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Receiving End Voltage using Sending End Current (LTL) Formula

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Receiving end voltage is the voltage developed at the receiving end of a long transmission line. Check FAQs

V r = (I s - I r \cdot \cosh (γ \cdot L)) \cdot (\frac{Z 0}{\sinh (γ \cdot L)})

V_r - Receiving End Voltage?I_s - Sending End Current?I_r - Receiving End Current?γ - Propagation Constant?L - Length?Z₀ - Characteristic Impedance?

Receiving End Voltage using Sending End Current (LTL) Example

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Here is how the Receiving End Voltage using Sending End Current (LTL) equation looks like with Values.

Here is how the Receiving End Voltage using Sending End Current (LTL) equation looks like with Units.

Here is how the Receiving End Voltage using Sending End Current (LTL) equation looks like.

8.88 = (3865.49 - 6.19 \cdot \cosh (1.24 \cdot 3)) \cdot (\frac{48.989}{\sinh (1.24 \cdot 3)})

8.88kV = (3865.49A - 6.19A \cdot \cosh (1.24 \cdot 3m)) \cdot (\frac{48.989Ω}{\sinh (1.24 \cdot 3m)})

8.88 = (3865.49 - 6.19 \cdot \cosh (1.24 \cdot 3)) \cdot (\frac{48.989}{\sinh (1.24 \cdot 3)})

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Receiving End Voltage using Sending End Current (LTL) Solution

Follow our step by step solution on how to calculate Receiving End Voltage using Sending End Current (LTL)?

FIRST Step Consider the formula

V r = (I s - I r \cdot \cosh (γ \cdot L)) \cdot (\frac{Z 0}{\sinh (γ \cdot L)})

Next Step Substitute values of Variables

∴

V r = (3865.49A - 6.19A \cdot \cosh (1.24 \cdot 3m)) \cdot (\frac{48.989Ω}{\sinh (1.24 \cdot 3m)})

Next Step Prepare to Evaluate

∴

V r = (3865.49 - 6.19 \cdot \cosh (1.24 \cdot 3)) \cdot (\frac{48.989}{\sinh (1.24 \cdot 3)})

Next Step Evaluate

∴

V r = 8879.99793237519V

Next Step Convert to Output's Unit

∴

V r = 8.87999793237519kV

LAST Step Rounding Answer

∴

V r = 8.88kV

Receiving End Voltage using Sending End Current (LTL) Formula Elements

Variables

Functions

Receiving End Voltage

Receiving end voltage is the voltage developed at the receiving end of a long transmission line.

Symbol: V_r

Measurement: Electric PotentialUnit: kV

Note: Value can be positive or negative.

Formulas to find Receiving End Voltage

Sending End Current

Sending end current is the voltage at the sending end of a short transmission line.

Symbol: I_s

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Sending End Current

Receiving End Current

Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.

Symbol: I_r

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Receiving End Current

Propagation Constant

Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Propagation Constant

Length

Length is defined as the end to end distance of the conductor used in a long transmission line.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length

Characteristic Impedance

Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.

Symbol: Z₀

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Characteristic Impedance

sinh

The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function.

Syntax: sinh(Number)

cosh

The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2.

Syntax: cosh(Number)

Other formulas in Current and Voltage category

Go Sending End Voltage (LTL)

V s = V r \cdot \cosh (γ \cdot L) + Z 0 \cdot I r \cdot \sinh (γ \cdot L)

Go Sending End Current (LTL)

I s = I r \cdot \cosh (γ \cdot L) + (\frac{V r \cdot \sinh (γ \cdot L)}{Z 0})

Go Receiving End Current using Sending End Voltage (LTL)

I r = \frac{V s - (V r \cdot \cosh (γ \cdot L))}{Z 0 \cdot \sinh (γ \cdot L)}

Go Receiving End Current using Sending End Current (LTL)

I r = \frac{I s - (V r \cdot \frac{\sinh (γ \cdot L)}{Z 0})}{\cosh (γ \cdot L)}

How to Evaluate Receiving End Voltage using Sending End Current (LTL)?

Receiving End Voltage using Sending End Current (LTL) evaluator uses Receiving End Voltage = (Sending End Current-Receiving End Current*cosh(Propagation Constant*Length))*(Characteristic Impedance/sinh(Propagation Constant*Length)) to evaluate the Receiving End Voltage, The Receiving End Voltage using Sending End Current (LTL) formula is defined as the voltage at the receiving end of the long transmission lines. Receiving End Voltage is denoted by V_r symbol.

How to evaluate Receiving End Voltage using Sending End Current (LTL) using this online evaluator? To use this online evaluator for Receiving End Voltage using Sending End Current (LTL), enter Sending End Current (I_s), Receiving End Current (I_r), Propagation Constant (γ), Length (L) & Characteristic Impedance (Z₀) and hit the calculate button.

FAQs on Receiving End Voltage using Sending End Current (LTL)

What is the formula to find Receiving End Voltage using Sending End Current (LTL)?

The formula of Receiving End Voltage using Sending End Current (LTL) is expressed as Receiving End Voltage = (Sending End Current-Receiving End Current*cosh(Propagation Constant*Length))*(Characteristic Impedance/sinh(Propagation Constant*Length)). Here is an example- 0.00888 = (3865.49-6.19*cosh(1.24*3))*(48.989/sinh(1.24*3)).

How to calculate Receiving End Voltage using Sending End Current (LTL)?

With Sending End Current (I_s), Receiving End Current (I_r), Propagation Constant (γ), Length (L) & Characteristic Impedance (Z₀) we can find Receiving End Voltage using Sending End Current (LTL) using the formula - Receiving End Voltage = (Sending End Current-Receiving End Current*cosh(Propagation Constant*Length))*(Characteristic Impedance/sinh(Propagation Constant*Length)). This formula also uses Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).

Can the Receiving End Voltage using Sending End Current (LTL) be negative?

Yes, the Receiving End Voltage using Sending End Current (LTL), measured in Electric Potential can be negative.

Which unit is used to measure Receiving End Voltage using Sending End Current (LTL)?

Receiving End Voltage using Sending End Current (LTL) is usually measured using the Kilovolt[kV] for Electric Potential. Volt[kV], Millivolt[kV], Microvolt[kV] are the few other units in which Receiving End Voltage using Sending End Current (LTL) can be measured.

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Receiving End Voltage using Sending End Current (LTL) Formula

Receiving End Voltage using Sending End Current (LTL) Example

Receiving End Voltage using Sending End Current (LTL) Solution

Receiving End Voltage using Sending End Current (LTL) Formula Elements

Other formulas in Current and Voltage category

How to Evaluate Receiving End Voltage using Sending End Current (LTL)?

FAQs on Receiving End Voltage using Sending End Current (LTL)

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