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

✖Three Phase Input Power is defined as the three phase power supplied an synchronous motor.ⓘ Three Phase Input Power [P_in(3Φ)]			+10% -10%
✖Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.ⓘ Voltage [V]			+10% -10%
✖Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.ⓘ Load Current [I_L]			+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 Load Voltage and Current given 3 Phase Input Power [Φ_s]

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

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current))
Φ_s = acos(P_in(3Φ)/(sqrt(3)*V*I_L))
This formula uses 3 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)
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., sqrt(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.
Three Phase Input Power - (Measured in Watt) - Three Phase Input Power is defined as the three phase power supplied an synchronous motor.
Voltage - (Measured in Volt) - Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.
Load Current - (Measured in Ampere) - Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

STEP 1: Convert Input(s) to Base Unit

Three Phase Input Power: 1584 Watt --> 1584 Watt No Conversion Required
Voltage: 240 Volt --> 240 Volt No Conversion Required
Load Current: 5.5 Ampere --> 5.5 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_s = acos(P_in(3Φ)/(sqrt(3)*V*I_L)) --> acos(1584/(sqrt(3)*240*5.5))

Evaluating ... ...

Φ_s = 0.805403500574443

STEP 3: Convert Result to Output's Unit

0.805403500574443 Radian -->46.1462213879866 Degree (Check conversion here)

FINAL ANSWER

46.1462213879866 ≈ 46.14622 Degree <-- Phase Difference

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Power Factor and Phase Angle » Phase Angle between Load Voltage and Current given 3 Phase Input Power

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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))

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

LaTeX Go

Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current))
Φ_s = acos(P_in(3Φ)/(sqrt(3)*V*I_L))

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 Load Voltage and Current given 3 Phase Input Power?

Phase Angle between Load Voltage and Current given 3 Phase Input Power calculator uses Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)) to calculate 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 calculate Phase Angle between Load Voltage and Current given 3 Phase Input Power using this online calculator? To use this online calculator 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. Here is how the Phase Angle between Load Voltage and Current given 3 Phase Input Power calculation can be explained with given input values -> 2643.984 = acos(1584/(sqrt(3)*240*5.5)).

FAQ

What is Phase Angle between Load Voltage and Current given 3 Phase Input Power?

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 and is represented as Φ_s = acos(P_in(3Φ)/(sqrt(3)*V*I_L)) or Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)). Three Phase Input Power is defined as the three phase power supplied an synchronous motor, Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines & Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

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

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 is calculated using Phase Difference = acos(Three Phase Input Power/(sqrt(3)*Voltage*Load Current)). To calculate Phase Angle between Load Voltage and Current given 3 Phase Input Power, you need Three Phase Input Power (P_in(3Φ)), Voltage (V) & Load Current (I_L). With our tool, you need to enter the respective value for Three Phase Input Power, Voltage & Load 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 Three Phase Input Power, Voltage & Load Current. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))

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