Back EMF of Synchronous Motor using Mechanical Power Calculator

✖Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.ⓘ Mechanical Power [P_m]			+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%
✖Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.ⓘ Load Angle [α]			+10% -10%
✖Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.ⓘ Phase Difference [Φ_s]			+10% -10%

✖Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.ⓘ Back EMF of Synchronous Motor using Mechanical Power [E_b]

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Back EMF of Synchronous Motor using Mechanical Power

Formula

`"E"_{"b"} = "P"_{"m"}/("I"_{"a"}*cos("α"-"Φ"_{"s"}))`

Example

`"179.8755V"="593W"/("3.70A"*cos("57°"-"30°"))`

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Back EMF of Synchronous Motor using Mechanical Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference))
E_b = P_m/(I_a*cos(α-Φ_s))
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Back EMF - (Measured in Volt) - Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.
Mechanical Power - (Measured in Watt) - Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.
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.
Load Angle - (Measured in Radian) - Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.
Phase Difference - (Measured in Radian) - Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

STEP 1: Convert Input(s) to Base Unit

Mechanical Power: 593 Watt --> 593 Watt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
Load Angle: 57 Degree --> 0.994837673636581 Radian (Check conversion here)
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_b = P_m/(I_a*cos(α-Φ_s)) --> 593/(3.7*cos(0.994837673636581-0.5235987755982))

Evaluating ... ...

E_b = 179.875529437067

STEP 3: Convert Result to Output's Unit

179.875529437067 Volt --> No Conversion Required

FINAL ANSWER

179.875529437067 ≈ 179.8755 Volt <-- Back EMF

(Calculation completed in 00.004 seconds)

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< 6 Voltage & EMF Calculators

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power

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

Load Voltage of Synchronous Motor using 3 Phase Input Power

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

Back EMF of Synchronous Motor using Mechanical Power

Go Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference))

Voltage of Synchronous Motor given Input Power

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

Back EMF of Synchronous Motor given Armature Winding Constant

Go Back EMF = Armature Winding Constant*Magnetic Flux*Synchronous Speed

Voltage Equation of Synchronous Motor

Go Voltage = Back EMF+Armature Current*Synchronous Impedance

< 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

Back EMF of Synchronous Motor using Mechanical Power Formula

Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference))
E_b = P_m/(I_a*cos(α-Φ_s))

How does back EMF affects synchronous motor?

Back EMF (Electromotive Force) is an opposing voltage generated by the rotor of a synchronous motor when it rotates. In synchronous motors, the back EMF plays a crucial role in maintaining the synchronization between the rotor and the stator magnetic fields. If the rotor speed changes, the back EMF also changes, which causes a corresponding change in the current flowing through the DC excitation field.

How to Calculate Back EMF of Synchronous Motor using Mechanical Power?

Back EMF of Synchronous Motor using Mechanical Power calculator uses Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)) to calculate the Back EMF, The Back EMF of Synchronous Motor using Mechanical Power formula is defined as the electromotive force induced by the synchronous motor at the opposite side. Back EMF is denoted by E_b symbol.

How to calculate Back EMF of Synchronous Motor using Mechanical Power using this online calculator? To use this online calculator for Back EMF of Synchronous Motor using Mechanical Power, enter Mechanical Power (P_m), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s) and hit the calculate button. Here is how the Back EMF of Synchronous Motor using Mechanical Power calculation can be explained with given input values -> 179.8755 = 593/(3.7*cos(0.994837673636581-0.5235987755982)).

FAQ

What is Back EMF of Synchronous Motor using Mechanical Power?

The Back EMF of Synchronous Motor using Mechanical Power formula is defined as the electromotive force induced by the synchronous motor at the opposite side and is represented as E_b = P_m/(I_a*cos(α-Φ_s)) or Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)). Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity, Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor, Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage & Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

How to calculate Back EMF of Synchronous Motor using Mechanical Power?

The Back EMF of Synchronous Motor using Mechanical Power formula is defined as the electromotive force induced by the synchronous motor at the opposite side is calculated using Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)). To calculate Back EMF of Synchronous Motor using Mechanical Power, you need Mechanical Power (P_m), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s). With our tool, you need to enter the respective value for Mechanical Power, Armature Current, Load Angle & Phase Difference 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 Back EMF?

In this formula, Back EMF uses Mechanical Power, Armature Current, Load Angle & Phase Difference. We can use 1 other way(s) to calculate the same, which is/are as follows -

Back EMF = Armature Winding Constant*Magnetic Flux*Synchronous Speed

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