AC Phase Angle

Formula

Description

The phase angle between voltage and current in an AC circuit depends on the ratio of net reactance to resistance. When XL > XC (inductive), the phase angle is positive (voltage leads current). When XC > XL (capacitive), the phase angle is negative (current leads voltage). At resonance (XL = XC), the phase angle is zero and the circuit is purely resistive. The power factor equals cos(φ), so the phase angle directly determines how efficiently the circuit converts apparent power to real power.

Variables

• X_L — Inductive reactance, ωL (Ω)
• X_C — Capacitive reactance, 1/(ωC) (Ω)
• R — Resistance (Ω)

Practical Notes

Result is in degrees. A phase angle of 90° means purely reactive (no real power consumed). A phase angle of 0° means purely resistive (maximum power factor). Most utility loads are inductive (motors, transformers) with phase angles of 20-40°, corresponding to power factors of 0.77-0.94. Power factor correction aims to reduce this angle toward zero.