Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power Solution

STEP 0: Pre-Calculation Summary
Formula Used
Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)
Ra = (Pin(3Φ)-Pme(3Φ))/(3*Ia^2)
This formula uses 4 Variables
Variables Used
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.
Three Phase Input Power - (Measured in Watt) - Three Phase Input Power is defined as the three phase power supplied an synchronous motor.
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.
STEP 1: Convert Input(s) to Base Unit
Three Phase Input Power: 1584 Watt --> 1584 Watt No Conversion Required
Three Phase Mechanical Power: 1056.2505 Watt --> 1056.2505 Watt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ra = (Pin(3Φ)-Pme(3Φ))/(3*Ia^2) --> (1584-1056.2505)/(3*3.7^2)
Evaluating ... ...
Ra = 12.85
STEP 3: Convert Result to Output's Unit
12.85 Ohm --> No Conversion Required
FINAL ANSWER
12.85 Ohm <-- Armature Resistance
(Calculation completed in 00.004 seconds)

Credits

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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2 Impedance Calculators

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)
Armature Resistance of Synchronous Motor given Input Power
Go Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)

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

Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power Formula

Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)
Ra = (Pin(3Φ)-Pme(3Φ))/(3*Ia^2)

How does a synchronous motor work?

Working of synchronous motors depends on the interaction of the magnetic field of the stator with the magnetic field of the rotor. The stator contains 3 phase windings and is supplied with 3 phase power. Thus, stator winding produces a 3 phased rotating Magnetic- Field.

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

Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power calculator uses Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2) to calculate the Armature Resistance, The Armature Resistance of Synchronous Motor given 3 phase Mechanical Power formula is defined as the resistance of the armature winding of the synchronous motor. Armature Resistance is denoted by Ra symbol.

How to calculate Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power using this online calculator? To use this online calculator for Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power, enter Three Phase Input Power (Pin(3Φ)), Three Phase Mechanical Power (Pme(3Φ)) & Armature Current (Ia) and hit the calculate button. Here is how the Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power calculation can be explained with given input values -> 12.85 = (1584-1056.2505)/(3*3.7^2).

FAQ

What is Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power?
The Armature Resistance of Synchronous Motor given 3 phase Mechanical Power formula is defined as the resistance of the armature winding of the synchronous motor and is represented as Ra = (Pin(3Φ)-Pme(3Φ))/(3*Ia^2) or Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2). Three Phase Input Power is defined as the three phase power supplied an synchronous motor, 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.
How to calculate Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power?
The Armature Resistance of Synchronous Motor given 3 phase Mechanical Power formula is defined as the resistance of the armature winding of the synchronous motor is calculated using Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2). To calculate Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power, you need Three Phase Input Power (Pin(3Φ)), Three Phase Mechanical Power (Pme(3Φ)) & Armature Current (Ia). With our tool, you need to enter the respective value for Three Phase Input Power, Three Phase Mechanical Power & 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 Armature Resistance?
In this formula, Armature Resistance uses Three Phase Input Power, Three Phase Mechanical Power & Armature Current. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)
  • Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)
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