RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS) Solution

STEP 0: Pre-Calculation Summary
Formula Used
Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Vrms = sqrt(((2+sqrt(2))*L*ρ*(P^2))/(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
Root Mean Square Voltage - (Measured in Volt) - Root Mean Square Voltage is the square root of the time average of the voltage squared.
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
Vrms = sqrt(((2+sqrt(2))*L*ρ*(P^2))/(A*Ploss*((cos(Φ))^2))) --> sqrt(((2+sqrt(2))*10.63*1.7E-05*(890^2))/(0.79*8.23*((cos(0.5235987755982))^2)))
Evaluating ... ...
Vrms = 10.0111126023934
STEP 3: Convert Result to Output's Unit
10.0111126023934 Volt --> No Conversion Required
FINAL ANSWER
10.0111126023934 10.01111 Volt <-- Root Mean Square Voltage
(Calculation completed in 00.004 seconds)

Credits

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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12 Current & Voltage Calculators

Maximum Voltage using Area of X-Section(Two-Phase Three-Wire OS)
Go Maximum Voltage Overhead AC = sqrt((Length of Overhead AC Wire*Resistivity*(Power Transmitted^2)*(2+sqrt(2)))/(2*Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS)
Go Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Maximum Voltage using Line Losses (Two-Phase Three-Wire OS)
Go Maximum Voltage Overhead AC = (Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Area of Overhead AC Wire*Line Losses)))/cos(Phase Difference)
Maximum Voltage using Volume of Conductor Material (Two-Phase Three-Wire OS)
Go Maximum Voltage Overhead AC = (2+sqrt(2))*sqrt(Resistivity*(Power Transmitted*Length of Overhead AC Wire)^2/(Line Losses*Volume of Conductor*(cos(Phase Difference))^2))
RMS Voltage using Line Losses (Two-Phase Three-Wire OS)
Go Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Area of Overhead AC Wire*Line Losses))/cos(Phase Difference)
Load Current using Area of X-Section(Two-Phase Three-Wire OS)
Go Current Overhead AC = sqrt(Line Losses*Area of Overhead AC Wire/((2+sqrt(2))*Resistivity*Length of Overhead AC Wire))
Maximum Voltage using Load Current (Two-Phase Three-Wire OS)
Go Maximum Voltage Overhead AC = Power Transmitted/(sqrt(2)*cos(Phase Difference)*Current Overhead AC)
Load Current in Each Outer (Two-Phase Three-Wire OS)
Go Current Overhead AC = Power Transmitted/(sqrt(2)*Maximum Voltage Overhead AC*cos(Phase Difference))
Load Current(Two-Phase Three-Wire OS)
Go Current Overhead AC = Power Transmitted/(sqrt(2)*Maximum Voltage Overhead AC*cos(Phase Difference))
RMS Voltage using Load Current (Two-Phase Three-Wire OS)
Go Root Mean Square Voltage = Power Transmitted/(2*cos(Phase Difference)*Current Overhead AC)
Load Current of Neutral Wire (Two-Phase Three-Wire OS)
Go Current in Neutral Wire = sqrt(2)*Current Overhead AC
Maximum Voltage(Two-Phase Three-Wire OS)
Go Voltage Overhead AC = (1)*Maximum Voltage Overhead AC

RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS) Formula

Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Vrms = sqrt(((2+sqrt(2))*L*ρ*(P^2))/(A*Ploss*((cos(Φ))^2)))

What is the value of maximum voltage and volume of conductor material in 2-phase 3-wire system?

The volume of conductor material required in this system is 1.457/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 RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS)?

RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS) calculator uses Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))) to calculate the Root Mean Square Voltage, The RMS Voltage using Area of X-section(two-phase three-wire OS) formula is defined as the square root of the time average of the voltage squared. Root Mean Square Voltage is denoted by Vrms symbol.

How to calculate RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS) using this online calculator? To use this online calculator for RMS Voltage using Area of X-Section(Two-Phase Three-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 RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS) calculation can be explained with given input values -> 10.01111 = sqrt(((2+sqrt(2))*10.63*1.7E-05*(890^2))/(0.79*8.23*((cos(0.5235987755982))^2))).

FAQ

What is RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS)?
The RMS Voltage using Area of X-section(two-phase three-wire OS) formula is defined as the square root of the time average of the voltage squared and is represented as Vrms = sqrt(((2+sqrt(2))*L*ρ*(P^2))/(A*Ploss*((cos(Φ))^2))) or Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(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 RMS Voltage using Area of X-Section(Two-Phase Three-Wire OS)?
The RMS Voltage using Area of X-section(two-phase three-wire OS) formula is defined as the square root of the time average of the voltage squared is calculated using Root Mean Square Voltage = sqrt(((2+sqrt(2))*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))). To calculate RMS Voltage using Area of X-Section(Two-Phase Three-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 Root Mean Square Voltage?
In this formula, Root Mean Square Voltage uses Length of Overhead AC Wire, Resistivity, Power Transmitted, Area of Overhead AC Wire, Line Losses & Phase Difference. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Area of Overhead AC Wire*Line Losses))/cos(Phase Difference)
  • Root Mean Square Voltage = Power Transmitted/(2*cos(Phase Difference)*Current Overhead AC)
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