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Angle using Line Losses (3 Phase 4 Wire US) Formula

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GoAngle using Area of X-Section (3 Phase 4 Wire US) Formula

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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. Check FAQs

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

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

Angle using Line Losses (3 Phase 4 Wire US) Example

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Here is how the Angle using Line Losses (3 Phase 4 Wire US) equation looks like with Values.

Here is how the Angle using Line Losses (3 Phase 4 Wire US) equation looks like with Units.

Here is how the Angle using Line Losses (3 Phase 4 Wire US) equation looks like.

88.8451 = a \cos ((\frac{300}{230}) \cdot \sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{2.67 \cdot 1.28}})

88.8451° = a \cos ((\frac{300W}{230V}) \cdot \sqrt{2 \cdot 1.7E-5Ω*m \cdot \frac{24m}{2.67W \cdot 1.28m²}})

88.8451 = a \cos ((\frac{300}{230}) \cdot \sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{2.67 \cdot 1.28}})

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Angle using Line Losses (3 Phase 4 Wire US) Solution

Follow our step by step solution on how to calculate Angle using Line Losses (3 Phase 4 Wire US)?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Φ = a \cos ((\frac{300W}{230V}) \cdot \sqrt{2 \cdot 1.7E-5Ω*m \cdot \frac{24m}{2.67W \cdot 1.28m²}})

Next Step Prepare to Evaluate

∴

Φ = a \cos ((\frac{300}{230}) \cdot \sqrt{2 \cdot 1.7E-5 \cdot \frac{24}{2.67 \cdot 1.28}})

Next Step Evaluate

∴

Φ = 1.55064019034272rad

Next Step Convert to Output's Unit

∴

Φ = 88.8451384500174°

LAST Step Rounding Answer

∴

Φ = 88.8451°

Angle using Line Losses (3 Phase 4 Wire US) Formula Elements

Variables

Functions

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

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

Maximum Voltage Underground AC

Maximum Voltage Underground 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 Underground AC

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

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

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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

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 Phase Difference

Go Angle using Load Current (3 Phase 4 Wire US)

Φ = a \cos (\sqrt{6} \cdot \frac{P}{3 \cdot V m \cdot I})

Go Angle using Area of X-Section (3 Phase 4 Wire US)

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

Other formulas in Wire Parameters category

Go Area of X-Section using Volume of Conductor Material (3 Phase 4 Wire US)

A = \frac{V}{(3.5) \cdot L}

Go Line Losses using Volume of Conductor Material (3 Phase 4 Wire US)

P loss = 7 \cdot {(P)}^{2} \cdot ρ \cdot \frac{{(L)}^{2}}{{(V m \cdot \cos (Φ))}^{2} \cdot V}

How to Evaluate Angle using Line Losses (3 Phase 4 Wire US)?

Angle using Line Losses (3 Phase 4 Wire US) evaluator uses Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Line Losses*Area of Underground AC Wire))) to evaluate the Phase Difference, The Angle using Line Losses (3 phase 4 wire US) formula is defined as the phase angle between reactive and active power. Phase Difference is denoted by Φ symbol.

How to evaluate Angle using Line Losses (3 Phase 4 Wire US) using this online evaluator? To use this online evaluator for Angle using Line Losses (3 Phase 4 Wire US), enter Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistivity (ρ), Length of Underground AC Wire (L), Line Losses (P_loss) & Area of Underground AC Wire (A) and hit the calculate button.

FAQs on Angle using Line Losses (3 Phase 4 Wire US)

What is the formula to find Angle using Line Losses (3 Phase 4 Wire US)?

The formula of Angle using Line Losses (3 Phase 4 Wire US) is expressed as Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Line Losses*Area of Underground AC Wire))). Here is an example- 5090.451 = acos((300/230)*sqrt(2*1.7E-05*24/(2.67*1.28))).

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

With Power Transmitted (P), Maximum Voltage Underground AC (V_m), Resistivity (ρ), Length of Underground AC Wire (L), Line Losses (P_loss) & Area of Underground AC Wire (A) we can find Angle using Line Losses (3 Phase 4 Wire US) using the formula - Phase Difference = acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Line Losses*Area of Underground AC Wire))). This formula also uses Cosine (cos)Inverse Cosine (acos), Square Root (sqrt) function(s).

What are the other ways to Calculate Phase Difference?

Here are the different ways to Calculate Phase Difference-

Phase Difference=acos(sqrt(6)*Power Transmitted/(3*Maximum Voltage Underground AC*Current Underground AC))
Phase Difference=acos((Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire*Line Losses)))

Can the Angle using Line Losses (3 Phase 4 Wire US) be negative?

No, the Angle using Line Losses (3 Phase 4 Wire US), measured in Angle cannot be negative.

Which unit is used to measure Angle using Line Losses (3 Phase 4 Wire US)?

Angle using Line Losses (3 Phase 4 Wire US) is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle using Line Losses (3 Phase 4 Wire US) can be measured.

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Angle using Line Losses (3 Phase 4 Wire US) Formula

​GoAngle using Load Current (3 Phase 4 Wire US) Formula

​GoAngle using Area of X-Section (3 Phase 4 Wire US) Formula

Angle using Line Losses (3 Phase 4 Wire US) Example

Angle using Line Losses (3 Phase 4 Wire US) Solution

Angle using Line Losses (3 Phase 4 Wire US) Formula Elements

Other Formulas to find Phase Difference

Other formulas in Wire Parameters category

How to Evaluate Angle using Line Losses (3 Phase 4 Wire US)?

FAQs on Angle using Line Losses (3 Phase 4 Wire US)

Variable Name

GoAngle using Load Current (3 Phase 4 Wire US) Formula

GoAngle using Area of X-Section (3 Phase 4 Wire US) Formula