RMS Voltage using Line Losses (Single-Phase Three-Wire OS) Calculator

✖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%
✖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 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%

✖Root Mean Square Voltage is the square root of the time average of the voltage squared.ⓘ RMS Voltage using Line Losses (Single-Phase Three-Wire OS) [V_rms]

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RMS Voltage using Line Losses (Single-Phase Three-Wire OS) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = (Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Overhead AC Wire/(Area of Overhead AC Wire*Line Losses))
V_rms = (P/cos(Φ))*sqrt(ρ*L/(A*P_loss))
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 defined as the product of current and voltage phasor in a overhead ac line at the receiving end.
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 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.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 890 Watt --> 890 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 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

V_rms = 5.41797509853976

STEP 3: Convert Result to Output's Unit

5.41797509853976 Volt --> No Conversion Required

FINAL ANSWER

5.41797509853976 ≈ 5.417975 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.011 seconds)

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Home » Engineering » Electrical » Power System » Overhead AC Supply » 1 Φ 3 Wire System » Current and Voltage » RMS Voltage using Line Losses (Single-Phase Three-Wire OS)

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< Current and Voltage Calculators

Maximum Voltage using Area of X-Section(Single-Phase Three-Wire OS)

LaTeX Go Maximum Voltage Overhead AC = sqrt((Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))

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

LaTeX Go Root Mean Square Voltage = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))

Load Current(Single-Phase Three-Wire OS)

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

Maximum Voltage(Single-Phase Three-Wire OS)

LaTeX Go Maximum Voltage Overhead AC = (2)*Voltage Overhead AC

RMS Voltage using Line Losses (Single-Phase Three-Wire OS) Formula

LaTeX Go

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

What is the value of maximum voltage and volume of conductor material in 1-phase 3-wire system?

The volume of conductor material required in this system is 5/8cos²θ times that of 2-wire d.c.system with the one conductor earthed. The maximum voltage between conductors is 2v_m so that r.m.s. value of voltage between them is √2/v_m.

How to Calculate RMS Voltage using Line Losses (Single-Phase Three-Wire OS)?

RMS Voltage using Line Losses (Single-Phase Three-Wire OS) calculator uses Root Mean Square Voltage = (Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Overhead AC Wire/(Area of Overhead AC Wire*Line Losses)) to calculate the Root Mean Square Voltage, The RMS Voltage using Line Losses (single-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 V_rms symbol.

How to calculate RMS Voltage using Line Losses (Single-Phase Three-Wire OS) using this online calculator? To use this online calculator for RMS Voltage using Line Losses (Single-Phase Three-Wire OS), enter Power Transmitted (P), Phase Difference (Φ), Resistivity (ρ), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A) & Line Losses (P_loss) and hit the calculate button. Here is how the RMS Voltage using Line Losses (Single-Phase Three-Wire OS) calculation can be explained with given input values -> 5.417975 = (890/cos(0.5235987755982))*sqrt(1.7E-05*10.63/(0.79*8.23)).

FAQ

What is RMS Voltage using Line Losses (Single-Phase Three-Wire OS)?

The RMS Voltage using Line Losses (single-Phase three-Wire OS) formula is defined as the square root of the time average of the voltage squared and is represented as V_rms = (P/cos(Φ))*sqrt(ρ*L/(A*P_loss)) or Root Mean Square Voltage = (Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Overhead AC Wire/(Area of Overhead AC Wire*Line Losses)). Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end, 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 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.

How to calculate RMS Voltage using Line Losses (Single-Phase Three-Wire OS)?

The RMS Voltage using Line Losses (single-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 = (Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Overhead AC Wire/(Area of Overhead AC Wire*Line Losses)). To calculate RMS Voltage using Line Losses (Single-Phase Three-Wire OS), you need Power Transmitted (P), Phase Difference (Φ), Resistivity (ρ), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A) & Line Losses (P_loss). With our tool, you need to enter the respective value for Power Transmitted, Phase Difference, Resistivity, Length of Overhead AC Wire, Area of Overhead AC Wire & Line Losses 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 Overhead AC Wire, Area of Overhead AC Wire & Line Losses. We can use 2 other way(s) to calculate the same, which is/are as follows -

Root Mean Square Voltage = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2)))
Root Mean Square Voltage = Power Transmitted/(Current Overhead AC*cos(Phase Difference))

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