In a series LCR circuit alternating e.m.f. and current are given by the equations V = V₀sin (ω t) and I = I₀sin (ω t + π/3) respectively. The average power dissipated in the circuit over one cycle of a.c. is (cos 60° = 0.5) (a) zero (b) (V₀ I₀)/(2) (c) √(3)/2V₀ I₀ (d) (V₀ I₀)/(4)

Answer: (d). P = VrmsIrmscos φ = (V₀I₀)/(2)cos φ Phase difference φ = π/3, cos 60° = 0.5 P = (V₀I₀)/(2)×1/2 = (V₀I₀)/(4) So the answer is (d) (V₀I₀)/(4).

In a series LCR circuit alternating e.m.f. and current are given by… | MHT CET 2026 (17 Apr, Shift 2)

Q1MHT CET 2026 · 17 APR · SHIFT 2Easy

Power, Power Factor & Wattless Current

In a series LCR circuit alternating e.m.f. and current are given by the equations $V = V_0\sin(\omega t)$ and $I = I_0\sin\left(\omega t + \frac{\pi}{3}\right)$ respectively. The average power dissipated in the circuit over one cycle of a.c. is $(\cos 60^\circ = 0.5)$

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Answer: (d)

$P = V_{rms}I_{rms}\cos\phi = \frac{V_0I_0}{2}\cos\phi$
Phase difference $\phi = \frac{\pi}{3}$ , $\cos 60^\circ = 0.5$
$P = \frac{V_0I_0}{2}\times\frac{1}{2} = \frac{V_0I_0}{4}$
So the answer is (d) $\frac{V_0I_0}{4}$ .

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Power, Power Factor & Wattless Current question from MHT CET 2026 (17 Apr, Shift 2)

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