Angle 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.ⓘ Angle using Area of X-Section (3 Phase 4 Wire US) [Φ]

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Formula

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

Formula

`"Φ" = acos(("P"/"V"_{"m"})*sqrt(2*"ρ"*"L"/("A"*"P"_{"loss"})))`

Example

`"88.84514°"=acos(("300W"/"230V")*sqrt(2*"0.000017Ω*m"*"24m"/("1.28m²"*"2.67W")))`

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Angle 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 00.020 seconds)

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

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< 18 Wire Parameters Calculators

Volume of Conductor Material when Resistance is Given(3 Phase 4 Wire US)

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

Angle 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)))

Angle using Line Losses (3 Phase 4 Wire US)

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

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

Go Length of Underground AC Wire = (Area of Underground AC Wire*Line Losses*(Maximum Voltage Underground AC^2)*(cos(Phase Difference))^2)/(4*Resistivity*(Power Transmitted^2))

Line Losses using Area of X-Section (3 Phase 4 Wire US)

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

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

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

Line Losses (3 Phase 4 Wire US)

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

Volume of Conductor Material (3 Phase 4 Wire US)

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

Line Losses using Volume of Conductor Material (3 Phase 4 Wire US)

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

Angle using Load Current (3 Phase 4 Wire US)

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

Length using Line Losses (3 Phase 4 Wire US)

Go Length of Underground AC Wire = Line Losses*Area of Underground AC Wire/(2*(Current Underground AC^2)*Resistivity)

Volume of Conductor Material using Load Current (3 Phase 4 Wire US)

Go Volume Of Conductor = 18*Resistivity*(Current Underground AC^2)*(Length of Underground AC Wire^2)/(2*Line Losses)

Line Losses using Load Current (3 Phase 4 Wire US)

Go Line Losses = 3*(Current Underground AC^2)*Resistivity*Length of Underground AC Wire/Area of Underground AC Wire

Area using Line Losses (3 Phase 4 Wire US)

Go Area of Underground AC Wire = (Current Underground AC^2)*2*Resistivity*Length of Underground AC Wire/Line Losses

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

Go Constant Underground AC = Volume Of Conductor*(cos(Phase Difference))^2/(1.75)

Volume of Conductor Material when K is Given(3 Phase 4 Wire US)

Go Volume Of Conductor = Constant Underground AC*1.75/(cos(Phase Difference)^2)

Area of X-Section using Volume of Conductor Material (3 Phase 4 Wire US)

Go Area of Underground AC Wire = Volume Of Conductor/((3.5)*Length of Underground AC Wire)

Volume of Conductor Material when Area and Length is Given(3 Phase 4 Wire US)

Go Volume Of Conductor = 3.5*Area of Underground AC Wire*Length of Underground AC Wire

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

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

Angle 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 Angle using Area Of X-Section (3 phase 4 wire US) formula is defined as the phase angle between reactive and active power. Phase Difference is denoted by Φ symbol.

How to calculate Angle using Area of X-Section (3 Phase 4 Wire US) using this online calculator? To use this online calculator for Angle 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 Angle 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 Angle using Area of X-Section (3 Phase 4 Wire US)?

The Angle using Area Of X-Section (3 phase 4 wire US) formula is defined as the phase angle between reactive and active power 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 Angle using Area of X-Section (3 Phase 4 Wire US)?

The Angle using Area Of X-Section (3 phase 4 wire US) formula is defined as the phase angle between reactive and active power 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 Angle 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 2 other way(s) to calculate the same, which is/are as follows -

Phase Difference = acos(sqrt(6)*Power Transmitted/(3*Maximum Voltage Underground AC*Current Underground AC))
Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Line Losses*Area of Underground AC Wire)))

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