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Power Factor of Synchronous Motor given 3 Phase Mechanical Power Formula

GoPower Factor of Synchronous Motor given Input Power Formula

GoPower Factor of Synchronous Motor using 3 Phase Input 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 me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot V L \cdot I L}

CosΦ - Power Factor?P_me(3Φ) - Three Phase Mechanical Power?I_a - Armature Current?R_a - Armature Resistance?V_L - Load Voltage?I_L - Load Current?

Power Factor of Synchronous Motor given 3 Phase Mechanical Power Example

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

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

Here is how the Power Factor of Synchronous Motor given 3 Phase Mechanical Power equation looks like.

0.866 = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 192 \cdot 5.5}

0.866 = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 192V \cdot 5.5A}

0.866 = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 192 \cdot 5.5}

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Power Factor of Synchronous Motor given 3 Phase Mechanical Power Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

CosΦ = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 192V \cdot 5.5A}

Next Step Prepare to Evaluate

∴

CosΦ = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\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 given 3 Phase Mechanical 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 Mechanical Power

Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.

Symbol: P_me(3Φ)

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Three Phase Mechanical Power

Armature Current

Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.

Symbol: I_a

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Armature Current

Armature Resistance

The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.

Symbol: R_a

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Armature Resistance

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 using 3 Phase Input Power

CosΦ = \frac{P in(3Φ)}{\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 given 3 Phase Mechanical Power?

Power Factor of Synchronous Motor given 3 Phase Mechanical Power evaluator uses Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current) to evaluate the Power Factor, The Power Factor of Synchronous Motor given 3 phase Mechanical 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 given 3 Phase Mechanical Power using this online evaluator? To use this online evaluator for Power Factor of Synchronous Motor given 3 Phase Mechanical Power, enter Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Voltage (V_L) & Load Current (I_L) and hit the calculate button.

FAQs on Power Factor of Synchronous Motor given 3 Phase Mechanical Power

What is the formula to find Power Factor of Synchronous Motor given 3 Phase Mechanical Power?

The formula of Power Factor of Synchronous Motor given 3 Phase Mechanical Power is expressed as Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current). Here is an example- 0.866025 = (1056.2505+3*3.7^2*12.85)/(sqrt(3)*192*5.5).

How to calculate Power Factor of Synchronous Motor given 3 Phase Mechanical Power?

With Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Voltage (V_L) & Load Current (I_L) we can find Power Factor of Synchronous Motor given 3 Phase Mechanical Power using the formula - Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current). This formula also uses Square Root Function 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 Input Power/(sqrt(3)*Load Voltage*Load Current)

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Power Factor of Synchronous Motor given 3 Phase Mechanical Power Formula

​GoPower Factor of Synchronous Motor given Input Power Formula

​GoPower Factor of Synchronous Motor using 3 Phase Input Power Formula

Power Factor of Synchronous Motor given 3 Phase Mechanical Power Example

Power Factor of Synchronous Motor given 3 Phase Mechanical Power Solution

Power Factor of Synchronous Motor given 3 Phase Mechanical Power Formula Elements

Other Formulas to find Power Factor

Other formulas in Power Factor and Phase Angle category

How to Evaluate Power Factor of Synchronous Motor given 3 Phase Mechanical Power?

FAQs on Power Factor of Synchronous Motor given 3 Phase Mechanical Power

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GoPower Factor of Synchronous Motor given Input Power Formula

GoPower Factor of Synchronous Motor using 3 Phase Input Power Formula