Lesson 3 of 8

Real, Reactive & Apparent Power

7 min read

In AC circuits, "power" splits into three related quantities — P, Q and S — and almost every discussion of grid stability, transformer sizing or your electricity bill eventually comes back to the relationship between them. This lesson is about building a solid intuition for what each one physically means, not just memorizing the triangle.

Active power (P)

Active power — also called real or average power — is the power that actually does useful work: spinning a motor shaft, producing light, generating heat. It's the time-average of the instantaneous power waveform, measured in watts (W). When you pay your electricity bill in kWh, you're paying for active power consumed over time.

Reactive power (Q)

Reactive power doesn't do useful work — but it isn't "wasted" either. It's the power that oscillates back and forth to build and collapse the magnetic and electric fields inside inductors and capacitors. Motors, transformers and transmission lines all need magnetic fields to function, and maintaining those fields draws reactive power from the system. It's measured in volt-amperes reactive (VAR).

Sign convention

By the standard convention, an inductive load (a motor, for example) absorbs positive reactive power, while a capacitive load supplies it (negative Q). This is why capacitor banks are installed across power systems: to locally supply the reactive power that inductive loads demand, instead of shipping it over the transmission network.

Apparent power (S) and the power triangle

Apparent power is what you get from simply multiplying rms voltage by rms current, without worrying about the phase angle between them — it's the total power the source has to be capable of delivering, measured in volt-amperes (VA). P and Q are the two components that combine, at a right angle to each other, to form S. That relationship is usually drawn as a right triangle, and written as a complex number:

S = P + jQ

Complex power

|S| = √(P² + Q²)

Magnitude of apparent power

Every piece of grid equipment — a transformer, a cable, a generator — is rated in kVA or MVA, not kW. That's because equipment has to be sized for the full apparent power it carries, whether or not that power is doing useful work.

Power factor

Power factor is the ratio of active power to apparent power — a single number between 0 and 1 that tells you how efficiently a load is using the capacity of the system supplying it:

cos φ = PS

Power factor

A power factor of 1.0 means every bit of apparent power is doing useful work (Q = 0). A power factor of 0.7 means a large share of the system's capacity is tied up carrying reactive power instead. Power factor is described as lagging when current lags voltage (inductive loads — most motors) and leading when current leads voltage (capacitive loads).

Why the grid cares

Low power factor forces more current to flow for the same amount of useful power, which means higher I²R losses in lines and transformers, larger voltage drops, and equipment that has to be oversized for capacity it isn't using productively. This is also why industrial customers are often billed a penalty for poor power factor, and why factories install capacitor banks to correct it back toward 1.0.

Key takeaways

Active power (P, in W) does useful work; it's what you're billed for in kWh.
Reactive power (Q, in VAR) sustains magnetic/electric fields; inductive loads absorb it, capacitors supply it.
Apparent power (S, in VA) is what equipment must be rated for: |S| = √(P² + Q²).
Power factor cos φ = P/S measures how efficiently capacity is used — low power factor means more losses for the same useful work.