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

✖Resistivity is the measure of how strongly a material opposes the flow of current through them.ⓘ Resistivity [ρ]			+10% -10%
✖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%
✖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%
✖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%
✖Volume Of Conductor the 3-dimensional space enclosed by a conductor material.ⓘ Volume Of Conductor [V]			+10% -10%

✖Root Mean Square Voltage is the square root of the time average of the voltage squared.ⓘ RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US) [V_rms]

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Formula

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

Formula

`"V"_{"rms"} = sqrt(4*"ρ"*("P"*"L")^2/("P"_{"loss"}*(cos("Φ"))^2*"V"))`

Example

`"5.416579V"=sqrt(4*"0.000017Ω*m"*("300W"*"24m")^2/("2.67W"*(cos("30°"))^2*"60m³"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor))
V_rms = sqrt(4*ρ*(P*L)^2/(P_loss*(cos(Φ))^2*V))
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 the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.
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.
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.
Volume Of Conductor - (Measured in Cubic Meter) - Volume Of Conductor the 3-dimensional space enclosed by a conductor material.

STEP 1: Convert Input(s) to Base Unit

Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Power Transmitted: 300 Watt --> 300 Watt 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
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Volume Of Conductor: 60 Cubic Meter --> 60 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_rms = sqrt(4*ρ*(P*L)^2/(P_loss*(cos(Φ))^2*V)) --> sqrt(4*1.7E-05*(300*24)^2/(2.67*(cos(0.5235987755982))^2*60))

Evaluating ... ...

V_rms = 5.41657879502335

STEP 3: Convert Result to Output's Unit

5.41657879502335 Volt --> No Conversion Required

FINAL ANSWER

5.41657879502335 ≈ 5.416579 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Underground AC Supply » 1-Φ 2-Wire System » Current & Voltage » RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US)

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< 17 Current & Voltage Calculators

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

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))

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

Go 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)))

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

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))

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

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

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

Go 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)

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

Go Root Mean Square Voltage = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor))

Load Current using Constant (1-Phase 2-Wire US)

Go Current Underground AC = sqrt(Constant Underground AC*Line Losses/(2*Resistivity*(Length of Underground AC Wire*cos(Phase Difference))^2))

Maximum Voltage using Constant (1-Phase 2-Wire US)

Go Maximum Voltage Underground AC = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Constant Underground AC*Line Losses))

RMS Voltage using Constant (1-Phase 2-Wire US)

Go Root Mean Square Voltage = 2*Power Transmitted*Length of Underground AC Wire*sqrt(2*Resistivity/(Line Losses*Constant Underground AC))

RMS Voltage using Resistance (1-Phase 2-Wire US)

Go Maximum Voltage Underground AC = 2*Power Transmitted*sqrt(2*Resistance Underground AC/Line Losses)/cos(Phase Difference)

Maximum Voltage using Resistance (1-Phase 2-Wire US)

Go Maximum Voltage Underground AC = 2*Power Transmitted*sqrt(Resistance Underground AC/Line Losses)/cos(Phase Difference)

Load Current using Line Losses (1-Phase 2-Wire US)

Go Current Underground AC = sqrt(Line Losses*Area of Underground AC Wire/(2*Resistivity*Length of Underground AC Wire))

Maximum Voltage using Load Current (1-Phase 2-Wire US)

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

Load Current (1-Phase 2-Wire US)

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

RMS Voltage using Load Current (1-Phase 2-Wire US)

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

Load Current using Resistance (1-Phase 2-Wire US)

Go Current Underground AC = sqrt(Line Losses/(2*Resistance Underground AC))

RMS Voltage(1-Phase 2-Wire US)

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

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

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 Volume of Conductor Material (1-Phase 2-Wire US)?

RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US) calculator uses Root Mean Square Voltage = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor)) to calculate the Root Mean Square Voltage, The RMS Voltage using Volume of Conductor Material (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 Volume of Conductor Material (1-Phase 2-Wire US) using this online calculator? To use this online calculator for RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US), enter Resistivity (ρ), Power Transmitted (P), Length of Underground AC Wire (L), Line Losses (P_loss), Phase Difference (Φ) & Volume Of Conductor (V) and hit the calculate button. Here is how the RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US) calculation can be explained with given input values -> 5.416579 = sqrt(4*1.7E-05*(300*24)^2/(2.67*(cos(0.5235987755982))^2*60)).

FAQ

What is RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US)?

The RMS Voltage using Volume of Conductor Material (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 = sqrt(4*ρ*(P*L)^2/(P_loss*(cos(Φ))^2*V)) or Root Mean Square Voltage = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor)). Resistivity is the measure of how strongly a material opposes the flow of current through them, 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, 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, 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 & Volume Of Conductor the 3-dimensional space enclosed by a conductor material.

How to calculate RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US)?

The RMS Voltage using Volume of Conductor Material (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 = sqrt(4*Resistivity*(Power Transmitted*Length of Underground AC Wire)^2/(Line Losses*(cos(Phase Difference))^2*Volume Of Conductor)). To calculate RMS Voltage using Volume of Conductor Material (1-Phase 2-Wire US), you need Resistivity (ρ), Power Transmitted (P), Length of Underground AC Wire (L), Line Losses (P_loss), Phase Difference (Φ) & Volume Of Conductor (V). With our tool, you need to enter the respective value for Resistivity, Power Transmitted, Length of Underground AC Wire, Line Losses, Phase Difference & Volume Of Conductor 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 Underground AC Wire, Line Losses, Phase Difference & Volume Of Conductor. We can use 5 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 = Power Transmitted/(Current Underground AC*cos(Phase Difference))
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)
Root Mean Square Voltage = 2*Power Transmitted*Length of Underground AC Wire*sqrt(2*Resistivity/(Line Losses*Constant Underground AC))

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