An AC voltage $V=20 \sin 200 \pi t$ is applied to a series LCR circuit which drives a current $I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)$. The average power dissipated is:

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Alternating Current

An AC voltage

V = 20 sin 200 π t

is applied to a series LCR circuit which drives a current

I = 10 sin (200 π t + \frac{π}{3})

. The average power dissipated is:

Answer: (D)

Average power in an AC circuit is

⟨ P ⟩ = V_{r m s} I_{r m s} cos ϕ

.

Here

V_{0} = 20

I_{0} = 10

A, and the phase difference

ϕ = π /3

V_{r m s} = \frac{20}{2}, I_{r m s} = \frac{10}{2}

⟨ P ⟩ = \frac{20}{2} \times \frac{10}{2} \times cos 6 0^{\circ} = 100 \times 0.5 = 50 W

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Single correct option