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Armature Winding Constant of Synchronous Motor Formula

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Armature Winding Constant is defined as the ratio of the voltage applied to the motor terminals to the speed of the motor under no-load conditions. Check FAQs

K a = \frac{E b}{Φ \cdot N s}

K_a - Armature Winding Constant?E_b - Back EMF?Φ - Magnetic Flux?N_s - Synchronous Speed?

Armature Winding Constant of Synchronous Motor Example

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Here is how the Armature Winding Constant of Synchronous Motor equation looks like with Values.

Here is how the Armature Winding Constant of Synchronous Motor equation looks like with Units.

Here is how the Armature Winding Constant of Synchronous Motor equation looks like.

0.6148 = \frac{180}{0.12 \cdot 23300}

0.6148 = \frac{180V}{0.12Wb \cdot 23300rev/min}

0.6148 = \frac{180}{0.12 \cdot 23300}

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Armature Winding Constant of Synchronous Motor Solution

Follow our step by step solution on how to calculate Armature Winding Constant of Synchronous Motor?

FIRST Step Consider the formula

K a = \frac{E b}{Φ \cdot N s}

Next Step Substitute values of Variables

∴

K a = \frac{180V}{0.12Wb \cdot 23300rev/min}

Next Step Convert Units

∴

K a = \frac{180V}{0.12Wb \cdot 2439.9703rad/s}

Next Step Prepare to Evaluate

∴

K a = \frac{180}{0.12 \cdot 2439.9703}

Next Step Evaluate

∴

K a = 0.6147615827897

LAST Step Rounding Answer

∴

K a = 0.6148

Armature Winding Constant of Synchronous Motor Formula Elements

Variables

Armature Winding Constant

Armature Winding Constant is defined as the ratio of the voltage applied to the motor terminals to the speed of the motor under no-load conditions.

Symbol: K_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Armature Winding Constant

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

Magnetic Flux

Magnetic flux (Φ) is the number of magnetic field lines passing through the magnetic core of an electrical dc motor.

Symbol: Φ

Measurement: Magnetic FluxUnit: Wb

Note: Value should be greater than 0.

Formulas to find Magnetic Flux

Synchronous Speed

Synchronous speed is a definite speed for an alternating-current machine that is dependent on the frequency of the supply circuit.

Symbol: N_s

Measurement: Angular VelocityUnit: rev/min

Note: Value can be positive or negative.

Formulas to find Synchronous Speed

Other formulas in Mechanical Specification 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 Armature Winding Constant of Synchronous Motor?

Armature Winding Constant of Synchronous Motor evaluator uses Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed) to evaluate the Armature Winding Constant, The Armature Winding Constant of Synchronous Motor given Back Emf formula is defined as the constant of the armature winding that is used for finding many quantities of synchronous motor. Armature Winding Constant is denoted by K_a symbol.

How to evaluate Armature Winding Constant of Synchronous Motor using this online evaluator? To use this online evaluator for Armature Winding Constant of Synchronous Motor, enter Back EMF (E_b), Magnetic Flux (Φ) & Synchronous Speed (N_s) and hit the calculate button.

FAQs on Armature Winding Constant of Synchronous Motor

What is the formula to find Armature Winding Constant of Synchronous Motor?

The formula of Armature Winding Constant of Synchronous Motor is expressed as Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed). Here is an example- 0.614762 = 180/(0.12*2439.97029416382).

How to calculate Armature Winding Constant of Synchronous Motor?

With Back EMF (E_b), Magnetic Flux (Φ) & Synchronous Speed (N_s) we can find Armature Winding Constant of Synchronous Motor using the formula - Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed).

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