Calculate the velocity factor of a coaxial cableused as a transmission line, with thecharacterisc impedance of 50 ohms,capacitance is 40 pF/m, and inductance equal to50 μH/m.

The velocity factor (VF) of a coaxial cable is a measure of how fast a signal travels through the cable compared to the speed of light in a vacuum. It can be calculated using the following formula:

\[
VF = \frac{1}{\sqrt{L \cdot C}}
\]

Where:
- \( L \) is the inductance per unit length (in henries per meter, H/m),
- \( C \) is the capacitance per unit length (in farads per meter, F/m).

### Given:
- Inductance \( L = 50 \, \mu H/m = 50 \times 10^{-6} \, H/m \),
- Capacitance \( C = 40 \, pF/m = 40 \times 10^{-12} \, F/m \).

Now let's calculate the velocity factor:

\[
VF = \frac{1}{\sqrt{50 \times 10^{-6} \times 40 \times 10^{-12}}}
\]

First, calculate the product of \( L \) and \( C \):

\[
L \cdot C = 50 \times 10^{-6} \times 40 \times 10^{-12} = 2 \times 10^{-15}
\]

Now, calculate the square root:

\[
\sqrt{L \cdot C} = \sqrt{2 \times 10^{-15}} = 1.414 \times 10^{-7}
\]

Finally, calculate the velocity factor:

\[
VF = \frac{1}{1.414 \times 10^{-7}} \approx 7.07 \times 10^6
\]

Since the speed of light is approximately \( 3 \times 10^8 \) meters per second, the velocity factor is typically expressed as a ratio, meaning:

\[
VF = \frac{1}{1.414} \approx 0.707
\]

Thus, the velocity factor of the coaxial cable is **0.707** or **70.7%** of the speed of light.

Would you like more details or have any further questions?

Here are some related questions you might be interested in:
1. How does the dielectric material of the coaxial cable affect the velocity factor?
2. What is the significance of the characteristic impedance in transmission lines?
3. How is the velocity of propagation related to the frequency of the signal?
4. What are the practical consequences of a low velocity factor in data transmission?
5. How do you calculate the phase velocity in a coaxial cable?

**Tip:** The velocity factor is heavily influenced by the dielectric constant of the material inside the coaxial cable. Lower dielectric constants result in higher velocity factors.

Calculate the velocity factor of a coaxial cable used as a transmission line, with the characteristic impedance of 50 ohms, capacitance is 40 pF/m, and inductance equal to 50 μH/m.

Learn how to calculate the velocity factor of a coaxial cable used as a transmission line, with 50 ohms characteristic impedance, 40 pF/m capacitance, and 50 μH/m inductance. This detailed solution includes key formulas and concepts in electromagnetic theory. Suitable for undergraduate electrical engineering students.

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