Improving Power Factors in an AC Circuit

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows how to improve the power factor in an AC circuit. A power factor correction for a given load voltage and current can reduce operating costs. As described in Details, the key formulas are , , , , where is the AC emf driving the circuit. The angular frequency is related to the frequency in hertz (Hz) by . In this Demonstration, the amplitude is set at 100 volts (V). You can vary the frequency in Hz, the resistance in ohms (), the inductance in millihenries (mH), and the capacitance in microfarads (F). The phase of lags that of by . The phase of lags that of by , where , .


The power factor (pf) is defined by pf =, a dimensionless number between 0 and 1. When the power factor equals 1, all the energy supplied by the source is consumed by the load. When the power factor equals 0, the energy flow is entirely reactive, and stored energy in the load is returned to the source in each cycle.


Contributed by: Anping Zeng (August 2011)
(Sichuan Chemical Technical College)
Open content licensed under CC BY-NC-SA



(a) The original inductive load. (b) The inductive load with improved power factor correction.

(c) The lower triangle of power factor correction; this shows the capacitance value needed to change the pf angle from to . (d) The affect of the capacitor on the total current; when paralleling the capacitance , the power factor is improved; .

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.