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 − 4 π ) . In one cycle of A . C . , the average power consumed by the circuit (in watt)

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 − 4 π ​ ) . In one cycle of A . C . , the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively:

TestHub · 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,
$P_{a v} = E_{r m s} I_{r m s} cos ϕ$
$= \frac{100}{2} \times \frac{20}{2} \times \frac{1}{2}$ $= \frac{1000}{2}$

Watt-less current is given by,
$I_{W L} = I_{r m s} sin ϕ$ $= \frac{I _{o}}{2} sin 4 5^{\circ}$ $\Rightarrow I_{W L} = \frac{20}{2} . \frac{1}{2} = 10 A$ .

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