A two-wire air line has the following line parameters: R'= 0.100 (Ω/m), L'= 25 (µ H/m),G'= 0, and C'= 25 (nF/m). For operation at 80 kHz, determine the attenuation constant α .

To determine the attenuation constant \( \alpha \) for a transmission line, we use the following general formula for the attenuation constant of a transmission line:

\[
\alpha = \text{Re} \left( \sqrt{(R' + j \omega L')(G' + j \omega C')} \right)
\]

Where:
- \( R' \) is the resistance per unit length (Ω/m)
- \( L' \) is the inductance per unit length (H/m)
- \( G' \) is the conductance per unit length (S/m)
- \( C' \) is the capacitance per unit length (F/m)
- \( \omega \) is the angular frequency \( \omega = 2 \pi f \), where \( f \) is the frequency (Hz)

We are given the following values:
- \( R' = 0.100 \, \Omega/\text{m} \)
- \( L' = 25 \, \mu\text{H/m} = 25 \times 10^{-6} \, \text{H/m} \)
- \( G' = 0 \, \text{S/m} \)
- \( C' = 25 \, \text{nF/m} = 25 \times 10^{-9} \, \text{F/m} \)
- \( f = 80 \, \text{kHz} = 80 \times 10^3 \, \text{Hz} \)

### Step 1: Calculate the angular frequency \( \omega \)
\[
\omega = 2 \pi f = 2 \pi \times 80 \times 10^3 \, \text{Hz} = 502,654.82 \, \text{rad/s}
\]

### Step 2: Plug in the values into the formula

Since \( G' = 0 \), the formula simplifies to:
\[
\alpha = \text{Re} \left( \sqrt{(R' + j \omega L') j \omega C'} \right)
\]

Let's compute the attenuation constant \( \alpha \) step by step.The attenuation constant \( \alpha \) for the given two-wire air line at 80 kHz is approximately \( 0.00158 \, \text{Np/m} \).

Would you like further details or have any additional questions?

Here are some related questions for deeper understanding:
1. How does the attenuation constant change with frequency?
2. What effect does increasing the resistance per unit length \( R' \) have on the attenuation constant?
3. How does the capacitance per unit length \( C' \) affect the transmission line’s behavior at higher frequencies?
4. What is the physical meaning of the attenuation constant in transmission lines?
5. How would the presence of conductance \( G' \) affect the calculation of \( \alpha \)?

**Tip:** The attenuation constant \( \alpha \) determines how much signal power is lost per unit length due to resistance and dielectric losses in the line.

A two-wire air line has the following line parameters: R' = 0.100 (Ω/m), L' = 25 (µH/m), G' = 0, and C' = 25 (nF/m). For operation at 80 kHz, determine the attenuation constant α.

This detailed solution explains how to calculate the attenuation constant α for a two-wire air line at 80 kHz. Using transmission line theory, we explore key parameters such as R', L', G', C', and the angular frequency ω to determine signal attenuation. Suitable for undergraduate electrical engineering students.

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