If φ = atan(X/R) for a series circuit, the power factor PF = cos φ. If X > 0, the power factor indicates which of the following?

• A. Lagging
• B. Leading
• C. Unity
• D. Zero

Answer: (A)

In a series circuit, the impedance Z has a real part R and an imaginary part X, so the phase angle φ = atan(X/R) tells us how the voltage and current relate in time. The power factor is PF = cos φ, and the sign of φ indicates lead or lag. With X > 0, the impedance is inductive, making φ positive. A positive φ means the current lags the voltage. Therefore, the power factor is described as lagging. The magnitude of PF depends on how large X is relative to R (larger X gives a smaller PF, approaching zero as φ approaches 90°). If X were negative (capacitive), φ would be negative and the current would lead, giving a leading PF. So, for X > 0, the correct description is lagging.