Power Factor using Area of X-Section (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%
✖Resistivity is the measure of how strongly a material opposes the flow of current through them.ⓘ Resistivity [ρ]			+10% -10%
✖Length of Underground AC Wire is the total length of the wire from one end to other end.ⓘ Length of Underground AC Wire [L]			+10% -10%
✖Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system.ⓘ Area of Underground AC Wire [A]			+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%

✖Phase Difference is defined as the difference between the phasor of apparent and real power (in degrees) or between voltage and current in an ac circuit.ⓘ Power Factor using Area of X-Section (3 Phase 4 Wire US) [Φ]

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

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses)))
Φ = acos((P/V_m)*sqrt(2*ρ*L/(A*P_loss)))
This formula uses 3 Functions, 7 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 is defined as the difference between the phasor of apparent and real power (in degrees) or between voltage and current in an ac 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.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
Length of Underground AC Wire - (Measured in Meter) - Length of Underground AC Wire is the total length of the wire from one end to other end.
Area of Underground AC Wire - (Measured in Square Meter) - Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system.
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
Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Length of Underground AC Wire: 24 Meter --> 24 Meter No Conversion Required
Area of Underground AC Wire: 1.28 Square Meter --> 1.28 Square Meter No Conversion Required
Line Losses: 2.67 Watt --> 2.67 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = acos((P/V_m)*sqrt(2*ρ*L/(A*P_loss))) --> acos((300/230)*sqrt(2*1.7E-05*24/(1.28*2.67)))

Evaluating ... ...

Φ = 1.55064019034272

STEP 3: Convert Result to Output's Unit

1.55064019034272 Radian -->88.8451384500174 Degree (Check conversion here)

FINAL ANSWER

88.8451384500174 ≈ 88.84514 Degree <-- Phase Difference

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Underground AC Supply » 3 Φ 4 Wire System » Power and Power Factor » Power Factor using Area of X-Section (3 Phase 4 Wire US)

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< Power and Power Factor Calculators

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

LaTeX 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 Load Current (3 Phase 4 Wire US)

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

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

LaTeX 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)

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

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

LaTeX Go

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 Area of X-Section (3 Phase 4 Wire US)?

Power Factor using Area of X-Section (3 Phase 4 Wire US) calculator uses Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))) to calculate the Phase Difference, The Power Factor using Area of X-Section (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. Phase Difference is denoted by Φ symbol.

How to calculate Power Factor using Area of X-Section (3 Phase 4 Wire US) using this online calculator? To use this online calculator for Power Factor using Area of X-Section (3 Phase 4 Wire US), enter Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A) & Line Losses (P_loss) and hit the calculate button. Here is how the Power Factor using Area of X-Section (3 Phase 4 Wire US) calculation can be explained with given input values -> 5090.451 = acos((300/230)*sqrt(2*1.7E-05*24/(1.28*2.67))).

FAQ

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

The Power Factor using Area of X-Section (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 Φ = acos((P/V_m)*sqrt(2*ρ*L/(A*P_loss))) or 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 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, Resistivity is the measure of how strongly a material opposes the flow of current through them, Length of Underground AC Wire is the total length of the wire from one end to other end, Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system & Line Losses is defined as the total losses occurring in an Underground AC line when in use.

How to calculate Power Factor using Area of X-Section (3 Phase 4 Wire US)?

The Power Factor using Area of X-Section (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 Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))). To calculate Power Factor using Area of X-Section (3 Phase 4 Wire US), you need Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A) & Line Losses (P_loss). With our tool, you need to enter the respective value for Power Transmitted, Maximum Voltage Underground AC, Resistivity, Length of Underground AC Wire, Area of Underground AC Wire & 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 Phase Difference?

In this formula, Phase Difference uses Power Transmitted, Maximum Voltage Underground AC, Resistivity, Length of Underground AC Wire, Area of Underground AC Wire & Line Losses. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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