RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point 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%
✖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%
✖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 Line Losses (Single-Phase Two-Wire Mid-Point OS) [V_rms]

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Formula

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RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS)

Formula

`"V"_{"rms"} = sqrt(("P"^2)*2*"ρ"*"L")/("A"*"P"_{"loss"}*cos("Φ")^2)`

Example

`"3.469828V"=sqrt((("890W")^2)*2*"0.000017Ω*m"*"10.63m")/("0.79m²"*"8.23W"*cos("30°")^2)`

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RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = sqrt((Power Transmitted^2)*2*Resistivity*Length of Overhead AC Wire)/(Area of Overhead AC Wire*Line Losses*cos(Phase Difference)^2)
V_rms = sqrt((P^2)*2*ρ*L)/(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.
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.
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.
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: 890 Watt --> 890 Watt No Conversion Required
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
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

V_rms = 3.46982768253166

STEP 3: Convert Result to Output's Unit

3.46982768253166 Volt --> No Conversion Required

FINAL ANSWER

3.46982768253166 ≈ 3.469828 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power System » Overhead AC Supply » 1-Φ 2-Wire Mid Point Earthed System » Current & Voltage » RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS)

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< 8 Current & Voltage Calculators

Maximum Voltage using Area of X-section(Single-Phase Two-Wire Mid-Point Earthed OS)

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 Line Losses (Single-Phase Two-Wire Mid-Point OS)

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

RMS Voltage using Area of X-Section(Single-Phase Two-Wire Mid-Point Earthed OS)

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)

Maximum Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS)

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

Maximum Voltage using Load Current (Single-Phase Two-Wire Mid-Point OS)

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

Load Current(Single-Phase Two-Wire Mid-Point Earthed)

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

RMS Voltage using Load Current (Single-Phase Two-Wire Mid-Point OS)

Go Root Mean Square Voltage = Power Transmitted/(sqrt(2)*Current Overhead AC*cos(Phase Difference))

Maximum Voltage(Single-Phase Two-Wire Mid-Point Earthed)

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

RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS) Formula

What is the value of maximum voltage and volume of conductor material in this system?

The volume of conductor material required in this system is 1/2cos²θ 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 √2v_m.

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

RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS) calculator uses Root Mean Square Voltage = sqrt((Power Transmitted^2)*2*Resistivity*Length of Overhead AC Wire)/(Area of Overhead AC Wire*Line Losses*cos(Phase Difference)^2) to calculate the Root Mean Square Voltage, RMS Voltage using Line Losses (single-Phase two-Wire Mid-Point 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 Two-Wire Mid-Point OS) using this online calculator? To use this online calculator for RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS), enter Power Transmitted (P), Resistivity (ρ), 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 Line Losses (Single-Phase Two-Wire Mid-Point OS) calculation can be explained with given input values -> 3.469828 = sqrt((890^2)*2*1.7E-05*10.63)/(0.79*8.23*cos(0.5235987755982)^2).

FAQ

What is RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS)?

RMS Voltage using Line Losses (single-Phase two-Wire Mid-Point OS)formula is defined as the square root of the time average of the voltage squared and is represented as V_rms = sqrt((P^2)*2*ρ*L)/(A*P_loss*cos(Φ)^2) or Root Mean Square Voltage = sqrt((Power Transmitted^2)*2*Resistivity*Length of Overhead AC Wire)/(Area of Overhead AC Wire*Line Losses*cos(Phase Difference)^2). Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end, 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 & 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 (Single-Phase Two-Wire Mid-Point OS)?

RMS Voltage using Line Losses (single-Phase two-Wire Mid-Point OS)formula is defined as the square root of the time average of the voltage squared is calculated using Root Mean Square Voltage = sqrt((Power Transmitted^2)*2*Resistivity*Length of Overhead AC Wire)/(Area of Overhead AC Wire*Line Losses*cos(Phase Difference)^2). To calculate RMS Voltage using Line Losses (Single-Phase Two-Wire Mid-Point OS), you need Power Transmitted (P), Resistivity (ρ), 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 Power Transmitted, Resistivity, 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 Power Transmitted, Resistivity, Length of Overhead AC Wire, 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 = 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/(sqrt(2)*Current Overhead AC*cos(Phase Difference))

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