Home / Topics / AC Circuits & EM Waves
Average power in AC
Intermediate
Average power over a cycle.
P = V_rms I_rms cosφP_avg = V_rms I_rms cosφ. For a purely resistive load P = I_rms²R.
230 V, 5 A with power factor 0.8: 920 W.
Don't use peak values for average power.
In more detail
In an AC circuit, average power depends on the phase angle between voltage and current, P = Vrms Irms cos φ. The cos φ term is called the power factor.
Real-world uses
- Industrial customers are charged for poor power factor.
- Engineers improve power factor with capacitors.
- Engineers check that the power delivered to a motor is the real power, which takes account of the phase between voltage and current.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
When is average power zero?
When voltage and current are 90 degrees out of phase, as for a pure inductor or capacitor.
Why does phase matter?
Because only the in-phase part of the current delivers real power.
Why does the cosine appear in the power?
Only the in-phase part of the current delivers average power, and the cosine of the phase angle gives that fraction.
Related topics in AC Circuits & EM Waves
Alternating current · Peak and RMS values · Phasors · Resistor in AC · Inductor in AC