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AC Power and Power Factor

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AC power and power factor

With a pure resistor, AC voltage and current are in step, or in phase. With inductors and capacitors, current can lead or lag voltage.

A useful first picture

Imagine pushing a swing. A push delivered at the right time does useful work. A push delivered at the wrong part of the swing may move energy back and forth without producing as much net work. Reactive AC circuits can similarly exchange energy with the source.

Three power quantities

Real power P — watts (W)
Apparent power S — volt-amperes (VA)
Power factor PF — real power divided by apparent power

PF = P/S

Worked example

A load uses 800 W but has 1000 VA of apparent power:

PF = 800/1000 = 0.8

Why electricians care

Motors and transformers are inductive loads, so power factor becomes important in AC systems. Poor power factor can increase current and conductor losses even when the useful wattage has not increased.

Try these yourself

In a purely resistive AC load, voltage and current are: In phase Always 90° apart Unrelated DC only

For an ideal resistor, voltage and current rise and fall together.

Power factor is the ratio of real power to: Charge Apparent power Resistance Frequency

PF = real power/apparent power.

A low power factor can cause: More current for the same real power Current to disappear Frequency to become zero All motors to stop

For the same real power and voltage, poorer power factor requires more current.

A little deeper

For sinusoidal voltage and current:

P = V_RMSI_RMS cos φ

The angle φ (phi) is the phase angle between voltage and current. The term cos φ is the power factor for a simple sinusoidal load.

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