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

GoRMS Voltage(1-Phase 2-Wire US) Formula

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

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Root Mean Square Voltage is the square root of the time average of the voltage squared. Check FAQs

V rms = 2 \cdot P \cdot \frac{\sqrt{2 \cdot ρ \cdot \frac{L}{A \cdot P loss}}}{\cos (Φ)}

V_rms - Root Mean Square Voltage?P - Power Transmitted?ρ - Resistivity?L - Length of Underground AC Wire?A - Area of Underground AC Wire?P_loss - Line Losses?Φ - Phase Difference?

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

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Here is how the RMS Voltage using Line Losses (1-Phase 2-Wire US) equation looks like with Values.

Here is how the RMS Voltage using Line Losses (1-Phase 2-Wire US) equation looks like with Units.

Here is how the RMS Voltage using Line Losses (1-Phase 2-Wire US) equation looks like.

10.7055 = 2 \cdot 300 \cdot \frac{\sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{1.28 \cdot 2.67}}}{\cos (30)}

10.7055V = 2 \cdot 300W \cdot \frac{\sqrt{2 \cdot 1.7E-5Ω*m \cdot \frac{24m}{1.28m² \cdot 2.67W}}}{\cos (30°)}

10.7055 = 2 \cdot 300 \cdot \frac{\sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{1.28 \cdot 2.67}}}{\cos (30)}

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

Follow our step by step solution on how to calculate RMS Voltage using Line Losses (1-Phase 2-Wire US)?

FIRST Step Consider the formula

V rms = 2 \cdot P \cdot \frac{\sqrt{2 \cdot ρ \cdot \frac{L}{A \cdot P loss}}}{\cos (Φ)}

Next Step Substitute values of Variables

∴

V rms = 2 \cdot 300W \cdot \frac{\sqrt{2 \cdot 1.7E-5Ω*m \cdot \frac{24m}{1.28m² \cdot 2.67W}}}{\cos (30°)}

Next Step Convert Units

∴

V rms = 2 \cdot 300W \cdot \frac{\sqrt{2 \cdot 1.7E-5Ω*m \cdot \frac{24m}{1.28m² \cdot 2.67W}}}{\cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

V rms = 2 \cdot 300 \cdot \frac{\sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{1.28 \cdot 2.67}}}{\cos (0.5236)}

Next Step Evaluate

∴

V rms = 10.7054538237776V

LAST Step Rounding Answer

∴

V rms = 10.7055V

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

Variables

Functions

Root Mean Square Voltage

Root Mean Square Voltage is the square root of the time average of the voltage squared.

Symbol: V_rms

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Root Mean Square Voltage

Power Transmitted

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.

Symbol: P

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Power Transmitted

Resistivity

Resistivity is the measure of how strongly a material opposes the flow of current through them.

Symbol: ρ

Measurement: Electric ResistivityUnit: Ω*m

Note: Value can be positive or negative.

Formulas to find Resistivity

Length of Underground AC Wire

Length of Underground AC Wire is the total length of the wire from one end to other end.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Underground AC Wire

Area of Underground AC Wire

Area of Underground AC Wire is defined as the cross-sectional area of the wire of an AC supply system.

Symbol: A

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Area of Underground AC Wire

Line Losses

Line Losses is defined as the total losses occurring in an Underground AC line when in use.

Symbol: P_loss

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Line Losses

Phase Difference

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.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Difference

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Root Mean Square Voltage

Go RMS Voltage(1-Phase 2-Wire US)

V rms = \frac{V m}{\sqrt{2}}

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

V rms = \sqrt{\frac{2 \cdot L \cdot ρ \cdot (P^{2})}{A \cdot P loss \cdot ({(\cos (Φ))}^{2})}}

Other formulas in Current and Voltage category

Go Load Current (1-Phase 2-Wire US)

I = P \cdot \frac{\sqrt{2}}{V m \cdot \cos (Φ)}

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

V m = \sqrt{\frac{4 \cdot L \cdot ρ \cdot (P^{2})}{A \cdot P loss \cdot {(\cos (Φ))}^{2}}}

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

RMS Voltage using Line Losses (1-Phase 2-Wire US) evaluator 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 evaluate 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 evaluate RMS Voltage using Line Losses (1-Phase 2-Wire US) using this online evaluator? To use this online evaluator 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.

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

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

The formula of RMS Voltage using Line Losses (1-Phase 2-Wire US) is expressed as 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). Here is an example- 10.70545 = 2*300*sqrt(2*1.7E-05*24/(1.28*2.67))/cos(0.5235987755982).

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

With Power Transmitted (P), Resistivity (ρ), Length of Underground AC Wire (L), Area of Underground AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ) we can find RMS Voltage using Line Losses (1-Phase 2-Wire US) using the formula - 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). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Root Mean Square Voltage?

Here are the different ways to Calculate Root Mean Square Voltage-

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))

Can the RMS Voltage using Line Losses (1-Phase 2-Wire US) be negative?

No, the RMS Voltage using Line Losses (1-Phase 2-Wire US), measured in Electric Potential cannot be negative.

Which unit is used to measure RMS Voltage using Line Losses (1-Phase 2-Wire US)?

RMS Voltage using Line Losses (1-Phase 2-Wire US) is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which RMS Voltage using Line Losses (1-Phase 2-Wire US) can be measured.

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

​GoRMS Voltage(1-Phase 2-Wire US) Formula

​GoRMS Voltage using Area of X-Section (1-Phase 2-Wire US) Formula

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

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

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

Other Formulas to find Root Mean Square Voltage

Other formulas in Current and Voltage category

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

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

Variable Name

GoRMS Voltage(1-Phase 2-Wire US) Formula

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