# Power Factor

The ratio of the actual electrical power dissipated by an AC circuit to the product of the r.m.s. values of current and voltage. The difference between the two is caused by reactance in the circuit and represents power that does no useful work.

Power can also be represented by a right-angled triangle of vectors. The diagram below demonstrates this using a resistive-inductive load as an example. The power triangle (right-hand illustration) can be derived directly from the voltage triangle (centre illustration) because the power equations S = U0·I, P = UR ·I and Q = UL·I all involve the same current I. The relationship between the various types of power is described by the equation: The angle between the active and apparent power components is equal to the phase displacement between the current and voltage. The cosine of the phase displacement is calculated with the following equation: This yields the following conversion: In other words:

 Active power is the product of the voltage, current and cos j.

Accordingly, reactive power is determined by the following formula: In other words

 Reactive power is the product of the voltage, current and sin j.

The ratio between active and apparent power is termed the  power factor. In the case of sinusoidal current, the power factor is equivalent to cos , which thus serves to indicate the proportion of apparent power converted into active power. If the active power is constant, the apparent power and current increase as cos falls. For instance, if active power is to be supplied to a consumer at a power factor cos = 0.5, the generator, transformer and power supply circuitry must be designed to handle twice the amount of power that is required when the power factor is 1, thus making it markedly more expensive in terms of infrastructure.

The ratio between reactive power and apparent power is termed the reactive factor. In the case of a sinusoidal current, this factor is equivalent to sin 