In an AC circuit, v = 20 sin (ωt + 60°) V and i = 10 sin (ωt + 30°) A. What are the apparent and reactive powers, respectively?

Concept

The apparent power in an AC circuit is given by:

\(S=V_{rms}I_{rms}\)

The active power in an AC circuit is given by:

\(P=V_{rms}I_{rms}\space cos(\theta_v-\theta_i)\)

The reactive power in an AC circuit is given by:

\(Q=V_{rms}I_{rms}\space sin(\theta_v-\theta_i)\)

Calculation

Given, v = 20 sin (ωt + 60°) V

i = 10 sin (ωt + 30°) A

\(S={20\over \sqrt{2}}\times{10\over \sqrt{2}}\)

S = 100 VA

\(Q={20\over \sqrt{2}}\times{10\over \sqrt{2}}\times sin(60-30)\)

Q = 50 VAr