= Apparent power
{title2=$|S|$}
<Apparent power> is the product of RMS terminal <electric potential difference> and <electric current>, conventionally expressed in <volt-amperes>:
$$
S_{\rm app}=V_{\rm rms}I_{\rm rms}.
$$
For sinusoidal signals at one frequency, it equals the magnitude $|S|$ of <complex electrical power> and satisfies $S_{\rm app}^2=P^2+Q^2$. It is not generally the average rate of net energy absorption, which is <active power>.<AC Power Flow in Linear Networks by James L. Kirtley Jr.>[Energy and Power, equations61–63 and §7.1, apparent/complex power and RMS convention]{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 $v(t)=\sqrt2(100)\cos\omega t$ and $i(t)=\sqrt2[3\cos\omega t+4\cos3\omega t]$, 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 $|P|\le S_{\rm app}$ without assuming a sinusoidal waveform.
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