It's a while since I did any physics, but it goes something like this, from memory.

With direct current, the power is equal to the current multiplied by the voltage. With alternating current, there is a complication: the current and the voltage may not be in phase. If they are, then the mean power is equal to the product of the RMS current and RMS voltage; otherwise it is less. The "power factor" is the ratio of the actual power to the "apparent power" (product of current and voltage).

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Note added at 59 mins (2005-10-09 04:20:18 GMT)
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Yes, Narasimhan is right. The power factor is equal to the cosine of the phase difference. (This explains why the actual power is zero if the current and voltage are 90 degrees out of phase.)

power factor is measured using a wattmeter


By definition, the power factor is a dimensionless number between 0 and 1. When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, all the energy supplied by the source is consumed by the load. Power factors are usually stated at "leading" or "lagging" to show the sign of the phase angle.

The power factor is determined by the type of loads connected to the power system. These can be

Resistive
Inductive
Capacitive
If a purely resistive load is connected to a power supply, current and voltage will change polarity in phase, the power factor will be unity (1), and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as transformers and motors (any type of wound coil) generate reactive power with current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cable generate reactive power with current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, only to send this energy back to the source during the rest of the cycle.

For example, to get 1 kW of real power if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kVA = 1 kW × 1). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor 5 kVA of apparent power needs to be transferred (1 kW = 5 kVA × 0.2).

It is often possible to adjust the power factor of a system to very near unity. This practice is known as power factor correction and is achieved by switching in or out banks of inductors or capacitors. For example the inductive effect of motor loads may be offset by locally connected capacitors.

Energy losses in transmission lines increase with increasing current. Where a load has a power factor lower than 1, more current is required to deliver the same amount of useful energy. Power companies therefore require that customers, especially those with large loads, maintain the power factors of their respective loads within specified limits or be subject to additional charges. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.

http://www.evaluationengineering.com/archive/articles/0903po...