If the circuit has inductive reactance X_L > 0, what is the phase relationship between current and voltage?

If the circuit has inductive reactance X_L > 0, what is the phase relationship between current and voltage?

• A. Current leads voltage by φ = arctan(X/R)
• B. Current lags voltage by φ = arctan(X/R)
• C. Current and voltage remain in phase
• D. Voltage leads current by φ = arctan(X/R)

Answer: (B)

In a circuit with inductive reactance, the impedance has both real and imaginary parts: Z = R + jX_L. The phase angle of this impedance is φ = arctan(X_L / R). Since current is V divided by Z, the current phasor lags the voltage phasor by that angle φ. Therefore, the current lags voltage by φ = arctan(X_L / R). If X_L were zero, there would be no lag (in phase). If it were a pure capacitor, the current would lead the voltage. In a pure inductor (R = 0) the lag would be 90 degrees.

In a circuit with inductive reactance, the impedance has both real and imaginary parts: Z = R + jX_L. The phase angle of this impedance is φ = arctan(X_L / R). Since current is V divided by Z, the current phasor lags the voltage phasor by that angle φ. Therefore, the current lags voltage by φ = arctan(X_L / R).

If X_L were zero, there would be no lag (in phase). If it were a pure capacitor, the current would lead the voltage. In a pure inductor (R = 0) the lag would be 90 degrees.