In an a.c. circuit, voltage and current are given by:
V=100 sin (100 t) V and I=100 sin (100 t+π/3) mA respectively.
The average power dissipated in one cycle is:

Solution

Physics sir · 3 steps

Convert mA to A, then use the half, the peaks and the cosine of the phase gap: three factors, none skipped.

1. Read the peaks. The peak voltage is V₀ = 100 V. The peak current is 100 mA, so I₀ = 0.1 A.
2. Phase difference. The current leads the voltage by φ = π/3, so the power factor is cos π/3 = 1/2.

   P_(avg) = 1/2 V₀ I₀ cos φ = 1/2 × 100 × 0.1 × 1/2

3. So. P_(avg) = 2.5 W, which is option (c).

The idea to keep. Average AC power is Vᵣₘₛ Iᵣₘₛ cos φ = 1/2 V₀ I₀ cos φ. Only the phase difference matters, whether current leads or lags.

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