Power Factor of Synchronous Motor given 3 Phase Mechanical Power Calculator

✖Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.ⓘ Three Phase Mechanical Power [P_me(3Φ)]			+10% -10%
✖Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.ⓘ Armature Current [I_a]			+10% -10%
✖The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.ⓘ Armature Resistance [R_a]			+10% -10%
✖The Load Voltage is defined as the voltage between two terminals of load.ⓘ Load Voltage [V_L]			+10% -10%
✖Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.ⓘ Load Current [I_L]			+10% -10%

✖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.ⓘ Power Factor of Synchronous Motor given 3 Phase Mechanical Power [CosΦ]

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Power Factor of Synchronous Motor given 3 Phase Mechanical Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
CosΦ = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*V_L*I_L)
This formula uses 1 Functions, 6 Variables

Functions Used

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., sqrt(Number)

Variables Used

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.
Three Phase Mechanical Power - (Measured in Watt) - Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.
Armature Current - (Measured in Ampere) - Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.
Armature Resistance - (Measured in Ohm) - The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.
Load Voltage - (Measured in Volt) - The Load Voltage is defined as the voltage between two terminals of load.
Load Current - (Measured in Ampere) - Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

STEP 1: Convert Input(s) to Base Unit

Three Phase Mechanical Power: 1056.2505 Watt --> 1056.2505 Watt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
Armature Resistance: 12.85 Ohm --> 12.85 Ohm No Conversion Required
Load Voltage: 192 Volt --> 192 Volt No Conversion Required
Load Current: 5.5 Ampere --> 5.5 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CosΦ = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*V_L*I_L) --> (1056.2505+3*3.7^2*12.85)/(sqrt(3)*192*5.5)

Evaluating ... ...

CosΦ = 0.866025403784439

STEP 3: Convert Result to Output's Unit

0.866025403784439 --> No Conversion Required

FINAL ANSWER

0.866025403784439 ≈ 0.866025 <-- Power Factor

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Power Factor and Phase Angle » Power Factor of Synchronous Motor given 3 Phase Mechanical Power

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< Power Factor and Phase Angle Calculators

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power

LaTeX Go Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))

Power Factor of Synchronous Motor given 3 Phase Mechanical Power

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

Phase Angle between Load Voltage and Current given 3 Phase Input Power

LaTeX Go Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current))

Phase Angle between Voltage and Armature Current given Input Power

LaTeX Go Phase Difference = acos(Input Power/(Voltage*Armature Current))

< Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))

Armature Current of Synchronous Motor given Mechanical Power

LaTeX Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)

Armature Current of Synchronous Motor given Input Power

LaTeX Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)

Power Factor of Synchronous Motor given 3 Phase Mechanical Power Formula

LaTeX Go

Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
CosΦ = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*V_L*I_L)

What is the power developed by a motor?

In an electric motor, the mechanical power is defined as the speed times the torque. Mechanical power is typically defined as kilowatts (kW) or horsepower (hp) with one watt equaling one joule per second or one Newton-Meter per second.

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

Power Factor of Synchronous Motor given 3 Phase Mechanical Power calculator uses Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current) to calculate 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 calculate Power Factor of Synchronous Motor given 3 Phase Mechanical Power using this online calculator? To use this online calculator 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. Here is how the Power Factor of Synchronous Motor given 3 Phase Mechanical Power calculation can be explained with given input values -> 0.866025 = (1056.2505+3*3.7^2*12.85)/(sqrt(3)*192*5.5).

FAQ

What is Power Factor of Synchronous Motor given 3 Phase Mechanical Power?

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 and is represented as CosΦ = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*V_L*I_L) or Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current). Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft, Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor, The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor, The Load Voltage is defined as the voltage between two terminals of load & Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

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

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 is calculated using Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current). To calculate Power Factor of Synchronous Motor given 3 Phase Mechanical Power, you need Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Voltage (V_L) & Load Current (I_L). With our tool, you need to enter the respective value for Three Phase Mechanical Power, Armature Current, Armature Resistance, Load Voltage & Load Current and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Power Factor?

In this formula, Power Factor uses Three Phase Mechanical Power, Armature Current, Armature Resistance, Load Voltage & Load Current. We can use 3 other way(s) to calculate the same, which is/are as follows -

Power Factor = Input Power/(Voltage*Armature Current)
Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
Power Factor = Input Power/(Voltage*Armature Current)

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