RMS Voltage using Load Current Per Phase (3-Phase 3-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%
✖Current underground DC is defined as the current flowing through the overhead ac supply wire.ⓘ Current underground DC [C₁]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%

✖Root Mean Square Voltage is the square root of the time average of the voltage squared.ⓘ RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US) [V_rms]

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Formula

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RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)

Formula

`"V"_{"rms"} = "P"/(3*"C"_{"1"}*cos("θ"))`

Example

`"38.49002V"="300W"/(3*"3A"*cos("30°"))`

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RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta))
V_rms = P/(3*C₁*cos(θ))
This formula uses 1 Functions, 4 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)

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.
Current underground DC - (Measured in Ampere) - Current underground DC is defined as the current flowing through the overhead ac supply wire.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Current underground DC: 3 Ampere --> 3 Ampere No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_rms = P/(3*C₁*cos(θ)) --> 300/(3*3*cos(0.5235987755982))

Evaluating ... ...

V_rms = 38.4900179459751

STEP 3: Convert Result to Output's Unit

38.4900179459751 Volt --> No Conversion Required

FINAL ANSWER

38.4900179459751 ≈ 38.49002 Volt <-- Root Mean Square Voltage

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Underground DC Supply » 3-Wire System » Current & Voltage » RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)

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< 14 Current & Voltage Calculators

RMS Voltage using Area of X-Section (3-Phase 3-Wire US)

Go Root Mean Square Voltage = (2*Power Transmitted/cos(Theta))*sqrt(Resistivity*Length of Wire DC/(Line Losses*Area of underground dc wire))

Maximum Voltage using Area of X-Section (3-Phase 3-Wire US)

Go Maximum Voltage = (Power Transmitted/cos(Theta))*sqrt(2*Resistivity*Length of Wire DC/(Line Losses*Area of underground dc wire))

Maximum Voltage using Volume of Conductor Material (3-Phase 3-Wire US)

Go Maximum Voltage = sqrt(6*Resistivity*(Power Transmitted*Length of Wire DC)^2/(Line Losses*Volume Of Conductor*(cos(Theta))^2))

Maximum Voltage using Area of X-Section (DC Three-Wire US)

Go Maximum Voltage = sqrt(2*(Power Transmitted^2)*Resistivity*Length of Wire DC/(Line Losses*Area of underground dc wire))

Maximum Voltage using Volume of Conductor Material(DC Three-Wire US)

Go Maximum Voltage = sqrt(5*Resistivity*(Power Transmitted*Length of Wire DC)^2/(Line Losses*Volume Of Conductor))

Maximum Voltage using Load Current Per Phase (3-Phase 3-Wire US)

Go Maximum Voltage = (sqrt(6)*Power Transmitted)/(3*Current underground DC*cos(Theta))

Load Current Per Phase (3-Phase 3-Wire US)

Go Current underground DC = (sqrt(6)*Power Transmitted)/(3*Maximum Voltage*cos(Theta))

Maximum Voltage using Line Losses (DC Three-Wire US)

Go Maximum Voltage = sqrt(2*(Power Transmitted^2)*Resistance underground DC/(Line Losses))

RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)

Go Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta))

Load Current using Line Losses (DC Three-Wire US)

Go Current underground DC = sqrt(Line Losses/(2*Resistance underground DC))

Current using Line Losses (3-Phase 3-Wire US)

Go Current underground DC = sqrt(Line Losses/(3*Resistance underground DC))

RMS Voltage Per Phase (3-Phase 3-Wire US)

Go Root Mean Square Voltage = Maximum Voltage/(sqrt(6))

Maximum Voltage using RMS Voltage Per Phase (3-Phase 3-Wire US)

Go Maximum Voltage = sqrt(6)*Root Mean Square Voltage

Maximum Voltage between Each Phase and Neutral (3-Phase 3-Wire US)

Go Maximum phase voltage = Maximum Voltage/sqrt(3)

RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US) Formula

Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta))
V_rms = P/(3*C₁*cos(θ))

What is the value of volume of conductor material in 3-phase 3-wire US?

The volume of conductor material required in this system is 1.5/cos²θ times that of 2-wire d.c.system with the one conductor earthed.

How to Calculate RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)?

RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US) calculator uses Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta)) to calculate the Root Mean Square Voltage, The RMS Voltage using Load Current Per Phase (3-phase 3-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 Load Current Per Phase (3-Phase 3-Wire US) using this online calculator? To use this online calculator for RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US), enter Power Transmitted (P), Current underground DC (C₁) & Theta (θ) and hit the calculate button. Here is how the RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US) calculation can be explained with given input values -> 38.49002 = 300/(3*3*cos(0.5235987755982)).

FAQ

What is RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)?

The RMS Voltage using Load Current Per Phase (3-phase 3-wire US) formula is defined as the square root of the time average of the voltage squared and is represented as V_rms = P/(3*C₁*cos(θ)) or Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta)). 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, Current underground DC is defined as the current flowing through the overhead ac supply wire & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

How to calculate RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US)?

The RMS Voltage using Load Current Per Phase (3-phase 3-wire US) formula is defined as the square root of the time average of the voltage squared is calculated using Root Mean Square Voltage = Power Transmitted/(3*Current underground DC*cos(Theta)). To calculate RMS Voltage using Load Current Per Phase (3-Phase 3-Wire US), you need Power Transmitted (P), Current underground DC (C₁) & Theta (θ). With our tool, you need to enter the respective value for Power Transmitted, Current underground DC & Theta 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, Current underground DC & Theta. We can use 2 other way(s) to calculate the same, which is/are as follows -

Root Mean Square Voltage = Maximum Voltage/(sqrt(6))
Root Mean Square Voltage = (2*Power Transmitted/cos(Theta))*sqrt(Resistivity*Length of Wire DC/(Line Losses*Area of underground dc wire))

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