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

STEP 0: Pre-Calculation Summary
Formula Used
Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity)
L = (Ploss*A*(Vm*cos(Φ))^2)/(4*(P^2)*ρ)
This formula uses 1 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)
Variables Used
Length of Overhead AC Wire - (Measured in Meter) - Length of Overhead AC Wire is the total length of the wire from one end to other end.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Overhead AC line when in use.
Area of Overhead AC Wire - (Measured in Square Meter) - Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.
Maximum Voltage Overhead AC - (Measured in Volt) - Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.
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 defined as the product of current and voltage phasor in a overhead ac line at the receiving end.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
STEP 1: Convert Input(s) to Base Unit
Line Losses: 8.23 Watt --> 8.23 Watt No Conversion Required
Area of Overhead AC Wire: 0.79 Square Meter --> 0.79 Square Meter No Conversion Required
Maximum Voltage Overhead AC: 62 Volt --> 62 Volt No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Power Transmitted: 890 Watt --> 890 Watt No Conversion Required
Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = (Ploss*A*(Vm*cos(Φ))^2)/(4*(P^2)*ρ) --> (8.23*0.79*(62*cos(0.5235987755982))^2)/(4*(890^2)*1.7E-05)
Evaluating ... ...
L = 348.002723586594
STEP 3: Convert Result to Output's Unit
348.002723586594 Meter --> No Conversion Required
FINAL ANSWER
348.002723586594 348.0027 Meter <-- Length of Overhead AC Wire
(Calculation completed in 00.004 seconds)

Credits

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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15 Wire Parameters Calculators

Line Losses using Area of X-Section(Single-Phase Two-Wire OS)
Go Line Losses = (4*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*((cos(Phase Difference))^2))
Length of Wire using Area of X-Section(Single-Phase Two-Wire OS)
Go Length of Overhead AC Wire = (Area of Overhead AC Wire*Maximum Voltage Overhead AC^2*Line Losses*cos(Phase Difference)^2)/(4*Resistivity*(Power Transmitted^2))
Length using Line Losses (Single-Phase Two-Wire OS)
Go Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity)
Area of X-Section using Line Losses (Single-Phase Two-Wire OS)
Go Area of Overhead AC Wire = (4*Resistivity*Length of Overhead AC Wire*Power Transmitted^2)/(Line Losses*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)
Area of X-Section(Single-Phase Two-Wire OS)
Go Area of Overhead AC Wire = (4*(Power Transmitted^2)*Resistivity*Length of Overhead AC Wire)/(((cos(Phase Difference))^2)*Line Losses*(Voltage Overhead AC^2))
Volume of Conductor Material using Line Losses (Single-Phase Two-Wire OS)
Go Volume of Conductor = (8*Resistivity*(Power Transmitted*Length of Overhead AC Wire)^2)/(Line Losses*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)
Constant using Load Current (Single-Phase Two-Wire OS)
Go Constant Overhead AC = (2*Current Overhead AC^2*cos(Phase Difference)^2*Resistivity*Length of Overhead AC Wire^2)/Line Losses
Constant using Line Losses (Single-Phase Two-Wire OS)
Go Constant Overhead AC = (4*Resistivity*(Power Transmitted*Length of Overhead AC Wire)^2)/(Line Losses*(Maximum Voltage Overhead AC)^2)
Constant(Single-Phase Two-Wire OS)
Go Constant Overhead AC = (4*(Power Transmitted^2)*Resistivity*Length of Overhead AC Wire)/(Line Losses*(Voltage Overhead AC^2))
Length using Load Current (Single-Phase Two-Wire OS)
Go Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire)/(2*(Current Overhead AC)^2*Resistivity)
Volume of Conductor Material using Load Current (Single-Phase Two-Wire OS)
Go Volume of Conductor = (4*(Current Overhead AC^2)*Resistivity*(Length of Overhead AC Wire^2))/(Line Losses)
Area of X-Section using Load Current (Single-Phase Two-Wire OS)
Go Area of Overhead AC Wire = (2*Current Overhead AC^2*Resistivity*Length of Overhead AC Wire)/(Line Losses)
Volume of Conductor Material(Single-Phase Two-Wire OS)
Go Volume of Conductor = 2*Area of Overhead AC Wire*Length of Overhead AC Wire
Line Losses(Single-Phase Two-Wire OS)
Go Line Losses = (2)*((Current Overhead AC)^2)*Resistance Overhead AC
Line Losses using Load Current (Single-Phase Two-Wire OS)
Go Line Losses = 2*Resistance Overhead AC*(Current Overhead AC)^2

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

Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity)
L = (Ploss*A*(Vm*cos(Φ))^2)/(4*(P^2)*ρ)

What is the value of maximum voltage and volume of conductor material in 1-phase 2-wire system?

The volume of conductor material required in this system is 2/cos2θ times that of 2-wire d.c.system with the one conductor earthed. The maximum voltage between conductors is vm so that r.m.s. value of voltage between them is vm/√2.

How to Calculate Length using Line Losses (Single-Phase Two-Wire OS)?

Length using Line Losses (Single-Phase Two-Wire OS) calculator uses Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity) to calculate the Length of Overhead AC Wire, Length using Line Losses (single-Phase two-Wire OS) formula is defined as the total length of the wire that used in the single-phase two-wire system. Length of Overhead AC Wire is denoted by L symbol.

How to calculate Length using Line Losses (Single-Phase Two-Wire OS) using this online calculator? To use this online calculator for Length using Line Losses (Single-Phase Two-Wire OS), enter Line Losses (Ploss), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (Vm), Phase Difference (Φ), Power Transmitted (P) & Resistivity (ρ) and hit the calculate button. Here is how the Length using Line Losses (Single-Phase Two-Wire OS) calculation can be explained with given input values -> 348.0027 = (8.23*0.79*(62*cos(0.5235987755982))^2)/(4*(890^2)*1.7E-05).

FAQ

What is Length using Line Losses (Single-Phase Two-Wire OS)?
Length using Line Losses (single-Phase two-Wire OS) formula is defined as the total length of the wire that used in the single-phase two-wire system and is represented as L = (Ploss*A*(Vm*cos(Φ))^2)/(4*(P^2)*ρ) or Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity). Line Losses is defined as the total losses occurring in an Overhead AC line when in use, Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system, Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire, 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 is defined as the product of current and voltage phasor in a overhead ac line at the receiving end & Resistivity is the measure of how strongly a material opposes the flow of current through them.
How to calculate Length using Line Losses (Single-Phase Two-Wire OS)?
Length using Line Losses (single-Phase two-Wire OS) formula is defined as the total length of the wire that used in the single-phase two-wire system is calculated using Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire*(Maximum Voltage Overhead AC*cos(Phase Difference))^2)/(4*(Power Transmitted^2)*Resistivity). To calculate Length using Line Losses (Single-Phase Two-Wire OS), you need Line Losses (Ploss), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (Vm), Phase Difference (Φ), Power Transmitted (P) & Resistivity (ρ). With our tool, you need to enter the respective value for Line Losses, Area of Overhead AC Wire, Maximum Voltage Overhead AC, Phase Difference, Power Transmitted & Resistivity 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 Length of Overhead AC Wire?
In this formula, Length of Overhead AC Wire uses Line Losses, Area of Overhead AC Wire, Maximum Voltage Overhead AC, Phase Difference, Power Transmitted & Resistivity. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Length of Overhead AC Wire = (Area of Overhead AC Wire*Maximum Voltage Overhead AC^2*Line Losses*cos(Phase Difference)^2)/(4*Resistivity*(Power Transmitted^2))
  • Length of Overhead AC Wire = (Line Losses*Area of Overhead AC Wire)/(2*(Current Overhead AC)^2*Resistivity)
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