{2}},10$

$P_{av}=E_{rms}{I}_{rms}\cos \varphi =\left(\frac{E_0}{\sqrt{2}}\right)\left(\frac{I_0}{\sqrt{2}}\right)\cos {45}^{\circ }$
$=\frac{100}{\sqrt{2}}\times \frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}$
$=\frac{1000}{\sqrt{2}}$ watt
wattless current $I_{rms}\sin \varphi$
$=\frac{I_0}{\sqrt{2}}\sin \varphi$
$=\frac{20}{\sqrt{2}}\sin {45}^{\circ }$
$=\frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}$
$=10$ A