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RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Formula

GoRMS Voltage using Load Current (Single-Phase Three-Wire OS) Formula

GoRMS Voltage using Line Losses (Single-Phase Three-Wire OS) 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 = \sqrt{\frac{2 \cdot L \cdot ρ \cdot (P^{2})}{A \cdot P loss \cdot ({(\cos (Φ))}^{2})}}

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

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Example

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Here is how the RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) equation looks like with Values.

Here is how the RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) equation looks like with Units.

Here is how the RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) equation looks like.

7.6622 = \sqrt{\frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{0.79 \cdot 8.23 \cdot ({(\cos (30))}^{2})}}

7.6622V = \sqrt{\frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{0.79m² \cdot 8.23W \cdot ({(\cos (30°))}^{2})}}

7.6622 = \sqrt{\frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{0.79 \cdot 8.23 \cdot ({(\cos (30))}^{2})}}

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RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Solution

Follow our step by step solution on how to calculate RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V rms = \sqrt{\frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{0.79m² \cdot 8.23W \cdot ({(\cos (30°))}^{2})}}

Next Step Convert Units

∴

V rms = \sqrt{\frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{0.79m² \cdot 8.23W \cdot ({(\cos (0.5236rad))}^{2})}}

Next Step Prepare to Evaluate

∴

V rms = \sqrt{\frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{0.79 \cdot 8.23 \cdot ({(\cos (0.5236))}^{2})}}

Next Step Evaluate

∴

V rms = 7.66217386495464V

LAST Step Rounding Answer

∴

V rms = 7.6622V

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) 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

Length of Overhead AC Wire

Length of Overhead 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 Overhead AC Wire

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

Power Transmitted

Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end.

Symbol: P

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Power Transmitted

Area of Overhead AC Wire

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

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Overhead AC Wire

Line Losses

Line Losses is defined as the total losses occurring in an Overhead 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 using Load Current (Single-Phase Three-Wire OS)

V rms = \frac{P}{I \cdot \cos (Φ)}

Go RMS Voltage using Line Losses (Single-Phase Three-Wire OS)

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

Other formulas in Current and Voltage category

Go Load Current(Single-Phase Three-Wire OS)

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

Go Maximum Voltage(Single-Phase Three-Wire OS)

V m = (2) \cdot V ac

How to Evaluate RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) evaluator uses Root Mean Square Voltage = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))) to evaluate the Root Mean Square Voltage, The RMS Voltage using Area of X-Section(single-Phase three-Wire OS) 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 Area of X-Section(Single-Phase Three-Wire OS) using this online evaluator? To use this online evaluator for RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS), enter Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ) and hit the calculate button.

FAQs on RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)

What is the formula to find RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

The formula of RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) is expressed as Root Mean Square Voltage = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))). Here is an example- 7.662174 = sqrt((2*10.63*1.7E-05*(890^2))/(0.79*8.23*((cos(0.5235987755982))^2))).

How to calculate RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

With Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Line Losses (P_loss) & Phase Difference (Φ) we can find RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) using the formula - Root Mean Square Voltage = sqrt((2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(Area of Overhead AC Wire*Line Losses*((cos(Phase Difference))^2))). 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=Power Transmitted/(Current Overhead AC*cos(Phase Difference))
Root Mean Square Voltage=(Power Transmitted/cos(Phase Difference))*sqrt(Resistivity*Length of Overhead AC Wire/(Area of Overhead AC Wire*Line Losses))

Can the RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) be negative?

No, the RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS), measured in Electric Potential cannot be negative.

Which unit is used to measure RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) 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 Area of X-Section(Single-Phase Three-Wire OS) can be measured.

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RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Formula

​GoRMS Voltage using Load Current (Single-Phase Three-Wire OS) Formula

​GoRMS Voltage using Line Losses (Single-Phase Three-Wire OS) Formula

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Example

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Solution

RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS) Formula Elements

Other Formulas to find Root Mean Square Voltage

Other formulas in Current and Voltage category

How to Evaluate RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)?

FAQs on RMS Voltage using Area of X-Section(Single-Phase Three-Wire OS)

Variable Name

GoRMS Voltage using Load Current (Single-Phase Three-Wire OS) Formula

GoRMS Voltage using Line Losses (Single-Phase Three-Wire OS) Formula