Calculating Resistance of Coaxial Cable with Isolator

In summary, the conversation discusses the resistance of a coaxial cable with a copper core and shield, separated by an insulator with specific resistivity ζ. The problem involves determining the resistance of the cable with length L between the core and shield. The attempted solution involves using the equation R= ζ * l/S, but the solution sheet suggests using dR= ζ * dr/2πrL. There is some confusion about the area and thickness of the element, but it is clarified that the area is 2πrL and the thickness is dr. The conversation also mentions the direction of current flow and the need to integrate over r to get the resistance of a radial sliver.
  • #1
bolzano95
89
7

Homework Statement


Coaxial cable has radius a of copper core and radius b of copper shield. Between there is an isolator with specific resistance ζ. What is the resistance of this cable with length L between the core and the shield?

Homework Equations


First, I tried to solve this like this:
[tex]R= ζ \cdot \frac{l}{S}[/tex]
In our case the length is dr, and therefore I suppose that the area of this ring is 2πrdr:
[tex]dR= ζ \cdot \frac{dr}{2πrdr}[/tex]


The Attempt at a Solution


The solution sheet says: [tex]dR= ζ \cdot \frac{dr}{2πrL}[/tex]
I know that something is wrong with my equation, because dr goes away and then I cannot integrate from a to b. But why is in the solution L instead of dr? As I understand problem instruction L= b-a. And therefore L=dr which doesn't make sense to me.
 
Physics news on Phys.org
  • #2
The current flows in the radial direction. A volume element is ##dV=rdrd\theta dz.## The resistance of this is ##dR=\frac{\zeta dr}{rd\theta dz}## I would integrate over ##r## first to get the resistance of a radial sliver, ##dR_{sliver}##. I can do that because the stacked elements ##dV## in the radial direction are in series and their resistances add. Then note that all such slivers are in parallel which is how they should be added.
 
Last edited:
  • #3
bolzano95 said:
Between there is an isolator with specific resistance ζ.
should be ".. insulator with specific resistivity ... "
 
  • #4
True. Insulator with specific resistivity ζ. Thanks.
 
  • #5
I got an answer from fellow student that the area of the element is 2πrL and the thickness of the element is dr. But I wouldn't say so. I would suppose that the area of the element is 2πrdr. What am I missing?
 
  • #6
bolzano95 said:
I would suppose that the area of the element is 2πrdr. What am I missing?
Please read and understand post #2 to see what you are missing.
 

Related to Calculating Resistance of Coaxial Cable with Isolator

What is the resistance of coaxial cable?

The resistance of coaxial cable is dependent on several factors, including the length of the cable, the material it is made of, and the frequency of the signal being transmitted. Generally, the resistance of coaxial cable ranges from 50-75 ohms.

How does the resistance of coaxial cable affect signal quality?

The resistance of coaxial cable can affect signal quality by causing signal loss, also known as attenuation. This can result in a weaker or distorted signal reaching the end destination. To minimize signal loss, it is important to use high-quality coaxial cable and to keep the cable length as short as possible.

What factors can impact the resistance of coaxial cable?

The resistance of coaxial cable can be affected by various factors, including the type and thickness of the cable's inner and outer conductors, the dielectric material used between the conductors, and the frequency and strength of the signal being transmitted. Additionally, any damage or wear to the cable can also impact its resistance.

How can the resistance of coaxial cable be measured?

The resistance of coaxial cable can be measured using a multimeter or an impedance analyzer. These tools can provide a precise measurement of the cable's resistance and can help identify any potential issues or damage to the cable.

Why is it important to consider the resistance of coaxial cable?

The resistance of coaxial cable is an important factor to consider when setting up a communication or transmission system. A high resistance can result in signal loss and affect the overall performance of the system. By understanding and properly managing the resistance of coaxial cable, you can ensure optimal signal quality and reliable communication.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
236
  • Introductory Physics Homework Help
Replies
16
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Electromagnetism
Replies
26
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
4K
Back
Top