Editing Power factor (section)

==General case==
[[File:Power Factor General Case.svg|thumb|Schematic showing how power factor is calculated]]
The general expression for power factor is given by

:<math> \mbox{power factor} = P/P_a </math>
:<math> P_a = I_{rms} V_{rms}  </math>

where <math>P</math> is the real power measured by an ideal [[wattmeter]], <math>I_{rms}</math> is the rms current measured by an ideal [[ammeter]], and <math>V_{rms}</math> is the rms voltage measured by an ideal [[voltmeter]].  Apparent power, <math>P_a</math>, is the product of the rms current and the rms voltage.

If the load is sourcing power back toward the generator, then <math>P</math> and <math> \mbox{power factor} </math> will be negative.

===Periodic waveforms===
If the waveforms are periodic with the same fundamental period, then the power factor can be computed as follows:
<math display="block">\begin{align} P &=\frac{1}{T}  \int_{t'}^{t'+T} i(t)v(t) dt,\\
I_{rms} &=\sqrt{\frac{1}{T} \int_{t'}^{t'+T} {i(t)}^2 dt},\\
V_{rms} &=\sqrt{\frac{1}{T} \int_{t'}^{t'+T} {v(t)}^2 dt},\\
\mbox{power factor} &= \frac{P}{I_{rms}V_{rms}},
\end{align}</math>
where <math>i(t)</math> is the instantaneous current, <math>v(t)</math> is the instantaneous voltage, <math>t'</math> is an arbitrary starting time, and <math>T</math> is the period of the waveforms.

===Nonperiodic waveforms===

If the waveforms are not periodic and the physical meters have the same averaging time, then the equations for the periodic case can be used with the exception that <math>T</math> is the averaging time of the meters instead of the waveform period.

{{Clear}}