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 - 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:, 50, 0, 50, 10, 1000 2 , 10, 50 2 , 0

MARKS App · Accepted Answer

Instantaneous emf and current is given by, E = 100 sin 30 t , I = 20 sin 30 t - π 4 . Phase difference between emf and current is ϕ = 30 t - 30 t - π 4 = π 4 Average power is given by, P av = E rms I rms cosϕ = 100 2 × 20 2 × 1 2 = 1000 2 Watt-less current is given by, I WL = I rms sinϕ = I o √ 2 sin 45 ° ⇒ I WL = 20 2 . 1 2 = 10 A .

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