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Length using Line Losses (Single-Phase Three-Wire OS) Formula

GoLength of Wire using Area of X-Section(Single-Phase Three-Wire OS) Formula

GoLength using Load Current (Single-Phase Three-Wire OS) Formula

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Length of Overhead AC Wire is the total length of the wire from one end to other end. Check FAQs

L = P loss \cdot A \cdot \frac{{(V m \cdot \cos (Φ))}^{2}}{(P^{2}) \cdot ρ}

L - Length of Overhead AC Wire?P_loss - Line Losses?A - Area of Overhead AC Wire?V_m - Maximum Voltage Overhead AC?Φ - Phase Difference?P - Power Transmitted?ρ - Resistivity?

Length using Line Losses (Single-Phase Three-Wire OS) Example

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Here is how the Length using Line Losses (Single-Phase Three-Wire OS) equation looks like with Values.

Here is how the Length using Line Losses (Single-Phase Three-Wire OS) equation looks like with Units.

Here is how the Length using Line Losses (Single-Phase Three-Wire OS) equation looks like.

1392.0109 = 8.23 \cdot 0.79 \cdot \frac{{(62 \cdot \cos (30))}^{2}}{(890^{2}) \cdot 1.7E-5}

1392.0109m = 8.23W \cdot 0.79m² \cdot \frac{{(62V \cdot \cos (30°))}^{2}}{({890W}^{2}) \cdot 1.7E-5Ω*m}

1392.0109 = 8.23 \cdot 0.79 \cdot \frac{{(62 \cdot \cos (30))}^{2}}{(890^{2}) \cdot 1.7E-5}

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Length using Line Losses (Single-Phase Three-Wire OS) Solution

Follow our step by step solution on how to calculate Length using Line Losses (Single-Phase Three-Wire OS)?

FIRST Step Consider the formula

L = P loss \cdot A \cdot \frac{{(V m \cdot \cos (Φ))}^{2}}{(P^{2}) \cdot ρ}

Next Step Substitute values of Variables

∴

L = 8.23W \cdot 0.79m² \cdot \frac{{(62V \cdot \cos (30°))}^{2}}{({890W}^{2}) \cdot 1.7E-5Ω*m}

Next Step Convert Units

∴

L = 8.23W \cdot 0.79m² \cdot \frac{{(62V \cdot \cos (0.5236rad))}^{2}}{({890W}^{2}) \cdot 1.7E-5Ω*m}

Next Step Prepare to Evaluate

∴

L = 8.23 \cdot 0.79 \cdot \frac{{(62 \cdot \cos (0.5236))}^{2}}{(890^{2}) \cdot 1.7E-5}

Next Step Evaluate

∴

L = 1392.01089434638m

LAST Step Rounding Answer

∴

L = 1392.0109m

Length using Line Losses (Single-Phase Three-Wire OS) Formula Elements

Variables

Functions

Length of Overhead AC Wire

Length of Overhead AC Wire is the total length of the wire from one end to other end.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Overhead AC Wire

Line Losses

Line Losses is defined as the total losses occurring in an Overhead AC line when in use.

Symbol: P_loss

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Line Losses

Area of Overhead AC Wire

Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Overhead AC Wire

Maximum Voltage Overhead AC

Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.

Symbol: V_m

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Maximum Voltage Overhead AC

Phase Difference

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.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Difference

Power Transmitted

Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end.

Symbol: P

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Power Transmitted

Resistivity

Resistivity is the measure of how strongly a material opposes the flow of current through them.

Symbol: ρ

Measurement: Electric ResistivityUnit: Ω*m

Note: Value can be positive or negative.

Formulas to find Resistivity

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Length of Overhead AC Wire

Go Length of Wire using Area of X-Section(Single-Phase Three-Wire OS)

L = A \cdot ({V m}^{2}) \cdot P loss \cdot \frac{{(\cos (Φ))}^{2}}{ρ \cdot (P^{2})}

Go Length using Load Current (Single-Phase Three-Wire OS)

L = P loss \cdot \frac{A}{2 \cdot (I^{2}) \cdot ρ}

Other formulas in Wire Parameters category

Go Area of X-Section(Single-Phase Three-Wire OS)

A = (P^{2}) \cdot ρ \cdot \frac{L}{({(\cos (Φ))}^{2}) \cdot P loss \cdot ({V m}^{2})}

Go Constant(Single-Phase Three-Wire OS)

K = \frac{4 \cdot (P^{2}) \cdot ρ \cdot L}{P loss \cdot ({V ac}^{2})}

How to Evaluate Length using Line Losses (Single-Phase Three-Wire OS)?

Length using Line Losses (Single-Phase Three-Wire OS) evaluator uses Length of Overhead AC Wire = Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2/((Power Transmitted^2)*Resistivity) to evaluate the Length of Overhead AC Wire, The Length using Line Losses (single-Phase three-Wire OS) formula is defined as the total length of the wire that used in the single-phase three-wire system. Length of Overhead AC Wire is denoted by L symbol.

How to evaluate Length using Line Losses (Single-Phase Three-Wire OS) using this online evaluator? To use this online evaluator for Length using Line Losses (Single-Phase Three-Wire OS), enter Line Losses (P_loss), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (V_m), Phase Difference (Φ), Power Transmitted (P) & Resistivity (ρ) and hit the calculate button.

FAQs on Length using Line Losses (Single-Phase Three-Wire OS)

What is the formula to find Length using Line Losses (Single-Phase Three-Wire OS)?

The formula of Length using Line Losses (Single-Phase Three-Wire OS) is expressed as Length of Overhead AC Wire = Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2/((Power Transmitted^2)*Resistivity). Here is an example- 1392.011 = 8.23*0.79*(62*cos(0.5235987755982))^2/((890^2)*1.7E-05).

How to calculate Length using Line Losses (Single-Phase Three-Wire OS)?

With Line Losses (P_loss), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (V_m), Phase Difference (Φ), Power Transmitted (P) & Resistivity (ρ) we can find Length using Line Losses (Single-Phase Three-Wire OS) using the formula - Length of Overhead AC Wire = Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2/((Power Transmitted^2)*Resistivity). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Length of Overhead AC Wire?

Here are the different ways to Calculate Length of Overhead AC Wire-

Length of Overhead AC Wire=Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*Line Losses*((cos(Phase Difference))^2)/(Resistivity*(Power Transmitted^2))
Length of Overhead AC Wire=Line Losses*Area of Overhead AC Wire/(2*(Current Overhead AC^2)*Resistivity)
Length of Overhead AC Wire=sqrt(Volume of Conductor*Line Losses*(cos(Phase Difference)*Maximum Voltage Overhead AC)^2/((2.5)*Resistivity*(Power Transmitted^2)))

Can the Length using Line Losses (Single-Phase Three-Wire OS) be negative?

No, the Length using Line Losses (Single-Phase Three-Wire OS), measured in Length cannot be negative.

Which unit is used to measure Length using Line Losses (Single-Phase Three-Wire OS)?

Length using Line Losses (Single-Phase Three-Wire OS) is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length using Line Losses (Single-Phase Three-Wire OS) can be measured.

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Length using Line Losses (Single-Phase Three-Wire OS) Formula

​GoLength of Wire using Area of X-Section(Single-Phase Three-Wire OS) Formula

​GoLength using Load Current (Single-Phase Three-Wire OS) Formula

Length using Line Losses (Single-Phase Three-Wire OS) Example

Length using Line Losses (Single-Phase Three-Wire OS) Solution

Length using Line Losses (Single-Phase Three-Wire OS) Formula Elements

Other Formulas to find Length of Overhead AC Wire

Other formulas in Wire Parameters category

How to Evaluate Length using Line Losses (Single-Phase Three-Wire OS)?

FAQs on Length using Line Losses (Single-Phase Three-Wire OS)

Variable Name

GoLength of Wire using Area of X-Section(Single-Phase Three-Wire OS) Formula

GoLength using Load Current (Single-Phase Three-Wire OS) Formula