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Power Factor of Synchronous Motor using 3 Phase Input Power Formula

GoPower Factor of Synchronous Motor given Input Power Formula

GoPower Factor of Synchronous Motor given 3 Phase Mechanical Power Formula

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The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Check FAQs

CosΦ = \frac{P in(3Φ)}{\sqrt{3} \cdot V L \cdot I L}

CosΦ - Power Factor?P_in(3Φ) - Three Phase Input Power?V_L - Load Voltage?I_L - Load Current?

Power Factor of Synchronous Motor using 3 Phase Input Power Example

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Here is how the Power Factor of Synchronous Motor using 3 Phase Input Power equation looks like with Values.

Here is how the Power Factor of Synchronous Motor using 3 Phase Input Power equation looks like with Units.

Here is how the Power Factor of Synchronous Motor using 3 Phase Input Power equation looks like.

0.866 = \frac{1584}{\sqrt{3} \cdot 192 \cdot 5.5}

0.866 = \frac{1584W}{\sqrt{3} \cdot 192V \cdot 5.5A}

0.866 = \frac{1584}{\sqrt{3} \cdot 192 \cdot 5.5}

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Power Factor of Synchronous Motor using 3 Phase Input Power Solution

Follow our step by step solution on how to calculate Power Factor of Synchronous Motor using 3 Phase Input Power?

FIRST Step Consider the formula

CosΦ = \frac{P in(3Φ)}{\sqrt{3} \cdot V L \cdot I L}

Next Step Substitute values of Variables

∴

CosΦ = \frac{1584W}{\sqrt{3} \cdot 192V \cdot 5.5A}

Next Step Prepare to Evaluate

∴

CosΦ = \frac{1584}{\sqrt{3} \cdot 192 \cdot 5.5}

Next Step Evaluate

∴

CosΦ = 0.866025403784439

LAST Step Rounding Answer

∴

CosΦ = 0.866

Power Factor of Synchronous Motor using 3 Phase Input Power Formula Elements

Variables

Functions

Power Factor

The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.

Symbol: CosΦ

Measurement: NAUnit: Unitless

Note: Value should be between -0.999 to 1.001.

Formulas to find Power Factor

Three Phase Input Power

Three Phase Input Power is defined as the three phase power supplied an synchronous motor.

Symbol: P_in(3Φ)

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Three Phase Input Power

Load Voltage

The Load Voltage is defined as the voltage between two terminals of load.

Symbol: V_L

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Load Voltage

Load Current

Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

Symbol: I_L

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Load Current

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Power Factor

Go Power Factor of Synchronous Motor given Input Power

CosΦ = \frac{P in}{V \cdot I a}

Go Power Factor of Synchronous Motor given 3 Phase Mechanical Power

CosΦ = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot V L \cdot I L}

Other formulas in Power Factor and Phase Angle category

Go Armature Current of Synchronous Motor given 3 Phase Mechanical Power

I a = \sqrt{\frac{P in(3Φ) - P me(3Φ)}{3 \cdot R a}}

Go Armature Current of Synchronous Motor given Input Power

I a = \frac{P in}{\cos (Φ s) \cdot V}

Go Armature Current of Synchronous Motor given Mechanical Power

I a = \sqrt{\frac{P in - P m}{R a}}

Go Load Current of Synchronous Motor given 3 Phase Mechanical Power

I L = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot V L \cdot \cos (Φ s)}

How to Evaluate Power Factor of Synchronous Motor using 3 Phase Input Power?

Power Factor of Synchronous Motor using 3 Phase Input Power evaluator uses Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current) to evaluate the Power Factor, The Power Factor of Synchronous Motor using 3 phase Input Power formula is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Power Factor is denoted by CosΦ symbol.

How to evaluate Power Factor of Synchronous Motor using 3 Phase Input Power using this online evaluator? To use this online evaluator for Power Factor of Synchronous Motor using 3 Phase Input Power, enter Three Phase Input Power (P_in(3Φ)), Load Voltage (V_L) & Load Current (I_L) and hit the calculate button.

FAQs on Power Factor of Synchronous Motor using 3 Phase Input Power

What is the formula to find Power Factor of Synchronous Motor using 3 Phase Input Power?

The formula of Power Factor of Synchronous Motor using 3 Phase Input Power is expressed as Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current). Here is an example- 0.866025 = 1584/(sqrt(3)*192*5.5).

How to calculate Power Factor of Synchronous Motor using 3 Phase Input Power?

With Three Phase Input Power (P_in(3Φ)), Load Voltage (V_L) & Load Current (I_L) we can find Power Factor of Synchronous Motor using 3 Phase Input Power using the formula - Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Power Factor?

Here are the different ways to Calculate Power Factor-

Power Factor=Input Power/(Voltage*Armature Current)
Power Factor=(Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)

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