AC Power Factor Principle

An AC power system power factor is illustrated using a three-trace plot. The phase relationship between voltage and current can reduce the efficiency of power transmission and is known as the power factor. The power trace shows the instantaneous magnitude and direction of the power flow.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The power factor PF is mathematically defined as the cosine of the phase angle between voltage and current. True power is defined by the equation . The graphical representation produces a product of the voltage and current. This product is represented as a sine wave, which is twice the frequency of the voltage and current and represents the instantaneous power and its direction. If the power sine wave is completely on the positive side of the axis, it shows that the power in the system is traveling only in one direction, toward the load. The area under this power sine wave curve represents the amount of energy delivered to the load. If the power sine wave is shifted, the difference in area between the positive and the negative sides represents the power delivered to the load. The negative side of the power sine wave represents the reflected power from a reactive load. A lagging power factor is one in which the current is lagging behind the voltage and is characteristic of an inductive load. A leading power factor is one in which the current is leading the voltage and is characteristic of a capacitive load. If the phase angle were to be shifted to be greater than 90 degrees in either direction, the load would effectively become the source.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+