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Line Losses using Area of X-Section(3-Phase 3-Wire OS) Formula

GoLine Losses(3-Phase 3-Wire OS) Formula

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

P loss = \frac{2 \cdot L \cdot ρ \cdot (P^{2})}{3 \cdot A \cdot ({V m}^{2}) \cdot ({(\cos (Φ))}^{2})}

P_loss - Line Losses?L - Length of Overhead AC Wire?ρ - Resistivity?P - Power Transmitted?A - Area of Overhead AC Wire?V_m - Maximum Voltage Overhead AC?Φ - Phase Difference?

Line Losses using Area of X-Section(3-Phase 3-Wire OS) Example

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Here is how the Line Losses using Area of X-Section(3-Phase 3-Wire OS) equation looks like with Values.

Here is how the Line Losses using Area of X-Section(3-Phase 3-Wire OS) equation looks like with Units.

Here is how the Line Losses using Area of X-Section(3-Phase 3-Wire OS) equation looks like.

0.0419 = \frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{3 \cdot 0.79 \cdot (62^{2}) \cdot ({(\cos (30))}^{2})}

0.0419W = \frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{3 \cdot 0.79m² \cdot ({62V}^{2}) \cdot ({(\cos (30°))}^{2})}

0.0419 = \frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{3 \cdot 0.79 \cdot (62^{2}) \cdot ({(\cos (30))}^{2})}

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Line Losses using Area of X-Section(3-Phase 3-Wire OS) Solution

Follow our step by step solution on how to calculate Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

FIRST Step Consider the formula

P loss = \frac{2 \cdot L \cdot ρ \cdot (P^{2})}{3 \cdot A \cdot ({V m}^{2}) \cdot ({(\cos (Φ))}^{2})}

Next Step Substitute values of Variables

∴

P loss = \frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{3 \cdot 0.79m² \cdot ({62V}^{2}) \cdot ({(\cos (30°))}^{2})}

Next Step Convert Units

∴

P loss = \frac{2 \cdot 10.63m \cdot 1.7E-5Ω*m \cdot ({890W}^{2})}{3 \cdot 0.79m² \cdot ({62V}^{2}) \cdot ({(\cos (0.5236rad))}^{2})}

Next Step Prepare to Evaluate

∴

P loss = \frac{2 \cdot 10.63 \cdot 1.7E-5 \cdot (890^{2})}{3 \cdot 0.79 \cdot (62^{2}) \cdot ({(\cos (0.5236))}^{2})}

Next Step Evaluate

∴

P loss = 0.0418985705525333W

LAST Step Rounding Answer

∴

P loss = 0.0419W

Line Losses using Area of X-Section(3-Phase 3-Wire OS) Formula Elements

Variables

Functions

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

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

Maximum Voltage Overhead AC

Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.

Symbol: V_m

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Maximum Voltage Overhead AC

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)

Other Formulas to find Line Losses

Go Line Losses(3-Phase 3-Wire OS)

P loss = (3) \cdot ({(I)}^{2}) \cdot R

Other formulas in Wire Parameters category

Go Area of X-Section(3-Phase 3-Wire OS)

A = 2 \cdot (P^{2}) \cdot ρ \cdot \frac{L}{({(\cos (Φ))}^{2}) \cdot P loss \cdot 3 \cdot ({V m}^{2})}

Go Constant(3-Phase 3-Wire OS)

K = \frac{4 \cdot (P^{2}) \cdot ρ \cdot {(L)}^{2}}{P loss \cdot ({V m}^{2})}

How to Evaluate Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

Line Losses using Area of X-Section(3-Phase 3-Wire OS) evaluator uses Line Losses = (2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*((cos(Phase Difference))^2)) to evaluate the Line Losses, The Line Losses using Area of X-section(3-phase 3-wire OS) formula is defined as the loss of electric energy due to the heating of line wires by the current. Line Losses is denoted by P_loss symbol.

How to evaluate Line Losses using Area of X-Section(3-Phase 3-Wire OS) using this online evaluator? To use this online evaluator for Line Losses using Area of X-Section(3-Phase 3-Wire OS), enter Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (V_m) & Phase Difference (Φ) and hit the calculate button.

FAQs on Line Losses using Area of X-Section(3-Phase 3-Wire OS)

What is the formula to find Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

The formula of Line Losses using Area of X-Section(3-Phase 3-Wire OS) is expressed as Line Losses = (2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*((cos(Phase Difference))^2)). Here is an example- 0.041899 = (2*10.63*1.7E-05*(890^2))/(3*0.79*(62^2)*((cos(0.5235987755982))^2)).

How to calculate Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

With Length of Overhead AC Wire (L), Resistivity (ρ), Power Transmitted (P), Area of Overhead AC Wire (A), Maximum Voltage Overhead AC (V_m) & Phase Difference (Φ) we can find Line Losses using Area of X-Section(3-Phase 3-Wire OS) using the formula - Line Losses = (2*Length of Overhead AC Wire*Resistivity*(Power Transmitted^2))/(3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*((cos(Phase Difference))^2)). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Line Losses?

Here are the different ways to Calculate Line Losses-

Line Losses=(3)*((Current Overhead AC)^2)*Resistance Overhead AC

Can the Line Losses using Area of X-Section(3-Phase 3-Wire OS) be negative?

Yes, the Line Losses using Area of X-Section(3-Phase 3-Wire OS), measured in Power can be negative.

Which unit is used to measure Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

Line Losses using Area of X-Section(3-Phase 3-Wire OS) is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Line Losses using Area of X-Section(3-Phase 3-Wire OS) can be measured.

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Line Losses using Area of X-Section(3-Phase 3-Wire OS) Formula

​GoLine Losses(3-Phase 3-Wire OS) Formula

Line Losses using Area of X-Section(3-Phase 3-Wire OS) Example

Line Losses using Area of X-Section(3-Phase 3-Wire OS) Solution

Line Losses using Area of X-Section(3-Phase 3-Wire OS) Formula Elements

Other Formulas to find Line Losses

Other formulas in Wire Parameters category

How to Evaluate Line Losses using Area of X-Section(3-Phase 3-Wire OS)?

FAQs on Line Losses using Area of X-Section(3-Phase 3-Wire OS)

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GoLine Losses(3-Phase 3-Wire OS) Formula