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Sending End Voltage (LTL) Formula

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Sending end voltage is the voltage at the sending end of a long transmission line. Check FAQs

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

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

Sending End Voltage (LTL) Example

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

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

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

189.5744 = 8.88 \cdot \cosh (1.24 \cdot 3) + 48.989 \cdot 6.19 \cdot \sinh (1.24 \cdot 3)

189.5744kV = 8.88kV \cdot \cosh (1.24 \cdot 3m) + 48.989Ω \cdot 6.19A \cdot \sinh (1.24 \cdot 3m)

189.5744 = 8.88 \cdot \cosh (1.24 \cdot 3) + 48.989 \cdot 6.19 \cdot \sinh (1.24 \cdot 3)

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Sending End Voltage (LTL) Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V s = 8.88kV \cdot \cosh (1.24 \cdot 3m) + 48.989Ω \cdot 6.19A \cdot \sinh (1.24 \cdot 3m)

Next Step Convert Units

∴

V s = 8880V \cdot \cosh (1.24 \cdot 3m) + 48.989Ω \cdot 6.19A \cdot \sinh (1.24 \cdot 3m)

Next Step Prepare to Evaluate

∴

V s = 8880 \cdot \cosh (1.24 \cdot 3) + 48.989 \cdot 6.19 \cdot \sinh (1.24 \cdot 3)

Next Step Evaluate

∴

V s = 189574.381124362V

Next Step Convert to Output's Unit

∴

V s = 189.574381124363kV

LAST Step Rounding Answer

∴

V s = 189.5744kV

Sending End Voltage (LTL) Formula Elements

Variables

Functions

Sending End Voltage

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

Symbol: V_s

Measurement: Electric PotentialUnit: kV

Note: Value can be positive or negative.

Formulas to find Sending End Voltage

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

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

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

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 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)}

Go Receiving End Voltage using Sending End Current (LTL)

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

How to Evaluate Sending End Voltage (LTL)?

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

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

FAQs on Sending End Voltage (LTL)

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

The formula of Sending End Voltage (LTL) is expressed as Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length). Here is an example- 0.189574 = 8880*cosh(1.24*3)+48.989*6.19*sinh(1.24*3).

How to calculate Sending End Voltage (LTL)?

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

Can the Sending End Voltage (LTL) be negative?

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

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

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

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Sending End Voltage (LTL) Formula

Sending End Voltage (LTL) Example

Sending End Voltage (LTL) Solution

Sending End Voltage (LTL) Formula Elements

Other formulas in Current and Voltage category

How to Evaluate Sending End Voltage (LTL)?

FAQs on Sending End Voltage (LTL)

Variable Name