# Power Factor Formula Explanation

## Power Factor Formula

**Power Factor**is a very important thing when we talk about Alternating Current(AC). You should know what is the power factor and all the basic

**power factor formulas**. In this post, we will discuss all the basic

**formulas of power factor**for all types of circuit(Inductive circuit, Capacitive Circuit, Resistive Circuit). Actually, the efficiency of an electrical power system depends upon the power factor.

### What is Power Factor?

The main definition of the Power Factor is,

**Power Factor is**the cosine of the angle between Voltage and Current.In the DC circuit, when we connect a load to the source then the current drawn by the load is same phase with the voltage across the load. There is no angle between current and voltage.

But in the AC circuit, when we connect a load to the source then the current drawn by the load is not the same phase with the voltage across the load. There is some angle exists between the voltage and current which depends upon the type of the load.

The Power Factor can be defined as below,

**1.**Power Factor is the ratio of True Power or Active Power to the Apparent Power.

So, Power factor = Active Power/Apparent Power = VIcosÏ†/VI

**2.**Power factor is the ratio of the Resistance of a circuit to the Impedance of the same circuit.

So Power Factor = Resistance/Impedance = R/Z

### Power Factor of DC:

The voltage of the DC circuit =

**V**The flow of current =

**I**The angle between voltage and current =

**Ï•**As we know that there is no angle between the voltage and current in the DC circuit,

So

**Ï•**= 0We know that the power factor is the cosine of the angle between the current and voltage,

So the power factor =

**cos****Ï•**=**cos0**=**1**So it is clear that the

**power factor of DC is Unity or 1**As the unity power factor cannot change the value of the DC power, that is why we say

**DC has no Power Factor**.### Power Factor Formula for AC:

Voltage = V

Current = I

The angle between current and voltage =

**Ï•**#### Pure Resistive Circuit:

For a resistive circuit there is no angle between current and voltage, the current and voltage both are in the same phase.

so

**Ï•**= 0So the power factor = cos

**Ï•**= cos0=1

So the power factor of a purely resistive circuit is

**Unity**#### Pure Inductive Circuit:

In the purely inductive circuit, the current lags behind the voltage by 90 degrees. So the angle between voltage and current,

**Ï•**= 90 degreesPower Factor = cos

**Ï•**=**cos90**= 0So the power factor of a purely inductive circuit is

**Zero(0) Lagging**.#### Pure Capacitive Circuit:

In the Pure Capacitive Circuit, the current leads behind the voltage by 90 degrees. So the angle between voltage and current,

**Ï•**= 90 degreesPower Factor = cos

**Ï•**=**cos90**= 0So the Power factor of a pure capacitive circuit is

**Zero(0) Leading**.It is clear that the maximum value of the power factor is

**1**and the minimum value is**0**

Remember that the power factor in an electrical system indicates how effectively power is being transferred from the source to the load. A low power factor means that a significant portion of the supplied power is being wasted in reactive components, such as inductive or capacitive loads. By improving the power factor, the efficiency of power transfer can be increased, reducing losses and improving the overall performance of the electrical system.

Power factor influences the capacity of electrical systems, especially in transmission and distribution networks. Low power factor increases the current required to deliver a given amount of power, leading to higher losses and voltage drops along the lines. It reduces the effective capacity of the system, requiring larger conductor sizes and additional equipment. By maintaining a high power factor, system capacity can be utilized more efficiently, and voltage stability can be improved.

**Read Also:**

- Impedance Formula and Theory Explanation
- All Inductance Formula Analysis
- Electrical Power Theory and Formula Explanation
- Capacitance Formula | All Formulas and Equations Explain
- Resistance Formula | All Formulas and Equations Explain

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Power Factor Formula Explanation
Reviewed by Author
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March 01, 2019
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