Phase Angle between Voltage and Armature Current given Input Power Calculator

✖Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it.ⓘ Input Power [P_in]			+10% -10%
✖Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.ⓘ Voltage [V]			+10% -10%
✖Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.ⓘ Armature Current [I_a]			+10% -10%

✖Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.ⓘ Phase Angle between Voltage and Armature Current given Input Power [Φ_s]

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Phase Angle between Voltage and Armature Current given Input Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos(Input Power/(Voltage*Armature Current))
Φ_s = acos(P_in/(V*I_a))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., acos(Number)

Variables Used

Phase Difference - (Measured in Radian) - Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.
Input Power - (Measured in Watt) - Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it.
Voltage - (Measured in Volt) - Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.
Armature Current - (Measured in Ampere) - Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.

STEP 1: Convert Input(s) to Base Unit

Input Power: 769 Watt --> 769 Watt No Conversion Required
Voltage: 240 Volt --> 240 Volt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_s = acos(P_in/(V*I_a)) --> acos(769/(240*3.7))

Evaluating ... ...

Φ_s = 0.523667597083409

STEP 3: Convert Result to Output's Unit

0.523667597083409 Radian -->30.0039431806423 Degree (Check conversion here)

FINAL ANSWER

30.0039431806423 ≈ 30.00394 Degree <-- Phase Difference

(Calculation completed in 00.020 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Power Factor and Phase Angle Calculators

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

LaTeX Go Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))

Power Factor of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)

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

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

Phase Angle between Voltage and Armature Current given Input Power

LaTeX Go Phase Difference = acos(Input Power/(Voltage*Armature Current))

< Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))

Armature Current of Synchronous Motor given Mechanical Power

LaTeX Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)

Armature Current of Synchronous Motor given Input Power

LaTeX Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)

Phase Angle between Voltage and Armature Current given Input Power Formula

LaTeX Go

Phase Difference = acos(Input Power/(Voltage*Armature Current))
Φ_s = acos(P_in/(V*I_a))

Is synchronous motor a fixed speed motor?

This is where the term synchronous motor comes from, as the speed of the rotor of the motor is the same as the rotating magnetic field. It is a fixed speed motor because it has only one speed, which is synchronous speed.

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

Phase Angle between Voltage and Armature Current given Input Power calculator uses Phase Difference = acos(Input Power/(Voltage*Armature Current)) to calculate 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 calculate Phase Angle between Voltage and Armature Current given Input Power using this online calculator? To use this online calculator 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. Here is how the Phase Angle between Voltage and Armature Current given Input Power calculation can be explained with given input values -> 1719.099 = acos(769/(240*3.7)).

FAQ

What is Phase Angle between Voltage and Armature Current given Input Power?

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 and is represented as Φ_s = acos(P_in/(V*I_a)) or Phase Difference = acos(Input Power/(Voltage*Armature Current)). Input Power is defined as the total power supplied to the electrical motor from the source which is connected to it, Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines & Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.

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

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 is calculated using Phase Difference = acos(Input Power/(Voltage*Armature Current)). To calculate Phase Angle between Voltage and Armature Current given Input Power, you need Input Power (P_in), Voltage (V) & Armature Current (I_a). With our tool, you need to enter the respective value for Input Power, Voltage & Armature Current and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Phase Difference?

In this formula, Phase Difference uses Input Power, Voltage & Armature Current. We can use 2 other way(s) to calculate the same, which is/are as follows -

Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current))
Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))

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