In a circuit with R = 20 Ω and X_L = 40 Ω, what is the power factor cosφ?

In a circuit with R = 20 Ω and X_L = 40 Ω, what is the power factor cosφ?

• A. 0.300
• B. 0.447
• C. 0.600
• D. 0.800

Answer: (B)

Power factor is the cosine of the phase angle between voltage and current. In a series RL circuit, the impedance magnitude is Z = sqrt(R^2 + X_L^2), and the angle φ satisfies tanφ = X_L / R, so cosφ = R / Z. With R = 20 Ω and X_L = 40 Ω, Z = sqrt(20^2 + 40^2) = sqrt(400 + 1600) = sqrt(2000) ≈ 44.72 Ω. Therefore cosφ = 20 / 44.72 ≈ 0.447. Since the circuit has inductive reactance, the current lags the voltage, giving a lagging power factor of about 0.447.

Power factor is the cosine of the phase angle between voltage and current. In a series RL circuit, the impedance magnitude is Z = sqrt(R^2 + X_L^2), and the angle φ satisfies tanφ = X_L / R, so cosφ = R / Z.

With R = 20 Ω and X_L = 40 Ω, Z = sqrt(20^2 + 40^2) = sqrt(400 + 1600) = sqrt(2000) ≈ 44.72 Ω. Therefore cosφ = 20 / 44.72 ≈ 0.447.

Since the circuit has inductive reactance, the current lags the voltage, giving a lagging power factor of about 0.447.