Glossary term
Apparent Power
The total power magnitude in an AC circuit, equal to the product of RMS voltage and RMS current regardless of phase angle.
Definition
quantityApparent power is the product of the RMS voltage and RMS current in an AC circuit, representing the total power magnitude that the source must supply and the electrical infrastructure must be rated to carry, regardless of how much of it performs useful work.
Apparent power is the quantity that determines the physical sizing requirements of AC electrical equipment — generators, transformers, cables, switchgear, and protection devices — because these components must carry the full current magnitude irrespective of its phase relationship with voltage. It is the vector magnitude of complex power, which combines active power (doing useful work) and reactive power (oscillating between source and reactive elements). The ratio of active to apparent power is the power factor.
In an AC circuit, the apparent power S is defined as the product of the RMS (root mean square) voltage V_\text{rms} and the RMS current I_\text{rms}:
The unit of apparent power is the volt-ampere (VA), deliberately distinct from the watt to indicate that apparent power is not the same as active power — it includes both the work-producing component and the reactive component that oscillates without doing net work.
Complex power
Apparent power is the magnitude of the complex power \tilde{S}, which combines active power P and reactive power Q into a single complex quantity:
where j is the imaginary unit. The magnitude is:
This is the power triangle relation. In phasor notation, complex power is computed as:
where \tilde{V} is the voltage phasor and \tilde{I}^* is the complex conjugate of the current phasor. The real part of \tilde{S} gives active power; the imaginary part gives reactive power.
Why apparent power matters for equipment sizing
Electrical equipment — generators, transformers, cables, busbars, circuit breakers — must be physically capable of carrying the full current flowing through them. That current magnitude is determined by I_\text{rms} = S / V_\text{rms}, regardless of the phase angle between current and voltage. A transformer rated at 1 MVA can deliver 1 MW to a purely resistive load (power factor 1) or only 800 kW to a load with power factor 0.8 — in both cases, the transformer is operating at its thermal current limit.
This is why electrical equipment is rated in volt-amperes (VA or kVA or MVA) rather than watts: the VA rating reflects the thermal and electromagnetic loading of the equipment, which depends on current and voltage magnitudes, not on their phase relationship. Active power output in watts depends additionally on the power factor of the load.
Apparent power and power factor correction
When the power factor \cos\phi = P/S is low, a large apparent power S is required to deliver a given active power P. This means larger currents, larger conductors, larger transformers, and greater resistive losses for the same useful work delivered. Power factor correction — typically by installing capacitor banks near inductive loads — reduces the reactive power demand and brings the power factor closer to unity, reducing S for the same P and allowing existing infrastructure to deliver more active power or to be built smaller. Power factor correction is economically significant in industrial facilities with large inductive loads such as motors, welding equipment, and arc furnaces.