= Reactive power
{title2=$Q$}
<Reactive power> is the imaginary part of <complex electrical power> in sinusoidal steady operation. With RMS phasors, the <passive sign convention> and $e^{j\omega t}$ time convention,
$$
S=VI^*=P+jQ,\qquad Q=|V||I|\sin\varphi,
$$
where $\varphi$ is potential-difference phase minus current phase. Inductive current lag gives positive $Q$, while capacitive current lead gives negative $Q$. Its conventional unit is the <reactive volt-ampere>, written var. These definitions retain the specified phasor and sign conventions.<AC Power Flow in Linear Networks by James L. Kirtley Jr.>[Energy and Power, equations61–65; §7.1, RMS amplitudes]{ref}
The physical role is periodic energy exchange rather than an additional dissipated-energy average. For an ideal <inductor>, $v=L\,di/dt$ and stored energy is $w=Li^2/2$, so $p=dw/dt$. Its energy returns to its initial value after a steady cycle and mean absorbed power is zero. Nevertheless,
$$
Q_L=\omega L I_{\rm rms}^2=2\omega\langle w\rangle.
$$
For an ideal <capacitor>, $Q_C=-\omega C V_{\rm rms}^2$, with the negative sign representing the opposite exchange phase. Primary circuit derivations explicitly separate these exchanges from resistor dissipation.<University Physics Volume 2 by Samuel J. Ling and others>[§15.4, Figure15.16, ideal inductive/capacitive instantaneous power]{ref}
For an original example, $L=20\,\mathrm{mH}$, $I_{\rm rms}=5\,\mathrm A$ and $f=50\,\mathrm{Hz}$ give $Q_L\approx157.08\,\mathrm{var}$. Peak stored energy is0.50J and mean stored energy0.25J, consistent with $2\omega\langle w\rangle$. Zero ideal average dissipation therefore does not mean zero current or zero energy storage.
For a separate ideal single-frequency compensation example, a100V load with $S=400+j300\,\mathrm{VA}$ can have its source reactive component canceled by a parallel capacitor satisfying
$$
C=\frac{300}{2\pi(50)(100)^2}\approx95.49\,\mathrm{\mu F}.
$$
The capacitor contributes $-j300\,\mathrm{VA}$, leaving400W of source <active power> and4A RMS source current. This illustrates <power factor correction> under the stated ideal assumptions, rather than selecting a real component or proving its ratings.
Reactive exchange can increase the current carried through resistive wiring and thereby affect real losses. For distorted waveforms, definitions of non-active power need additional care; the one-frequency imaginary-part definition should not silently be extended to every waveform.
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