In an A.C. circuit, the instantaneous e.m.f. and current are given by, E = 100 sin 30 t , I = 20 sin 30 t - π 4 . In one cycle of A.C. , the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively:

Question

In an A.C. circuit, the instantaneous e.m.f. and current are given by, E = 100 sin 30 t , I = 20 sin 30 t - &#960; 4 . In one cycle of A.C. , the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively:

Aicharya · Accepted Answer

Instantaneous emf and current is given by, $E = 100 \sin 30 t$ , $I = 20 \sin (30 t - \frac{π}{4})$ .
Phase difference between emf and current is
$ϕ = 30 t - (30 t - \frac{π}{4}) = \frac{π}{4}$
Average power is given by,
$P_{av} = E_{rms} I_{rms} cosϕ$
$= \frac{100}{\sqrt{2}} \times \frac{20}{\sqrt{2}} \times \frac{1}{\sqrt{2}}$ $= \frac{1000}{\sqrt{2}}$

Watt-less current is given by,
$I_{WL} = I_{rms} sinϕ$ $= \frac{I_{o}}{\sqrt 2} \sin 45 °$ $\Rightarrow I_{WL} = \frac{20}{\sqrt{2}} . \frac{1}{\sqrt{2}} = 10 A$ .

In an A.C. circuit, the instantaneous e.m.f. and current are given by, E = 100 sin 30 t , I = 20 sin 30 t -…

Solution