What will be the value of average power (in Watt) of a sinusoidal voltage applied across a series circuit is 20 sinωt V and the current flowing the circuit is 10 sin(ωt + 60)A?

• A. 50
• B. 80
• C. 60
• D. 100

Answer: (D)

Given
The instantaneous value of Voltage V = Vmsinωt = 20 sinωt = 20 V
The instantaneous value of voltage I = Imsin(ωt + φ) = 10 sin(ωt + 60) = 10 A
Phase angle φ = 60°
Average Power delivered by an AC circuit
Pavg = IRMS.VRMS.Cosφ
Where
IRMS = Im ⁄ √2 = 20 ⁄ √2
VRMS = Vm ⁄ √2 = 10 ⁄ √2
P=100 Watt