Power Factor using Line Losses (3 Phase 4 Wire US) Calculator

✖Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.ⓘ Power Transmitted [P]			+10% -10%
✖Maximum Voltage Underground AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.ⓘ Maximum Voltage Underground AC [V_m]			+10% -10%
✖Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it.ⓘ Resistance Underground AC [R]			+10% -10%
✖Line Losses is defined as the total losses occurring in an Underground AC line when in use.ⓘ Line Losses [P_loss]			+10% -10%

✖The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.ⓘ Power Factor using Line Losses (3 Phase 4 Wire US) [PF]

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Formula

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Power Factor using Line Losses (3 Phase 4 Wire US)

Formula

`"PF" = (("P"/"V"_{"m"})*sqrt(2*"R"/("P"_{"loss"})))`

Example

`"2.524282"=(("300W"/"230V")*sqrt(2*"5Ω"/("2.67W")))`

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Power Factor using Line Losses (3 Phase 4 Wire US) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses)))
PF = ((P/V_m)*sqrt(2*R/(P_loss)))
This formula uses 1 Functions, 5 Variables

Functions Used

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

Power Factor - The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.
Power Transmitted - (Measured in Watt) - Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.
Maximum Voltage Underground AC - (Measured in Volt) - Maximum Voltage Underground AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.
Resistance Underground AC - (Measured in Ohm) - Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Underground AC line when in use.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Maximum Voltage Underground AC: 230 Volt --> 230 Volt No Conversion Required
Resistance Underground AC: 5 Ohm --> 5 Ohm No Conversion Required
Line Losses: 2.67 Watt --> 2.67 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

PF = ((P/V_m)*sqrt(2*R/(P_loss))) --> ((300/230)*sqrt(2*5/(2.67)))

Evaluating ... ...

PF = 2.52428152081364

STEP 3: Convert Result to Output's Unit

2.52428152081364 --> No Conversion Required

FINAL ANSWER

2.52428152081364 ≈ 2.524282 <-- Power Factor

(Calculation completed in 00.004 seconds)

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< 13 Power & Power Factor Calculators

Power Factor using Area of X-Section (3 Phase 4 Wire US)

Go Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses)))

Power Transmitted using Volume of Conductor Material (3 Phase 4 Wire US)

Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(7*Resistivity*(Length of Underground AC Wire)^2))

Power Transmitted using Area of X-Section (3 Phase 4 Wire US)

Go Power Transmitted = Maximum Voltage Underground AC*cos(Phase Difference)*sqrt(Area of Underground AC Wire*Line Losses/(2*Resistivity*Length of Underground AC Wire))

RMS Voltage using Area of X-Section (3 Phase 4 Wire US)

Go Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire))

RMS Voltage using Volume of Conductor Material (3 Phase 4 Wire US)

Go Root Mean Square Voltage = (Power Transmitted*Length of Underground AC Wire/cos(Phase Difference))*sqrt(Resistivity/(Line Losses*Volume Of Conductor))

Power Transmitted using Line Losses (3 Phase 4 Wire US)

Go Power Transmitted = Maximum Voltage Underground AC*cos(Phase Difference)*sqrt(Line Losses/(2*Resistance Underground AC))

RMS Voltage using Line Losses (3 Phase 4 Wire US)

Go Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses))

Power Factor using Line Losses (3 Phase 4 Wire US)

Go Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses)))

Power Transmitted using Load Current (3 Phase 4 Wire US)

Go Power Transmitted = (3*Maximum Voltage Underground AC*cos(Phase Difference)*Current Underground AC)/sqrt(6)

Power Factor using Load Current (3 Phase 4 Wire US)

Go Power Factor = (sqrt(6)*Power Transmitted)/(3*Maximum Voltage Underground AC*Current Underground AC)

RMS Voltage using Load Current (3 Phase 4 Wire US)

Go Root Mean Square Voltage = (2*Power Transmitted/3*Current Underground AC*cos(Phase Difference))

Angle of PF using Volume of Conductor Material (3 Phase 4 Wire US)

Go Phase Difference = acos(sqrt((1.75)*Constant Underground AC/Volume Of Conductor))

Power Factor using Volume of Conductor Material (3 Phase 4 Wire US)

Go Power Factor = sqrt((1.75)*Constant Underground AC/Volume Of Conductor)

Power Factor using Line Losses (3 Phase 4 Wire US) Formula

Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses)))
PF = ((P/V_m)*sqrt(2*R/(P_loss)))

What is the correct power factor?

The ideal power factor is unity, or one. Anything less than one means that extra power is required to achieve the actual task at hand. All current flow causes losses both in the supply and distribution system. A load with a power factor of 1.0 results in the most efficient loading of the supply.

How to Calculate Power Factor using Line Losses (3 Phase 4 Wire US)?

Power Factor using Line Losses (3 Phase 4 Wire US) calculator uses Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses))) to calculate the Power Factor, The Power Factor using Line Losses (3 phase 4 wire US) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit. Power Factor is denoted by PF symbol.

How to calculate Power Factor using Line Losses (3 Phase 4 Wire US) using this online calculator? To use this online calculator for Power Factor using Line Losses (3 Phase 4 Wire US), enter Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistance Underground AC (R) & Line Losses (P_loss) and hit the calculate button. Here is how the Power Factor using Line Losses (3 Phase 4 Wire US) calculation can be explained with given input values -> 2.524282 = ((300/230)*sqrt(2*5/(2.67))).

FAQ

What is Power Factor using Line Losses (3 Phase 4 Wire US)?

The Power Factor using Line Losses (3 phase 4 wire US) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit and is represented as PF = ((P/V_m)*sqrt(2*R/(P_loss))) or Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses))). Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work, Maximum Voltage Underground AC is defined as the peak amplitude of the AC voltage supplied to the line or wire, Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it & Line Losses is defined as the total losses occurring in an Underground AC line when in use.

How to calculate Power Factor using Line Losses (3 Phase 4 Wire US)?

The Power Factor using Line Losses (3 phase 4 wire US) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit is calculated using Power Factor = ((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistance Underground AC/(Line Losses))). To calculate Power Factor using Line Losses (3 Phase 4 Wire US), you need Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistance Underground AC (R) & Line Losses (P_loss). With our tool, you need to enter the respective value for Power Transmitted, Maximum Voltage Underground AC, Resistance Underground AC & Line Losses 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 Power Factor?

In this formula, Power Factor uses Power Transmitted, Maximum Voltage Underground AC, Resistance Underground AC & Line Losses. We can use 2 other way(s) to calculate the same, which is/are as follows -

Power Factor = sqrt((1.75)*Constant Underground AC/Volume Of Conductor)
Power Factor = (sqrt(6)*Power Transmitted)/(3*Maximum Voltage Underground AC*Current Underground AC)

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