RMS Voltage using Line Losses (1-Phase 2-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%
✖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%
✖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%
✖Line Losses is defined as the total losses occurring in an Underground 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 (1-Phase 2-Wire US) [V_rms]

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RMS Voltage using Line Losses (1-Phase 2-Wire US) Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Evaluating ... ...

V_rms = 10.7054538237776

STEP 3: Convert Result to Output's Unit

10.7054538237776 Volt --> No Conversion Required

FINAL ANSWER

10.7054538237776 ≈ 10.70545 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.020 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Current and Voltage Calculators

Maximum Voltage using Area of X-Section (1-Phase 2-Wire US)

LaTeX Go Maximum Voltage Underground AC = sqrt((4*Length of Underground AC Wire*Resistivity*(Power Transmitted^2))/(Area of Underground AC Wire*Line Losses*(cos(Phase Difference))^2))

Maximum Voltage using Volume of Conductor Material (1-Phase 2-Wire US)

LaTeX Go Maximum Voltage Underground AC = sqrt(8*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*Volume Of Conductor*(cos(Phase Difference))^2))

Load Current (1-Phase 2-Wire US)

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

RMS Voltage(1-Phase 2-Wire US)

LaTeX Go Root Mean Square Voltage = Maximum Voltage Underground AC/sqrt(2)

RMS Voltage using Line Losses (1-Phase 2-Wire US) Formula

LaTeX Go

What is the value of maximum voltage and volume of conductor material in 1-phase 2-wire system?

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

How to Calculate RMS Voltage using Line Losses (1-Phase 2-Wire US)?

RMS Voltage using Line Losses (1-Phase 2-Wire US) calculator uses Root Mean Square Voltage = 2*Power Transmitted*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 (1-Phase 2-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 Line Losses (1-Phase 2-Wire US) using this online calculator? To use this online calculator for RMS Voltage using Line Losses (1-Phase 2-Wire US), enter Power Transmitted (P), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ) and hit the calculate button. Here is how the RMS Voltage using Line Losses (1-Phase 2-Wire US) calculation can be explained with given input values -> 10.70545 = 2*300*sqrt(2*1.7E-05*24/(1.28*2.67))/cos(0.5235987755982).

FAQ

What is RMS Voltage using Line Losses (1-Phase 2-Wire US)?

The RMS Voltage using Line Losses (1-Phase 2-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*sqrt(2*ρ*L/(A*P_loss))/cos(Φ) or Root Mean Square Voltage = 2*Power Transmitted*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 (1-Phase 2-Wire US)?

The RMS Voltage using Line Losses (1-Phase 2-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*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 (1-Phase 2-Wire US), you need Power Transmitted (P), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground 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 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/sqrt(2)
Root Mean Square Voltage = sqrt((2*Length of Underground AC Wire*Resistivity*(Power Transmitted^2))/(Area of Underground AC Wire*Line Losses*((cos(Phase Difference))^2)))
Root Mean Square Voltage = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor))

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