In an A.C. circuit, the instantaneous e.m.f. and current are given...

Instantaneous emf and current is given by, $E = 100\sin 30t$, $I = 20\sin \left(30t - \dfrac{\pi}{4}\right)$.

Phase difference between emf and current is

$ϕ = 30t - \left(30t - \dfrac{\pi}{4}\right) = \dfrac{\pi}{4}$

Average power is given by,

${P}_{av} = {E}_{rms}{I}_{rms}cosϕ$
$= \dfrac{100}{\sqrt{2}} \times \dfrac{20}{\sqrt{2}} \times \dfrac{1}{\sqrt{2}}$$= \dfrac{1000}{\sqrt{2}}$

Watt-less current is given by,

${I}_{WL} = {I}_{rms}sinϕ$$= \dfrac{{I}_{o}}{√ 2}\sin 45 °$$⇒ {I}_{WL} = \dfrac{20}{\sqrt{2}} . \dfrac{1}{\sqrt{2}} = 10A$.