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Phase 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}{V \cdot I a})

Φ_s - Phase Difference?P_in - Input Power?V - Voltage?I_a - Armature Current?

Phase Angle between Voltage and Armature Current given Input Power Example

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

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

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

30.0039 = a \cos (\frac{769}{240 \cdot 3.7})

30.0039° = a \cos (\frac{769W}{240V \cdot 3.7A})

30.0039 = a \cos (\frac{769}{240 \cdot 3.7})

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Phase Angle between Voltage and Armature Current given Input Power Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Φ s = a \cos (\frac{769W}{240V \cdot 3.7A})

Next Step Prepare to Evaluate

∴

Φ s = a \cos (\frac{769}{240 \cdot 3.7})

Next Step Evaluate

∴

Φ s = 0.523667597083409rad

Next Step Convert to Output's Unit

∴

Φ s = 30.0039431806423°

LAST Step Rounding Answer

∴

Φ s = 30.0039°

Phase Angle between Voltage and Armature Current given 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

Input Power

Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it.

Symbol: P_in

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find 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

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

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)

Other formulas in Power Factor and Phase Angle 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 Phase Angle between Voltage and Armature Current given Input Power?

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

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

FAQs on Phase Angle between Voltage and Armature Current given Input Power

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

The formula of Phase Angle between Voltage and Armature Current given Input Power is expressed as Phase Difference = acos(Input Power/(Voltage*Armature Current)). Here is an example- 1719.099 = acos(769/(240*3.7)).

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

With Input Power (P_in), Voltage (V) & Armature Current (I_a) we can find Phase Angle between Voltage and Armature Current given Input Power using the formula - Phase Difference = acos(Input Power/(Voltage*Armature Current)). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

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

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

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

Phase Angle between Voltage and Armature Current given Input 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 Input Power can be measured.

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