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

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

✖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 3-Wire OS) [V_rms]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V_rms = sqrt(ρ*(P^2*L^2)/(3*A*P_loss*(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.
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.
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.
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

Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Power Transmitted: 890 Watt --> 890 Watt No Conversion Required
Length of Overhead AC Wire: 10.63 Meter --> 10.63 Meter 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

V_rms = sqrt(ρ*(P^2*L^2)/(3*A*P_loss*(cos(Φ)^2))) --> sqrt(1.7E-05*(890^2*10.63^2)/(3*0.79*8.23*(cos(0.5235987755982)^2)))

Evaluating ... ...

V_rms = 10.1986575556142

STEP 3: Convert Result to Output's Unit

10.1986575556142 Volt --> No Conversion Required

FINAL ANSWER

10.1986575556142 ≈ 10.19866 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Overhead AC Supply » 3 3 Wire System » Current and Voltage » RMS Voltage using Area of X-Section(3-Phase 3-Wire OS)

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< Current and Voltage Calculators

Resistivity using Area of X-Section(3-Phase 3-Wire OS)

LaTeX 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)

LaTeX Go Current Overhead AC = (sqrt(2)*Power Transmitted)/((3)*Maximum Voltage Overhead AC*cos(Phase Difference))

Resistance(3-Phase 3-Wire OS)

LaTeX Go Resistance Overhead AC = Resistivity*Length of Overhead AC Wire/Area of Overhead AC Wire

Maximum Voltage(3-Phase 3-Wire OS)

LaTeX Go Voltage Overhead AC = (1)*Maximum Voltage Overhead AC

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

LaTeX Go

How is a three-wire three-phase system is better than a two-wire single-phase system?

A three-wire, three-phase system can then transmit 73% more power than a two-wire, single-phase system by just the addition of one wire. A three-phase system also has some major advantages in the generation and use of electricity by rotating machines as will be explained later.

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

RMS Voltage using Area of X-Section(3-Phase 3-Wire OS) calculator uses 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))) to calculate the Root Mean Square Voltage, The RMS Voltage using Area of X-section(3-phase 3-wire OS) 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 3-Wire OS) using this online calculator? To use this online calculator for RMS Voltage using Area of X-Section(3-Phase 3-Wire OS), enter Resistivity (ρ), Power Transmitted (P), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ) and hit the calculate button. Here is how the RMS Voltage using Area of X-Section(3-Phase 3-Wire OS) calculation can be explained with given input values -> 10.19866 = sqrt(1.7E-05*(890^2*10.63^2)/(3*0.79*8.23*(cos(0.5235987755982)^2))).

FAQ

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

The RMS Voltage using Area of X-section(3-phase 3-wire OS) formula is defined as the square root of the time average of the voltage squared and is represented as V_rms = sqrt(ρ*(P^2*L^2)/(3*A*P_loss*(cos(Φ)^2))) or 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 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, Length of Overhead AC Wire is the total length of the wire from one end to other 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(3-Phase 3-Wire OS)?

The RMS Voltage using Area of X-section(3-phase 3-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(Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(cos(Phase Difference)^2))). To calculate RMS Voltage using Area of X-Section(3-Phase 3-Wire OS), you need Resistivity (ρ), Power Transmitted (P), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ). With our tool, you need to enter the respective value for Resistivity, Power Transmitted, Length of Overhead AC Wire, 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 Resistivity, Power Transmitted, Length of Overhead AC Wire, 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 -

Root Mean Square Voltage = Power Transmitted/(3*cos(Phase Difference)*Current Overhead AC)

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