RMS Voltage using Line Losses (2-Phase 3-Wire US) Solution

STEP 0: Pre-Calculation Summary
Formula Used
Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))/cos(Phase Difference)
Vrms = P*sqrt((2+sqrt(2))*ρ*L/(A*Ploss))/cos(Φ)
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.
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.
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.
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
Power Transmitted: 300 Watt --> 300 Watt 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
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vrms = P*sqrt((2+sqrt(2))*ρ*L/(A*Ploss))/cos(Φ) --> 300*sqrt((2+sqrt(2))*1.7E-05*24/(1.28*2.67))/cos(0.5235987755982)
Evaluating ... ...
Vrms = 6.99367474417098
STEP 3: Convert Result to Output's Unit
6.99367474417098 Volt --> No Conversion Required
FINAL ANSWER
6.99367474417098 6.993675 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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14 Current & Voltage Calculators

Maximum Voltage using Line Losses (2-Phase 3-Wire US)
Go Maximum Voltage Underground AC = (Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses)))/cos(Phase Difference)
Maximum Voltage using Volume of Conductor Material (2-phase 3-wire US)
Go Maximum Voltage Underground AC = (2+sqrt(2))*sqrt(Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*Volume Of Conductor*(cos(Phase Difference))^2))
RMS Voltage using Line Losses (2-Phase 3-Wire US)
Go Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))/cos(Phase Difference)
Maximum Voltage using Current in Neutral Wire (2-Phase 3-Wire US)
Go Maximum Voltage Underground AC = sqrt(2)*Power Transmitted/(cos(Phase Difference)*Current Underground AC)
Current in Neutral Wire (2-Phase 3-Wire US)
Go Current Underground AC = sqrt(2)*Power Transmitted/(Maximum Voltage Underground AC*cos(Phase Difference))
RMS Voltage using Current in Neutral Wire (2-Phase 3-Wire US)
Go Root Mean Square Voltage = Power Transmitted/(sqrt(2)*cos(Phase Difference)*Current Underground AC)
Maximum Voltage using Current in Each Outer (2-Phase 3-Wire US)
Go Maximum Voltage Underground AC = Power Transmitted/(cos(Phase Difference)*Current Underground AC)
Current in Each Outer (2-Phase 3-Wire US)
Go Current Underground AC = Power Transmitted/(Maximum Voltage Underground AC*cos(Phase Difference))
RMS Voltage using Current in Each Outer (2-Phase 3-Wire US)
Go Root Mean Square Voltage = Power Transmitted/(2*cos(Phase Difference)*Current Underground AC)
Maximum Phase Voltage between Outer and Neutral Wire (2-Phase 3-Wire US)
Go Peak Phase Voltage = Maximum Voltage Underground AC/(sqrt(2))
Current in Each Outer using Current in Neutral Wire (2-Phase 3-Wire US)
Go Current Underground AC = Current in Neutral Wire/sqrt(2)
Current in Neutral Wire using Current in Each Outer (2-Phase 3-Wire US)
Go Current in Neutral Wire = sqrt(2)*Current Underground AC
Maximum Voltage using RMS Voltage between Outer and Neutral Wire (2-Phase 3-Wire US)
Go Maximum Voltage Underground AC = 2*Root Mean Square Voltage
RMS Voltage between Outer and Neutral Wire (2-Phase 3-Wire US)
Go Root Mean Square Voltage = Maximum Voltage Underground AC/2

RMS Voltage using Line Losses (2-Phase 3-Wire US) Formula

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

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

How to Calculate RMS Voltage using Line Losses (2-Phase 3-Wire US)?

RMS Voltage using Line Losses (2-Phase 3-Wire US) calculator uses Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))/cos(Phase Difference) to calculate the Root Mean Square Voltage, The RMS Voltage using Line Losses (2-Phase 3-Wire US) 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 Line Losses (2-Phase 3-Wire US) using this online calculator? To use this online calculator for RMS Voltage using Line Losses (2-Phase 3-Wire US), enter Power Transmitted (P), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A), Line Losses (Ploss) & Phase Difference (Φ) and hit the calculate button. Here is how the RMS Voltage using Line Losses (2-Phase 3-Wire US) calculation can be explained with given input values -> 6.993675 = 300*sqrt((2+sqrt(2))*1.7E-05*24/(1.28*2.67))/cos(0.5235987755982).

FAQ

What is RMS Voltage using Line Losses (2-Phase 3-Wire US)?
The RMS Voltage using Line Losses (2-Phase 3-Wire US) formula is defined as the square root of the time average of the voltage squared and is represented as Vrms = P*sqrt((2+sqrt(2))*ρ*L/(A*Ploss))/cos(Φ) or Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))/cos(Phase Difference). 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, 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 & 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 Line Losses (2-Phase 3-Wire US)?
The RMS Voltage using Line Losses (2-Phase 3-Wire US) formula is defined as the square root of the time average of the voltage squared is calculated using Root Mean Square Voltage = Power Transmitted*sqrt((2+sqrt(2))*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses))/cos(Phase Difference). To calculate RMS Voltage using Line Losses (2-Phase 3-Wire US), you need Power Transmitted (P), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A), Line Losses (Ploss) & Phase Difference (Φ). With our tool, you need to enter the respective value for Power Transmitted, Resistivity, Length of Underground AC Wire, Area of Underground 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 Power Transmitted, Resistivity, Length of Underground AC Wire, Area of Underground AC Wire, Line Losses & Phase Difference. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Root Mean Square Voltage = Maximum Voltage Underground AC/2
  • Root Mean Square Voltage = Power Transmitted/(2*cos(Phase Difference)*Current Underground AC)
  • Root Mean Square Voltage = Power Transmitted/(sqrt(2)*cos(Phase Difference)*Current Underground AC)
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