AC foundations
Series impedance phase angle
- where
- impedance phase angle (°)
- inductive reactance magnitude (Ω)
- capacitive reactance magnitude (Ω)
- resistance (Ω)
Explain this equation
Works out the phase angle between voltage and current in a series RLC circuit. Gives the power factor, which matters for real power and correction.
φ is the angle by which the voltage leads the current, in degrees. R is resistance. Xₗ − X꜀ is the net reactance. A positive φ means inductive (current lags); negative means capacitive (current leads).
In the impedance triangle, R is the adjacent side and net reactance is the opposite side, so the angle is the arctangent of their ratio.
Sense check: 3 Ω with a net 4 Ω inductive gives about 53°, so cos φ is 0.6. If Xₗ = X꜀, φ is 0° and the circuit looks purely resistive.
Watch out: φ is voltage relative to current. Say whether current lags or leads so the sign is not misread.
For positive resistance, arctangent of net reactance over resistance gives the impedance angle. Positive means inductive: current lags voltage. Negative means capacitive: current leads voltage.
Set a calculator to degrees or convert radians explicitly. A displayed negative angle is meaningful, not automatically an error.
Enter your values to see the result.
Common mistake
Confusing voltage-relative-to-current with current-relative-to-voltage.
Limits
Positive R in a series sinusoidal circuit.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.