Question Detail

Apparent power (S) in an AC circuit is given by S = Vrms × Irms. First, calculate the impedance (Z) of the series RL circuit.Given:Inductance L = 0.5 HResistance R = 250 ΩRMS voltage Vrms = 100 VFrequency f = 50 HzCalculate the angular frequency ω = 2πf:ω = 2π × 50 Hz = 100π rad/sCalculate the inductive reactance XL = ωL:XL = 100π rad/s × 0.5 H = 50π Ω ≈ 157.08 ΩCalculate the impedance Z = √(R2 + XL2):Z = √(2502 + (50π)2)Z = √(62500 + 24674.01) = √87174.01 ≈ 295.25 ΩCalculate the RMS current Irms = Vrms / Z:Irms = 100 V / 295.25 Ω ≈ 0.3387 ACalculate the apparent power S = Vrms × Irms:S = 100 V × 0.3387 A = 33.87 VARounding to one decimal place, the apparent power is 33.9 VA.