AC power is the rate of energy transfer in an alternating-current circuit. It is described by active power (real work), reactive power (energy exchanged with reactances) and apparent power (the product of RMS voltage and current).
Learning objectives
- Distinguish active, reactive and apparent power
- Calculate each component from voltage, current and phase angle
- Apply the power triangle and check the result
- Explain why reactive power oscillates but does no net work
- Interpret power analyser readings correctly
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
The three form a right triangle: apparent power is the hypotenuse, active power the horizontal side and reactive power the vertical side.
Intermediate How it behaves in a circuit
A purely resistive load has φ = 0, so P = S and Q = 0. A purely reactive load has φ = 90°, so P = 0 and Q = S: energy oscillates but no net work is done.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Active power | P | watt (W) |
| Reactive power | Q | volt-ampere reactive (var) |
| Apparent power | S | volt-ampere (VA) |
| Phase angle | φ | degree (°) |
Worked examples
Lagging load at 30°
Problem. A load draws 10 A at 230 V with the current lagging the voltage by 30°. Find P, Q and S.
Solution. S = 230 × 10 = 2300 VA. P = 2300 × cos 30° = 2300 × 0.866 = 1992 W. Q = 2300 × sin 30° = 2300 × 0.5 = 1150 var.
Purely capacitive load
Problem. A capacitor draws 5 A at 230 V with the current leading by 90°. Find the three power components.
Solution. S = 230 × 5 = 1150 VA. cos 90° = 0, so P = 0. sin 90° = 1, so Q = 1150 var.
Using the power triangle
Problem. A load has a power factor of 0.6 and draws 10 A at 230 V. Find P and Q.
Solution. S = 2300 VA. P = 2300 × 0.6 = 1380 W. Q = √(2300² − 1380²) = √(5 290 000 − 1 904 400).
Practical applications
- Motor and transformer loading
- Uninterruptible power supply sizing
- Power-quality analysis
- Electricity billing and demand charges
- Filter and compensation design
- Generator and inverter rating
Automotive applications
AC charging of electric vehicles, inverter outputs for auxiliaries and the alternator AC side all involve reactive behaviour. In DC traction systems the power is essentially active, but the AC side of chargers must meet power-factor and distortion requirements.
Industrial applications
Motors and transformers absorb reactive power to create their fields, so industrial supplies are sized in kVA as well as kW. Power-factor correction, harmonic filters and demand management all depend on separating the three power components.
Measurement procedure
- Use a power analyser to read P, Q, S and power factor together.
- Confirm the instrument uses true RMS and states which reactive-power definition it applies.
- Check the phase polarity of the current probe; a reversed probe gives a misleading sign.
- For distorted loads, record harmonics along with the total values.
Common mistakes
- Adding active and reactive power arithmetically instead of as a right triangle.
- Believing reactive power is useless; it is necessary to sustain magnetic and electric fields.
- Using an averaging meter and misreading the RMS values.
- Ignoring harmonic distortion when interpreting apparent power.
Safety considerations
- Reactive components store energy; capacitors and inductors can remain hazardous after isolation.
- High-power AC equipment presents arc-flash risk; use the correct procedures and PPE.
- Discharge and verify before touching terminals of power-factor correction equipment.