Power Factor of Synchronous Motor given Input Power Solution

STEP 0: Pre-Calculation Summary
Formula Used
Power Factor = Input Power/(Voltage*Armature Current)
CosΦ = Pin/(V*Ia)
This formula uses 4 Variables
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.
Input Power - (Measured in Watt) - Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it.
Voltage - (Measured in Volt) - Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.
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.
STEP 1: Convert Input(s) to Base Unit
Input Power: 769 Watt --> 769 Watt No Conversion Required
Voltage: 240 Volt --> 240 Volt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
CosΦ = Pin/(V*Ia) --> 769/(240*3.7)
Evaluating ... ...
CosΦ = 0.865990990990991
STEP 3: Convert Result to Output's Unit
0.865990990990991 --> No Conversion Required
FINAL ANSWER
0.865990990990991 0.865991 <-- Power Factor
(Calculation completed in 00.006 seconds)

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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6 Power Factor & Phase Angle Calculators

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power
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
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
Go Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current))
Power Factor of Synchronous Motor using 3 Phase Input Power
Go Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
Phase Angle between Voltage and Armature Current given Input Power
Go Phase Difference = acos(Input Power/(Voltage*Armature Current))
Power Factor of Synchronous Motor given Input Power
Go Power Factor = Input Power/(Voltage*Armature Current)

25 Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power
Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))
Power Factor of Synchronous Motor given 3 Phase Mechanical Power
Go Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
Distribution Factor in Synchronous Motor
Go Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))
Load Current of Synchronous Motor using 3 Phase Input Power
Go Load Current = Three Phase Input Power/(sqrt(3)*Load Voltage*cos(Phase Difference))
3 Phase Input Power of Synchronous Motor
Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)
Mechanical Power of Synchronous Motor
Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)
Armature Current of Synchronous Motor given 3 Phase Mechanical Power
Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))
Armature Current of Synchronous Motor given Mechanical Power
Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)
Power Factor of Synchronous Motor using 3 Phase Input Power
Go Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power
Go Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)
3 Phase Mechanical Power of Synchronous Motor
Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance
Phase Angle between Voltage and Armature Current given Input Power
Go Phase Difference = acos(Input Power/(Voltage*Armature Current))
Armature Current of Synchronous Motor given Input Power
Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)
Input Power of Synchronous Motor
Go Input Power = Armature Current*Voltage*cos(Phase Difference)
Armature Resistance of Synchronous Motor given Input Power
Go Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)
Magnetic Flux of Synchronous Motor given Back EMF
Go Magnetic Flux = Back EMF/(Armature Winding Constant*Synchronous Speed)
Armature Winding Constant of Synchronous Motor
Go Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)
Mechanical Power of Synchronous Motor given Input Power
Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance
Power Factor of Synchronous Motor given Input Power
Go Power Factor = Input Power/(Voltage*Armature Current)
Angular Slot Pitch in Synchronous Motor
Go Angular Slot Pitch = (Number of Poles*180)/(Number of Slots*2)
Output Power for Synchronous Motor
Go Output Power = Armature Current^2*Armature Resistance
Number of Poles given Synchronous Speed in Synchronous Motor
Go Number of Poles = (Frequency*120)/Synchronous Speed
Synchronous Speed of Synchronous Motor
Go Synchronous Speed = (120*Frequency)/Number of Poles
Synchronous Speed of Synchronous Motor given Mechanical Power
Go Synchronous Speed = Mechanical Power/Gross Torque
Mechanical Power of Synchronous Motor given Gross Torque
Go Mechanical Power = Gross Torque*Synchronous Speed

Power Factor of Synchronous Motor given Input Power Formula

Power Factor = Input Power/(Voltage*Armature Current)
CosΦ = Pin/(V*Ia)

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 Input Power?

Power Factor of Synchronous Motor given Input Power calculator uses Power Factor = Input Power/(Voltage*Armature Current) to calculate the Power Factor, The Power Factor of Synchronous Motor given 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 calculate Power Factor of Synchronous Motor given Input Power using this online calculator? To use this online calculator for Power Factor of Synchronous Motor given Input Power, enter Input Power (Pin), Voltage (V) & Armature Current (Ia) and hit the calculate button. Here is how the Power Factor of Synchronous Motor given Input Power calculation can be explained with given input values -> 0.865991 = 769/(240*3.7).

FAQ

What is Power Factor of Synchronous Motor given Input Power?
The Power Factor of Synchronous Motor given Input 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 = Pin/(V*Ia) or Power Factor = Input Power/(Voltage*Armature Current). Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it, Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines & Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.
How to calculate Power Factor of Synchronous Motor given Input Power?
The Power Factor of Synchronous Motor given Input 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 = Input Power/(Voltage*Armature Current). To calculate Power Factor of Synchronous Motor given Input Power, you need Input Power (Pin), Voltage (V) & Armature Current (Ia). With our tool, you need to enter the respective value for Input Power, Voltage & Armature 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 Input Power, Voltage & Armature Current. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
  • Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
  • Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
  • Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
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