In an a.c circuit, the instantaneous e.m.f and current are given by $e = 100 \sin 30 t$, $i=20\sin\left(30t+\frac{\pi}{4}\right)$. In one cycle of a.c the average power consumed by the circuit and the wattless current are, respectively:
Answer & explanation
Correct answer: option 4
$\text{Average Power consumed is }P_{av} =V_{rms}I_{rms}cos\phi $
$\Rightarrow P_{av} = \frac{100}{\sqrt 2} \frac{20}{\sqrt 2} \frac{1}{\sqrt 2} = \frac{1000}{\sqrt 2}$
$\text{Wattless Current } I = I_{rms} cos \phi = 10A$