Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS) Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Vm = sqrt((2*L*ρ*(P^2))/(3*A*Ploss*((cos(Φ))^2)))
This formula uses 2 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)
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
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.
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.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
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.
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.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Overhead AC line when in use.
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.
STEP 1: Convert Input(s) to Base Unit
Length of Overhead AC Wire: 10.63 Meter --> 10.63 Meter No Conversion Required
Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Power Transmitted: 890 Watt --> 890 Watt No Conversion Required
Area of Overhead AC Wire: 0.79 Square Meter --> 0.79 Square Meter No Conversion Required
Line Losses: 8.23 Watt --> 8.23 Watt No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vm = sqrt((2*L*ρ*(P^2))/(3*A*Ploss*((cos(Φ))^2))) --> sqrt((2*10.63*1.7E-05*(890^2))/(3*0.79*8.23*((cos(0.5235987755982))^2)))
Evaluating ... ...
Vm = 4.42375814350928
STEP 3: Convert Result to Output's Unit
4.42375814350928 Volt --> No Conversion Required
FINAL ANSWER
4.42375814350928 4.423758 Volt <-- Maximum Voltage Overhead AC
(Calculation completed in 00.004 seconds)

Credits

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8 Current & Voltage Calculators

Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS)
Go Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
RMS Voltage using Area of X-Section(3-Phase 3-Wire OS)
Go Root Mean Square Voltage = sqrt(Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(cos(Phase Difference)^2)))
Resistivity using Area of X-Section(3-Phase 3-Wire OS)
Go Resistivity = 3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*Line Losses*((cos(Phase Difference))^2)/(2*Length of Overhead AC Wire*(Power Transmitted^2))
Load Current(3-Phase 3-Wire OS)
Go Current Overhead AC = (sqrt(2)*Power Transmitted)/((3)*Maximum Voltage Overhead AC*cos(Phase Difference))
Maximum Voltage using Load Current(3-Phase 3-Wire OS)
Go Maximum Voltage Overhead AC = (sqrt(2)*Power Transmitted)/(3*Current Overhead AC*cos(Phase Difference))
RMS Voltage using Load Current(3-Phase 3-Wire OS)
Go Root Mean Square Voltage = Power Transmitted/(3*cos(Phase Difference)*Current Overhead AC)
Resistance(3-Phase 3-Wire OS)
Go Resistance Overhead AC = Resistivity*Length of Overhead AC Wire/Area of Overhead AC Wire
Maximum Voltage(3-Phase 3-Wire OS)
Go Voltage Overhead AC = (1)*Maximum Voltage Overhead AC

Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS) Formula

Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Vm = sqrt((2*L*ρ*(P^2))/(3*A*Ploss*((cos(Φ))^2)))

What is the value of maximum voltage and volume of conductor material in 3-phase 3-wire system?

The volume of conductor material required in this system is 0.5/cos2θ times that of 2-wire DC 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 Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS)?

Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS) calculator uses Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))) to calculate the Maximum Voltage Overhead AC, The Maximum Voltage using Area of X-section(3-phase 3-wire OS) formula is defined as the highest voltage rating for electrical devices and equipment that can be used with the voltage definition. Maximum Voltage Overhead AC is denoted by Vm symbol.

How to calculate Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS) using this online calculator? To use this online calculator for Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS), enter Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Line Losses (Ploss) & Phase Difference (Φ) and hit the calculate button. Here is how the Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS) calculation can be explained with given input values -> 4.423758 = sqrt((2*10.63*1.7E-05*(890^2))/(3*0.79*8.23*((cos(0.5235987755982))^2))).

FAQ

What is Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS)?
The Maximum Voltage using Area of X-section(3-phase 3-wire OS) formula is defined as the highest voltage rating for electrical devices and equipment that can be used with the voltage definition and is represented as Vm = sqrt((2*L*ρ*(P^2))/(3*A*Ploss*((cos(Φ))^2))) or Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))). Length of Overhead AC Wire is the total length of the wire from one end to other end, Resistivity is the measure of how strongly a material opposes the flow of current through them, Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end, Area of Overhead 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 Overhead AC line when in use & 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.
How to calculate Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS)?
The Maximum Voltage using Area of X-section(3-phase 3-wire OS) formula is defined as the highest voltage rating for electrical devices and equipment that can be used with the voltage definition is calculated using Maximum Voltage Overhead AC = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))). To calculate Maximum Voltage using Area of X-Section(3-Phase 3-Wire OS), you need Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Line Losses (Ploss) & Phase Difference (Φ). With our tool, you need to enter the respective value for Length of Overhead AC Wire, Resistivity, Power Transmitted, Area of Overhead AC Wire, Line Losses & Phase Difference 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 Maximum Voltage Overhead AC?
In this formula, Maximum Voltage Overhead AC uses Length of Overhead AC Wire, Resistivity, Power Transmitted, Area of Overhead AC Wire, Line Losses & Phase Difference. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Maximum Voltage Overhead AC = (sqrt(2)*Power Transmitted)/(3*Current Overhead AC*cos(Phase Difference))
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