Power triangle (real, reactive, apparent)
In an AC circuit, not all the power sloshing back and forth actually does work. The power triangle splits it into three parts: real power P (watts, W) — the useful muscle that heats, lights, and spins things; reactive power Q (volt-amperes reactive, VAR) — energy that surges into magnetic fields and capacitors and surges back out, doing no net work; and apparent power S (volt-amperes, VA) — the total the wires and transformers must actually carry. Picture pulling a sled by a rope held at an angle: the forward pull is real power, the useless sideways pull is reactive power, and the full rope tension is apparent power.
Geometrically S is the hypotenuse: S² = P² + Q². Reactive power matters because cables, breakers, and transformers must be sized for the apparent power S even though the customer is billed (mostly) for real power P. A motor drawing 10 kW of real power but 7.5 kVAR of reactive power forces the utility to supply 12.5 kVA — so they push customers to shrink that reactive component.
Reactive power isn't 'wasted' — it's essential to magnetize motors and transformers. But moving it across long lines causes real I²R losses and voltage sag, which is why it's generated locally with capacitor banks.