A circuit having the power factor of 0.8 consumes 40 W. What will be the value of reactive power (in VAR) of the circuit?

• A. 40
• B. 10
• C. 30
• D. 20

Answer: (C)

The power triangle or Impedance triangle of the AC circuit is shown Below
Cosφ = Base ⁄ Hypotenuse = Active Power  ⁄ Apparent Power
Active Power = Apparent power × Cosφ
Sinφ = Perpendicular ⁄ Hypotenuse = Reactive Power  ⁄ Apparent Power
Reactive Power = Apparent power × Sinφ
or
Reactive Power = (Active Power × Sinφ) ⁄ Cosφ
cosφ = 0.8
Sin2φ = 1 − cos2φ
Sin2φ = 1 − (0.8)2
Sinφ = 0.6
Reactive Power =(40 × 0.6) ⁄ 0.8
Reactive Power = 30 VAR