Potential of coaxial with two dielectrics?

In summary, you have correctly calculated the potential of the ungrounded outer conducting sheath of a coaxial cable with given parameters to be 107.5 kV when the inner conductor has a voltage of \frac{220}{\sqrt{3}} kV.
  • #1
lam58
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The question asks to find the potential of the ungrounded outer conducting sheath of a coaxial cable when the inner conductor has a voltage of [tex]\frac{220}{\sqrt{3}} kV[/tex].

Coaxial conditions:
i) Central copper conductor of diameter 4.8 cm.
ii) Insulating layer of XPLE of thickness 2.3 cm and relative permittivity k = 2.2.
iii) Conducting lead sheath of thickness 2.9 mm.
iv) Insulating HDPE layer of thickness 5 mm and k = 2.4.
v) Outer coating negligible thickness in contact with soil.

My attempt:

I found the XPLE to have a capacitance of 310.70x10^-12 F/m.

To find the potential I assumed the charge between both conductors would equal 0, thus the charge on the inner conductor = -'ve charge on sheath. Hence I can use Q = CV to find the charge:

[tex] 310.73x10^{-12} * \frac{220}{\sqrt{3}} = 3.95x10^{-5} C [/tex]

Then to find potential between the two I use:

[tex] v = \frac{-Q}{2\pi\epsilon_0\epsilon_r}.ln(b/a)[/tex]

[tex]\Rightarrow v = \frac{-Q}{2\pi * 8.8x10^{-12} * 2.4}.ln(0.0789/0.0739) = -19.5 kV[/tex]

Which implies the potential on the lead sheath = [tex]\frac{220}{\sqrt{3}} kV + -19.5kV = 107.5kV[/tex]

Have I done this right?
 
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  • #2


Yes, your calculations and approach seem correct. You have correctly used the capacitance formula to find the charge on the inner conductor and then used the potential formula to find the potential on the outer conducting sheath. Your final answer of 107.5 kV seems reasonable based on the given parameters. However, it is always a good idea to double check your calculations and make sure you have used the correct units throughout.
 

1. What is a coaxial cable?

A coaxial cable is a type of electrical cable that is commonly used to transmit high-frequency signals. It consists of a central conductor, surrounded by a dielectric insulator, and an outer conductor. This structure allows for efficient transmission of signals while minimizing signal loss and interference.

2. How does a coaxial cable with two dielectrics work?

A coaxial cable with two dielectrics works by using two layers of insulating material between the central conductor and the outer conductor. This allows for an even more efficient transmission of signals, as the two dielectrics have different properties that can further reduce signal loss and interference.

3. What are the benefits of using a coaxial cable with two dielectrics?

Some of the benefits of using a coaxial cable with two dielectrics include improved signal quality, lower signal loss, and better resistance to interference. This can result in a more reliable and efficient transmission of high-frequency signals, making it a popular choice for various applications such as telecommunications and data transmission.

4. What are the different types of dielectrics used in coaxial cables?

The most commonly used dielectrics in coaxial cables are air, foam, and solid dielectrics. Air is the most commonly used due to its low dielectric constant and low loss, while foam is used for its ability to reduce signal reflection. Solid dielectrics, such as polyethylene and Teflon, are used for their higher dielectric constants and better insulation properties.

5. Can a coaxial cable with two dielectrics be used for both analog and digital signals?

Yes, a coaxial cable with two dielectrics can be used for both analog and digital signals. The efficient transmission and low signal loss make it suitable for a wide range of applications, including both analog and digital signal transmission. However, the specific type and properties of the dielectrics used may vary depending on the type of signal being transmitted.

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