# Formula of Power factor in electrical circuit

Power factor is an important parameter of an electrical circuit. To deal with a circuit, we need to know how much power is to be supplied to its components so that the circuit works. Because the dissipation of power in a circuit may not be the same as that of real power supplied by the source. The power factor gives a relation between the apparent power and actual power dissipation in a circuit. In this article, we are going to discuss the definition, formula, unit and other facts related to power factor of an electrical circuit.

1. Definition of Power factor in electrical circuit.
2. Formula of power factor
3. Unit of Power factor
4. Power factor correction
5. Significance of power factor

## Power factor definition

The power factor of an electrical circuit is defined as the ratio of actual power to the apparent power dissipated in the circuit. This gives the measurement of the electrical efficiency of a circuit to use the power supply.

The value of power factor depends on the type of elements or components that are used in the circuit. For a purely resistive circuit, the power factor is unity and for a purely inductive circuit, the power factor can be any between 0 to 1.

## Power factor formula

The power factor is the ratio of actual power to the apparent power. So, power factor formula is, $\small{\color{Blue}f=\frac{P_{actual}}{P_{apparent}}}$………..(1)

Now, the actual power dissipation = apparent power × power factor

Now, the apparent power is the RMS power of the AC power supply i.e. $\small{\color{Blue}P_{apparent}=I_{rms} .V_{rms}}$

Thus, the actual power dissipation in the AC circuit is, $\small{\color{Blue}P_{apparent}=I_{rms} .V_{rms}. f}$

Again, the power factor has a direct relation with the phase difference between the alternating voltage and alternating current in the electrical circuit. If $\small\color{Blue}\theta$ be the phase difference between the applied AC voltage and AC current in the circuit then we have another formula of power factor is, $\small\color{Blue}f=cos\theta$……(2)

Using equation-(1) and (2), one can easily determine the power factor of an electrical circuit.

## Power factor unit

Since, the power factor is the ratio of two same physical quantity (power), then it is unitless parameter. So, the power factor of a circuit do not have any unit. Also, it do not have any dimension i.e. dimensionless.

## Physical significance of power factor in electrical circuit

The power factor in an electrical circuit indicates the electrical efficiency of the circuit. It gives the measure of a fractional power that losses in the circuit.

## Power factor correction

If the actual or real power dissipation becomes same as the apparent power dissipation, then the circuit will have maximum efficiency. In this case, power factor remains unity (1). But, when the power factor of the circuit becomes lass than unity, the correction of power factor is required to make it closer to unity.

The power factor correction can be made by adjusting the phase difference between the alternating current and voltage of the circuit.

## Power factor of purely resistive circuit

In a purely resistive circuit, the phase difference between the alternating current and voltage is zero. Hence, from equation-(2), the power factor of a resistive circuit is unity i.e. f = 1.

You can read the article: Unity power factor of a resistive circuit.

## Power factor of purely reactive circuit

A purely reactive circuit consists of either only capacitors or only inductors or their combination. The circuit containing only inductors is known as purely inductive circuit and the circuit containing only capacitors is a purely capacitive circuit.

For a purely inductive circuit, the phase difference between alternating current and alternating voltage is – 90° and for a purely capacitive circuit, this phase difference is +90°. In both cases, the power factor, f = 0.

Thus, the power factor of a purely capacitive and purely inductive circuit is always zero. That means there is no actual power loss in those circuits. But for a purely reactive circuit containing both the capacitor and inductor as the elements, the power factor can be anything between 0 to 1. In this case, the power factor will not be zero as the phase difference may not be 90°.

This is all from this article on power factor of an AC circuit and its formula. If you have any doubts on this topic you can ask me in the comment section.

Thank you!

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