In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20 sin (30t - π/4) In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively (a) 50, 0 (b) 50, 10 (c) (1000)/(√(2)), 10 (d) (50)/(√(2))

Answer: (c). E₀=100 V, I₀=20 A, φ = π/4. Pav = (E₀ I₀)/(2)cos φ = 1000 × 1/√(2) = (1000)/(√(2)) W Wattless current = Irmssin φ = (20)/(√(2))·1/√(2) = 10 A So the answer is (c) (1000)/(√(2)), 10.

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Q65JEE Main 2018Medium

Power, Power Factor & Wattless Current

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

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Answer: (c)

$E_0=100$ V, $I_0=20$ A, $\phi = \pi/4$ .
$P_{av} = \frac{E_0 I_0}{2}\cos\phi = 1000 \times \frac{1}{\sqrt{2}} = \frac{1000}{\sqrt{2}}$ W
Wattless current $= I_{rms}\sin\phi = \frac{20}{\sqrt{2}}\cdot\frac{1}{\sqrt{2}} = 10$ A
So the answer is (c) $\frac{1000}{\sqrt{2}}, 10$ .

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