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Back EMF of Synchronous Motor using Mechanical Power Formula

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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. Check FAQs

E b = \frac{P m}{I a \cdot \cos (α - Φ s)}

E_b - Back EMF?P_m - Mechanical Power?I_a - Armature Current?α - Load Angle?Φ_s - Phase Difference?

Back EMF of Synchronous Motor using Mechanical Power Example

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Here is how the Back EMF of Synchronous Motor using Mechanical Power equation looks like with Values.

Here is how the Back EMF of Synchronous Motor using Mechanical Power equation looks like with Units.

Here is how the Back EMF of Synchronous Motor using Mechanical Power equation looks like.

179.8755 = \frac{593}{3.7 \cdot \cos (57 - 30)}

179.8755V = \frac{593W}{3.7A \cdot \cos (57° - 30°)}

179.8755 = \frac{593}{3.7 \cdot \cos (57 - 30)}

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Back EMF of Synchronous Motor using Mechanical Power Solution

Follow our step by step solution on how to calculate Back EMF of Synchronous Motor using Mechanical Power?

FIRST Step Consider the formula

E b = \frac{P m}{I a \cdot \cos (α - Φ s)}

Next Step Substitute values of Variables

∴

E b = \frac{593W}{3.7A \cdot \cos (57° - 30°)}

Next Step Convert Units

∴

E b = \frac{593W}{3.7A \cdot \cos (0.9948rad - 0.5236rad)}

Next Step Prepare to Evaluate

∴

E b = \frac{593}{3.7 \cdot \cos (0.9948 - 0.5236)}

Next Step Evaluate

∴

E b = 179.875529437067V

LAST Step Rounding Answer

∴

E b = 179.8755V

Back EMF of Synchronous Motor using Mechanical Power Formula Elements

Variables

Functions

Back EMF

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.

Symbol: E_b

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Back EMF

Mechanical Power

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.

Symbol: P_m

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find 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

Load Angle

Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Load Angle

Phase Difference

Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

Symbol: Φ_s

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Difference

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Voltage and EMF 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 Back EMF of Synchronous Motor using Mechanical Power?

Back EMF of Synchronous Motor using Mechanical Power evaluator uses Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)) to evaluate 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 evaluate Back EMF of Synchronous Motor using Mechanical Power using this online evaluator? To use this online evaluator 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.

FAQs on Back EMF of Synchronous Motor using Mechanical Power

What is the formula to find Back EMF of Synchronous Motor using Mechanical Power?

The formula of Back EMF of Synchronous Motor using Mechanical Power is expressed as Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)). Here is an example- 179.8755 = 593/(3.7*cos(0.994837673636581-0.5235987755982)).

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

With Mechanical Power (P_m), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s) we can find Back EMF of Synchronous Motor using Mechanical Power using the formula - Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference)). This formula also uses Cosine (cos) function(s).

Can the Back EMF of Synchronous Motor using Mechanical Power be negative?

Yes, the Back EMF of Synchronous Motor using Mechanical Power, measured in Electric Potential can be negative.

Which unit is used to measure Back EMF of Synchronous Motor using Mechanical Power?

Back EMF of Synchronous Motor using Mechanical Power is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Back EMF of Synchronous Motor using Mechanical Power can be measured.

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Back EMF of Synchronous Motor using Mechanical Power Formula

Back EMF of Synchronous Motor using Mechanical Power Example

Back EMF of Synchronous Motor using Mechanical Power Solution

Back EMF of Synchronous Motor using Mechanical Power Formula Elements

Other formulas in Voltage and EMF category

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

FAQs on Back EMF of Synchronous Motor using Mechanical Power

Variable Name