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Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula

GoLoad Voltage of Synchronous Motor using 3 Phase Input Power Formula

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The Load Voltage is defined as the voltage between two terminals of load. Check FAQs

V L = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot I L \cdot \cos (Φ s)}

V_L - Load Voltage?P_me(3Φ) - Three Phase Mechanical Power?I_a - Armature Current?R_a - Armature Resistance?I_L - Load Current?Φ_s - Phase Difference?

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Example

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Here is how the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power equation looks like with Values.

Here is how the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power equation looks like with Units.

Here is how the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power equation looks like.

192 = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot \cos (30)}

192V = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 5.5A \cdot \cos (30°)}

192 = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot \cos (30)}

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Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Solution

Follow our step by step solution on how to calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

FIRST Step Consider the formula

V L = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot I L \cdot \cos (Φ s)}

Next Step Substitute values of Variables

∴

V L = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 5.5A \cdot \cos (30°)}

Next Step Convert Units

∴

V L = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 5.5A \cdot \cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

V L = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot \cos (0.5236)}

LAST Step Evaluate

∴

V L = 192V

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula Elements

Variables

Functions

Load Voltage

The Load Voltage is defined as the voltage between two terminals of load.

Symbol: V_L

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Load Voltage

Three Phase Mechanical Power

Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.

Symbol: P_me(3Φ)

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Three Phase 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

Armature Resistance

The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.

Symbol: R_a

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Armature Resistance

Load Current

Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

Symbol: I_L

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Load Current

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)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Load Voltage

Go Load Voltage of Synchronous Motor using 3 Phase Input Power

V L = \frac{P in(3Φ)}{\sqrt{3} \cdot I L \cdot \cos (Φ s)}

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 Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power evaluator uses Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)) to evaluate the Load Voltage, The Load Voltage of Synchronous Motor given 3 phase Mechanical Power formula is defined as the voltage generated at the load of the synchronous motor. Load Voltage is denoted by V_L symbol.

How to evaluate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power using this online evaluator? To use this online evaluator for Load Voltage of Synchronous Motor given 3 Phase Mechanical Power, enter Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Phase Difference (Φ_s) and hit the calculate button.

FAQs on Load Voltage of Synchronous Motor given 3 Phase Mechanical Power

What is the formula to find Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

The formula of Load Voltage of Synchronous Motor given 3 Phase Mechanical Power is expressed as Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)). Here is an example- 192 = (1056.2505+3*3.7^2*12.85)/(sqrt(3)*5.5*cos(0.5235987755982)).

How to calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

With Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Phase Difference (Φ_s) we can find Load Voltage of Synchronous Motor given 3 Phase Mechanical Power using the formula - Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Load Voltage?

Here are the different ways to Calculate Load Voltage-

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

Can the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power be negative?

Yes, the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power, measured in Electric Potential can be negative.

Which unit is used to measure Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

Load Voltage of Synchronous Motor given 3 Phase 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 Load Voltage of Synchronous Motor given 3 Phase Mechanical Power can be measured.

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Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula

​GoLoad Voltage of Synchronous Motor using 3 Phase Input Power Formula

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Example

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Solution

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula Elements

Other Formulas to find Load Voltage

Other formulas in Voltage and EMF category

How to Evaluate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

FAQs on Load Voltage of Synchronous Motor given 3 Phase Mechanical Power

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GoLoad Voltage of Synchronous Motor using 3 Phase Input Power Formula