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Load Current of Synchronous Motor given 3 Phase Mechanical Power Formula

GoLoad Current of Synchronous Motor using 3 Phase Input Power Formula

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

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

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

Load Current of Synchronous Motor given 3 Phase Mechanical Power Example

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

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

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

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

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

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

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Load Current of Synchronous Motor given 3 Phase Mechanical Power Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

I L = \frac{1056.2505W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 192V \cdot \cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

I L = \frac{1056.2505 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 192 \cdot \cos (0.5236)}

LAST Step Evaluate

∴

I L = 5.5A

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

Variables

Functions

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

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 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

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 Current

Go Load Current of Synchronous Motor using 3 Phase Input Power

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

Other formulas in Current 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 Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power

R a = \frac{P in(3Φ) - P me(3Φ)}{3 \cdot {I a}^{2}}

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

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

How to evaluate Load Current of Synchronous Motor given 3 Phase Mechanical Power using this online evaluator? To use this online evaluator for Load Current 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 Voltage (V_L) & Phase Difference (Φ_s) and hit the calculate button.

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

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

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

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

What are the other ways to Calculate Load Current?

Here are the different ways to Calculate Load Current-

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

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

No, the Load Current of Synchronous Motor given 3 Phase Mechanical Power, measured in Electric Current cannot be negative.

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

Load Current of Synchronous Motor given 3 Phase Mechanical Power is usually measured using the Ampere[A] for Electric Current. Milliampere[A], Microampere[A], Centiampere[A] are the few other units in which Load Current of Synchronous Motor given 3 Phase Mechanical Power can be measured.

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Load Current of Synchronous Motor given 3 Phase Mechanical Power Formula

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

Load Current of Synchronous Motor given 3 Phase Mechanical Power Example

Load Current of Synchronous Motor given 3 Phase Mechanical Power Solution

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

Other Formulas to find Load Current

Other formulas in Current category

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

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

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GoLoad Current of Synchronous Motor using 3 Phase Input Power Formula