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+π/3). The average power dissipated is:

Solution

Physics sir · 4 steps

Read off the peaks and the phase gap, then use rms values with the power factor cos φ.

1. Read the data. Peak voltage V₀ = 20 V and peak current I₀ = 10 A. The current leads the voltage by φ = π/3.
2. Average power formula. Average power uses rms values, Vᵣₘₛ = V₀/√2 and Iᵣₘₛ = I₀/√2, times the power factor cos φ.

   P_(avg) = Vᵣₘₛ Iᵣₘₛ cos φ = 1/2 V₀ I₀ cos φ

3. Put in numbers. P_(avg) = 1/2 × 20 × 10 × cos π/3 = 100 × 1/2 = 50 W.
4. So. The average power dissipated is 50 W, option (d).

The idea to keep. Average AC power is 1/2V₀ I₀ cos φ. Two things to remember: the factor 1/2 from rms values, and cosine of the phase difference, not sine.

Answer from the NTA final answer key. Solution by PrepWiser.