RMS Voltage using Area of X-Section (3 Phase 4 Wire US) Calculator

✖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.ⓘ Power Transmitted [P]			+10% -10%
✖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.ⓘ Phase Difference [Φ]			+10% -10%
✖Resistivity is the measure of how strongly a material opposes the flow of current through them.ⓘ Resistivity [ρ]			+10% -10%
✖Length of Underground AC Wire is the total length of the wire from one end to other end.ⓘ Length of Underground AC Wire [L]			+10% -10%
✖Line Losses is defined as the total losses occurring in an Underground AC line when in use.ⓘ Line Losses [P_loss]			+10% -10%
✖Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system.ⓘ Area of Underground AC Wire [A]			+10% -10%

✖Root Mean Square Voltage is the square root of the time average of the voltage squared.ⓘ RMS Voltage using Area of X-Section (3 Phase 4 Wire US) [V_rms]

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RMS Voltage using Area of X-Section (3 Phase 4 Wire US) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire))
V_rms = (2*P/cos(Φ))*sqrt(ρ*L/(6*P_loss*A))
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.
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.
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.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Underground AC line when in use.
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.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
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
Line Losses: 2.67 Watt --> 2.67 Watt No Conversion Required
Area of Underground AC Wire: 1.28 Square Meter --> 1.28 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_rms = (2*P/cos(Φ))*sqrt(ρ*L/(6*P_loss*A)) --> (2*300/cos(0.5235987755982))*sqrt(1.7E-05*24/(6*2.67*1.28))

Evaluating ... ...

V_rms = 3.09039832347754

STEP 3: Convert Result to Output's Unit

3.09039832347754 Volt --> No Conversion Required

FINAL ANSWER

3.09039832347754 ≈ 3.090398 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.004 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Power and Power Factor Calculators

Power Transmitted using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(7*Resistivity*(Length of Underground AC Wire)^2))

Power Transmitted using Load Current (3 Phase 4 Wire US)

LaTeX Go Power Transmitted = (3*Maximum Voltage Underground AC*cos(Phase Difference)*Current Underground AC)/sqrt(6)

Angle of PF using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Phase Difference = acos(sqrt((1.75)*Constant Underground AC/Volume Of Conductor))

Power Factor using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Power Factor = sqrt((1.75)*Constant Underground AC/Volume Of Conductor)

RMS Voltage using Area of X-Section (3 Phase 4 Wire US) Formula

LaTeX Go

What is the value of maximum voltage in 3-phase 4-wire Underground system?

The maximum voltage between conductors is v_m/√3 so that r.m.s. value of voltage between them is v_m/√6.

How to Calculate RMS Voltage using Area of X-Section (3 Phase 4 Wire US)?

RMS Voltage using Area of X-Section (3 Phase 4 Wire US) calculator uses Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire)) to calculate the Root Mean Square Voltage, The RMS Voltage using Area of X-Section (3 phase 4 wire US) formula is defined as the square root of the time average of the voltage squared. Root Mean Square Voltage is denoted by V_rms symbol.

How to calculate RMS Voltage using Area of X-Section (3 Phase 4 Wire US) using this online calculator? To use this online calculator for RMS Voltage using Area of X-Section (3 Phase 4 Wire US), enter Power Transmitted (P), Phase Difference (Φ), Resistivity (ρ), Length of Underground AC Wire (L), Line Losses (P_loss) & Area of Underground AC Wire (A) and hit the calculate button. Here is how the RMS Voltage using Area of X-Section (3 Phase 4 Wire US) calculation can be explained with given input values -> 3.090398 = (2*300/cos(0.5235987755982))*sqrt(1.7E-05*24/(6*2.67*1.28)).

FAQ

What is RMS Voltage using Area of X-Section (3 Phase 4 Wire US)?

The RMS Voltage using Area of X-Section (3 phase 4 wire US) formula is defined as the square root of the time average of the voltage squared and is represented as V_rms = (2*P/cos(Φ))*sqrt(ρ*L/(6*P_loss*A)) or Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire)). 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, 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, 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, Line Losses is defined as the total losses occurring in an Underground AC line when in use & Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system.

How to calculate RMS Voltage using Area of X-Section (3 Phase 4 Wire US)?

The RMS Voltage using Area of X-Section (3 phase 4 wire US) formula is defined as the square root of the time average of the voltage squared is calculated using Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire)). To calculate RMS Voltage using Area of X-Section (3 Phase 4 Wire US), you need Power Transmitted (P), Phase Difference (Φ), Resistivity (ρ), Length of Underground AC Wire (L), Line Losses (P_loss) & Area of Underground AC Wire (A). With our tool, you need to enter the respective value for Power Transmitted, Phase Difference, Resistivity, Length of Underground AC Wire, Line Losses & Area of Underground AC Wire 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, Phase Difference, Resistivity, Length of Underground AC Wire, Line Losses & Area of Underground AC Wire. We can use 3 other way(s) to calculate the same, which is/are as follows -

Root Mean Square Voltage = (2*Power Transmitted/3*Current Underground AC*cos(Phase Difference))
Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses))
Root Mean Square Voltage = (Power Transmitted*Length of Underground AC Wire/cos(Phase Difference))*sqrt(Resistivity/(Line Losses*Volume Of Conductor))

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