# Active, Reactive and Apparent Power in AC Circuits

Active power:

If an active resistance (e.g. a heating element) is connected to an AC circuit, the resulting voltage and current are in phase (blue and red curves in the diagram below). Multiplying associated pairs of instantaneous voltage and current values provides the instantaneous power (green curve). Such a power curve is always positive, because for an active resistance voltage and current are always either both positive or both negative. Positive power is conveyed from the generator to the consumer. The green areas represent the active work performed. As the power has twice the frequency of the voltage or current, it cannot be plotted together with the current and voltage in a normal vector diagram.

AC power p(t) has a peak value p0 =  u0·i0 and can be converted by equating areas beneath the curve into the equivalent DC power, or active power P. The active power for an active resistance is half the peak power, i.e. In other words:

 Active power for an active resistance is the product of the rms voltage and rms current.

Reactive power:

If a pure reactance, i.e. capacitive or inductive impedance, is connected to an AC circuit, the phase displacement j between the current and voltage is 90°, the current leading the voltage in the case of the capacitance, and lagging behind the voltage in the case of the inductance (as shown in the diagram below). The power curve here is symmetrical about the time axis, so that the positive and negative (grey) areas cancel each other out and overall no active power is consumed. Negative values mean power is passed back from the consumer to the generator. During a single period, energy is fed back twice from the coil (consumer) to the generator. The overall energy constantly oscillates back and forth between the generator and consumer. This results in pure reactive power consumption of an inductive or capacitive nature depending on the component employed. Reactive power is designated Q and expressed in units Var Apparent power:

If a load involving active and reactive resistance components is connected to an alternating voltage, active and reactive power components result. The diagram below demonstrates this in the case of an inductive load, the current and voltage of which are phase-displaced by 60°. The power curve here is mainly above the time axis. The grey areas partially cancel one another out and represent the reactive power component, while the green areas represent the active power (or active work performed). Multiplying the measured values of the voltage and phase-shifted current here yields the apparent power S which is expressed in volt-amperes (VA): Apparent power is not a measure of the conversion of electrical energy in a circuit, instead serving purely as a computed variable made up of the active and reactive power. Accordingly, the active power P indicated by a power meter (wattmeter) in the presence of a phase shift between the current and voltage is always smaller than the apparent power S calculated from the rms current and voltage.