RMS Voltage using Line Losses (3 Phase 4 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%
✖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%
✖Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it.ⓘ Resistance Underground AC [R]			+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%

✖Root Mean Square Voltage is the square root of the time average of the voltage squared.ⓘ RMS Voltage using Line Losses (3 Phase 4 Wire US) [V_rms]

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RMS Voltage using Line Losses (3 Phase 4 Wire US) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses))
V_rms = (2*P/cos(Φ))*sqrt(R/(6*P_loss))
This formula uses 2 Functions, 5 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.
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.
Resistance Underground AC - (Measured in Ohm) - Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Underground AC line when in use.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Resistance Underground AC: 5 Ohm --> 5 Ohm No Conversion Required
Line Losses: 2.67 Watt --> 2.67 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_rms = (2*P/cos(Φ))*sqrt(R/(6*P_loss)) --> (2*300/cos(0.5235987755982))*sqrt(5/(6*2.67))

Evaluating ... ...

V_rms = 387.056499858092

STEP 3: Convert Result to Output's Unit

387.056499858092 Volt --> No Conversion Required

FINAL ANSWER

387.056499858092 ≈ 387.0565 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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< Power and Power Factor Calculators

Power Transmitted using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(7*Resistivity*(Length of Underground AC Wire)^2))

Power Transmitted using Load Current (3 Phase 4 Wire US)

LaTeX Go Power Transmitted = (3*Maximum Voltage Underground AC*cos(Phase Difference)*Current Underground AC)/sqrt(6)

Angle of PF using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Phase Difference = acos(sqrt((1.75)*Constant Underground AC/Volume Of Conductor))

Power Factor using Volume of Conductor Material (3 Phase 4 Wire US)

LaTeX Go Power Factor = sqrt((1.75)*Constant Underground AC/Volume Of Conductor)

RMS Voltage using Line Losses (3 Phase 4 Wire US) Formula

LaTeX Go

Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses))
V_rms = (2*P/cos(Φ))*sqrt(R/(6*P_loss))

What is the value of maximum voltage in 3-phase 4-wire Underground system?

The maximum voltage between conductors is v_m/√3 so that r.m.s. value of voltage between them is v_m/√6.

How to Calculate RMS Voltage using Line Losses (3 Phase 4 Wire US)?

RMS Voltage using Line Losses (3 Phase 4 Wire US) calculator uses Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses)) to calculate the Root Mean Square Voltage, The RMS Voltage using Line Losses (3 phase 4 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 (3 Phase 4 Wire US) using this online calculator? To use this online calculator for RMS Voltage using Line Losses (3 Phase 4 Wire US), enter Power Transmitted (P), Phase Difference (Φ), Resistance Underground AC (R) & Line Losses (P_loss) and hit the calculate button. Here is how the RMS Voltage using Line Losses (3 Phase 4 Wire US) calculation can be explained with given input values -> 387.0565 = (2*300/cos(0.5235987755982))*sqrt(5/(6*2.67)).

FAQ

What is RMS Voltage using Line Losses (3 Phase 4 Wire US)?

The RMS Voltage using Line Losses (3 phase 4 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/cos(Φ))*sqrt(R/(6*P_loss)) or Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses)). 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, 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, Resistance Underground AC is defined as the property of the wire or line that opposes the flow of current through it & Line Losses is defined as the total losses occurring in an Underground AC line when in use.

How to calculate RMS Voltage using Line Losses (3 Phase 4 Wire US)?

The RMS Voltage using Line Losses (3 phase 4 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/cos(Phase Difference))*sqrt(Resistance Underground AC/(6*Line Losses)). To calculate RMS Voltage using Line Losses (3 Phase 4 Wire US), you need Power Transmitted (P), Phase Difference (Φ), Resistance Underground AC (R) & Line Losses (P_loss). With our tool, you need to enter the respective value for Power Transmitted, Phase Difference, Resistance Underground AC & 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, Resistance Underground AC & Line Losses. We can use 3 other way(s) to calculate the same, which is/are as follows -

Root Mean Square Voltage = (2*Power Transmitted/3*Current Underground AC*cos(Phase Difference))
Root Mean Square Voltage = (2*Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Underground AC Wire/(6*Line Losses*Area of Underground AC Wire))
Root Mean Square Voltage = (Power Transmitted*Length of Underground AC Wire/cos(Phase Difference))*sqrt(Resistivity/(Line Losses*Volume Of Conductor))

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