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Active, Reactive and Apparent Power

In an AC circuit we distinguish three kinds of power: the active power that does useful work, the reactive power that sloshes back and forth in reactive components, and the apparent power the source must actually supply. The power factor states what fraction of the apparent power is useful.

P=UIcos⁡φP=UI\cos\varphiactive power
Q=UIsin⁡φQ=UI\sin\varphireactive power
S=UI, S2=P2+Q2S=UI,\ S^2=P^2+Q^2apparent power and the power triangle

Symbols

PPactive powerW
QQreactive powerVAr
SSapparent powerVA
cos⁡φ\cos\varphipower factor

Example

U=230U=230 V, I=5.29I=5.29 A, cos⁡φ≈0.69\cos\varphi\approx0.69:

P=UIcos⁡φ≈230⋅5.29⋅0.69≈840P=UI\cos\varphi\approx230\cdot5.29\cdot0.69\approx840 W.

Only the active power PP does useful work – SS is what the source must be rated for.
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Part of Electric Circuits: Alternating current.