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

✖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.ⓘ Mechanical Power [P_m]			+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%
✖The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.ⓘ Armature Resistance [R_a]			+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%
✖The Load Voltage is defined as the voltage between two terminals of load.ⓘ Load Voltage [V_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 Voltage and Armature Current given 3 Phase Mechanical Power [Φ_s]

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

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))
Φ_s = acos((P_m+3*I_a^2*R_a)/(sqrt(3)*I_L*V_L))
This formula uses 3 Functions, 6 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.
Mechanical Power - (Measured in Watt) - 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.
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.
Armature Resistance - (Measured in Ohm) - The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.
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.
Load Voltage - (Measured in Volt) - The Load Voltage is defined as the voltage between two terminals of load.

STEP 1: Convert Input(s) to Base Unit

Mechanical Power: 593 Watt --> 593 Watt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
Armature Resistance: 12.85 Ohm --> 12.85 Ohm No Conversion Required
Load Current: 5.5 Ampere --> 5.5 Ampere No Conversion Required
Load Voltage: 192 Volt --> 192 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_s = acos((P_m+3*I_a^2*R_a)/(sqrt(3)*I_L*V_L)) --> acos((593+3*3.7^2*12.85)/(sqrt(3)*5.5*192))

Evaluating ... ...

Φ_s = 0.911259388458349

STEP 3: Convert Result to Output's Unit

0.911259388458349 Radian -->52.2113170003456 Degree (Check conversion here)

FINAL ANSWER

52.2113170003456 ≈ 52.21132 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 Voltage and Armature Current given 3 Phase Mechanical 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 Voltage and Armature Current given 3 Phase Mechanical Power Formula

LaTeX Go

Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage))
Φ_s = acos((P_m+3*I_a^2*R_a)/(sqrt(3)*I_L*V_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 Voltage and Armature Current given 3 Phase Mechanical Power?

Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power calculator uses Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)) to calculate 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 calculate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power using this online calculator? To use this online calculator 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. Here is how the Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power calculation can be explained with given input values -> 2991.488 = acos((593+3*3.7^2*12.85)/(sqrt(3)*5.5*192)).

FAQ

What is Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power?

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 and is represented as Φ_s = acos((P_m+3*I_a^2*R_a)/(sqrt(3)*I_L*V_L)) or Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)). 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, Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor, The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor, Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it & The Load Voltage is defined as the voltage between two terminals of load.

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

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 is calculated using Phase Difference = acos((Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*Load Voltage)). To calculate Phase Angle between Voltage and Armature Current given 3 Phase Mechanical Power, you need Mechanical Power (P_m), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Load Voltage (V_L). With our tool, you need to enter the respective value for Mechanical Power, Armature Current, Armature Resistance, Load Current & Load Voltage 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 Mechanical Power, Armature Current, Armature Resistance, Load Current & Load Voltage. 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(Input Power/(Voltage*Armature Current))

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