Apparent power ($|S|$)

Apparent power is the product of RMS terminal electric potential difference and electric current, conventionally expressed in volt-amperes:For sinusoidal signals at one frequency, it equals the magnitude $|S|$ of complex electrical power and satisfies $S_{\mathrm{app}}^2=P^2+Q^2$. It is not generally the average rate of net energy absorption, which is active power.^[ref]

For an original example, a100V terminal pair carrying5A RMS has500VA of apparent power. If active power is400W, the power factor is0.8. In the sinusoidal case the magnitude of reactive power is $\sqrt{500^2-400^2}=300$ reactive volt-amperes; the magnitude calculation alone does not determine whether the current leads or lags.

Magnitudes do not add like complex quantities. Consider two parallel sinusoidal loads at the same supply, with complex powers $300+j400$ and $300-j400$ in volt-amperes. Each has500VA of apparent power, but the combined terminal complex power is600VA with zero imaginary part. The source therefore sees600VA rather than the1000VA sum of individual magnitudes. Their internal branch currents and individual component requirements still exist; reactive cancellation at the source does not erase those branch conditions.

For nonsinusoidal waveforms, the product definition remains useful, but the simple equality with the magnitude of one fundamental-frequency complex power needs qualification. With $v(t)=\sqrt{2}(100)\cos \omega t$ and $i(t)=\sqrt{2}[3\cos \omega t+4\cos 3\omega t]$, RMS current is5A and apparent power is500VA. The fundamental-frequency complex electrical power is only300VA. The extra RMS current is not represented by that one complex number.

Thus record the waveform convention with an apparent power rating or measurement. Separately measuring RMS potential difference and current gives this product, while recovering active power requires the corresponding average product or adequate phase-resolved information. The Cauchy-Schwarz inequality guarantees $|P|\le S_{\mathrm{app}}$ without assuming a sinusoidal waveform.

The volt-ampere, symbolVA, is the unit commonly used to express apparent power. At a terminal pair, RMS potential difference in volts multiplied by RMS current in amperes gives the numerical value in volt-amperes. The unit product has the same coherent SI dimensions as the watt:This unit identity does not make apparent power and active power the same quantity. The SI text explicitly warns that different physical quantities can share a unit and that the quantity must be specified.^[ref]

For an original example,250V RMS at8A RMS gives2000VA, or2kVA. If the absorbing load has power factor0.75, its active power is1500W. A1500W value cannot be inferred from the2kVA alone without the phase/waveform information summarized by that factor.

Hypothetical equipment can have separate apparent- and active-power limits. A1000VA/600W limit would permit a500W, factor0.5 load only at the apparent-power boundary, since it requires1000VA. A700W, factor-one load would require only700VA but exceed the separate600W limit. These examples interpret stated numerical constraints rather than specify an actual product's behavior.

For single-frequency sinusoids, the magnitude of complex electrical power is expressed in volt-amperes, while its real part is commonly expressed in watts and its imaginary part in reactive volt-amperes. Those names help keep the quantities distinct even though their base-unit dimensions agree.^[ref] With distorted signals, retain the actual RMS-product definition of apparent power rather than assuming a single fundamental phasor accounts for all current.