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Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Formula

GoPhase Angle between Load Voltage and Current given 3 Phase Input Power Formula

GoPhase Angle between Voltage and Armature Current given Input Power Formula

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

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

Φ_s - Phase Difference?P_m - Mechanical Power?I_a - Armature Current?R_a - Armature Resistance?I_L - Load Current?V_L - Load Voltage?

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Example

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Here is how the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power equation looks like with Values.

Here is how the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power equation looks like with Units.

Here is how the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power equation looks like.

52.2113 = a \cos (\frac{593 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot 192})

52.2113° = a \cos (\frac{593W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 5.5A \cdot 192V})

52.2113 = a \cos (\frac{593 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot 192})

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Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Solution

Follow our step by step solution on how to calculate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Φ s = a \cos (\frac{593W + 3 \cdot {3.7A}^{2} \cdot 12.85Ω}{\sqrt{3} \cdot 5.5A \cdot 192V})

Next Step Prepare to Evaluate

∴

Φ s = a \cos (\frac{593 + 3 \cdot {3.7}^{2} \cdot 12.85}{\sqrt{3} \cdot 5.5 \cdot 192})

Next Step Evaluate

∴

Φ s = 0.911259388458349rad

Next Step Convert to Output's Unit

∴

Φ s = 52.2113170003456°

LAST Step Rounding Answer

∴

Φ s = 52.2113°

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Formula Elements

Variables

Functions

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

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

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

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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

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 Phase Difference

Go Phase Angle between Load Voltage and Current given 3 Phase Input Power

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

Go Phase Angle between Voltage and Armature Current given Input Power

Φ s = a \cos (\frac{P in}{V \cdot I a})

Other formulas in Power Factor and Phase Angle category

Go Power Factor of Synchronous Motor given 3 Phase Mechanical Power

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

Go Power Factor of Synchronous Motor given Input Power

CosΦ = \frac{P in}{V \cdot I a}

Go Power Factor of Synchronous Motor using 3 Phase Input Power

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

How to Evaluate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power evaluator uses Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)) to evaluate the Phase Difference, The Phase Angle between Voltage and Armature Current given 3 phase Mechanical Power formula is defined as the angle created between voltage and armature current due to mechanical power. Phase Difference is denoted by Φ_s symbol.

How to evaluate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power using this online evaluator? To use this online evaluator for Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power, enter Mechanical Power (P_m), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Load Voltage (V_L) and hit the calculate button.

FAQs on Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power

What is the formula to find Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

The formula of Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power is expressed as Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)). Here is an example- 2991.488 = acos((593+3*3.7^2*12.85)/(sqrt(3)*5.5*192)).

How to calculate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

With Mechanical Power (P_m), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Load Voltage (V_L) we can find Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power using the formula - Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)). This formula also uses Cosine (cos)Inverse Cosine (acos), Square Root (sqrt) function(s).

What are the other ways to Calculate Phase Difference?

Here are the different ways to Calculate Phase Difference-

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

Can the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power be negative?

No, the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power, measured in Angle cannot be negative.

Which unit is used to measure Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power can be measured.

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Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Formula

​GoPhase Angle between Load Voltage and Current given 3 Phase Input Power Formula

​GoPhase Angle between Voltage and Armature Current given Input Power Formula

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Example

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Solution

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power Formula Elements

Other Formulas to find Phase Difference

Other formulas in Power Factor and Phase Angle category

How to Evaluate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

FAQs on Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power

Variable Name

GoPhase Angle between Load Voltage and Current given 3 Phase Input Power Formula

GoPhase Angle between Voltage and Armature Current given Input Power Formula