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

GoPhase Angle between Voltage and Armature Current given 3 Phase Mechanical 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 in(3Φ)}{\sqrt{3} \cdot V \cdot I L})

Φ_s - Phase Difference?P_in(3Φ) - Three Phase Input Power?V - Voltage?I_L - Load Current?

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

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

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

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

46.1462 = a \cos (\frac{1584}{\sqrt{3} \cdot 240 \cdot 5.5})

46.1462° = a \cos (\frac{1584W}{\sqrt{3} \cdot 240V \cdot 5.5A})

46.1462 = a \cos (\frac{1584}{\sqrt{3} \cdot 240 \cdot 5.5})

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Φ s = a \cos (\frac{1584W}{\sqrt{3} \cdot 240V \cdot 5.5A})

Next Step Prepare to Evaluate

∴

Φ s = a \cos (\frac{1584}{\sqrt{3} \cdot 240 \cdot 5.5})

Next Step Evaluate

∴

Φ s = 0.805403500574443rad

Next Step Convert to Output's Unit

∴

Φ s = 46.1462213879866°

LAST Step Rounding Answer

∴

Φ s = 46.1462°

Phase Angle between Load Voltage and Current given 3 Phase Input 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

Three Phase Input Power

Three Phase Input Power is defined as the three phase power supplied an synchronous motor.

Symbol: P_in(3Φ)

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Three Phase Input Power

Voltage

Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.

Symbol: V

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Voltage

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

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 Voltage and Armature Current given 3 Phase Mechanical Power

Φ s = a \cos (\frac{P m + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot I L \cdot V 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 Load Voltage and Current given 3 Phase Input Power?

Phase Angle between Load Voltage and Current given 3 Phase Input Power evaluator uses Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)) to evaluate the Phase Difference, The Phase Angle between Load Voltage and Current given 3 phase Input Power formula is defined as the angle created between voltage and Load current due to 3-phase input power. Phase Difference is denoted by Φ_s symbol.

How to evaluate Phase Angle between Load Voltage and Current given 3 Phase Input Power using this online evaluator? To use this online evaluator for Phase Angle between Load Voltage and Current given 3 Phase Input Power, enter Three Phase Input Power (P_in(3Φ)), Voltage (V) & Load Current (I_L) and hit the calculate button.

FAQs on Phase Angle between Load Voltage and Current given 3 Phase Input Power

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

The formula of Phase Angle between Load Voltage and Current given 3 Phase Input Power is expressed as Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)). Here is an example- 2643.984 = acos(1584/(sqrt(3)*240*5.5)).

How to calculate Phase Angle between Load Voltage and Current given 3 Phase Input Power?

With Three Phase Input Power (P_in(3Φ)), Voltage (V) & Load Current (I_L) we can find Phase Angle between Load Voltage and Current given 3 Phase Input Power using the formula - Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)). 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((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))
Phase Difference=acos(Input Power/(Voltage*Armature Current))

Can the Phase Angle between Load Voltage and Current given 3 Phase Input Power be negative?

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

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

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

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

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

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

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

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

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

Other Formulas to find Phase Difference

Other formulas in Power Factor and Phase Angle category

How to Evaluate Phase Angle between Load Voltage and Current given 3 Phase Input Power?

FAQs on Phase Angle between Load Voltage and Current given 3 Phase Input Power

Variable Name

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

GoPhase Angle between Voltage and Armature Current given Input Power Formula