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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?

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  1. 100 VA and 100 VAr
  2. 100 VA and 50 VAr
  3. 200 VA and 50 VAr
  4. 200 VA and 100 VAr

Answer (Detailed Solution Below)

Option 2 : 100 VA and 50 VAr
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Detailed Solution

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Concept

The apparent power in an AC circuit is given by:

The active power in an AC circuit is given by:

The reactive power in an AC circuit is given by:

Calculation

Given, v = 20 sin (ωt + 60°) V

i = 10 sin (ωt + 30°) A

S = 100 VA

Q = 50 VAr

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