How to calculate resistivity of coaxial cylinder

[jacobier]

Is it any model on resisivity of two tightly-attached coaxial cylinder? For example, a copper core wire is coated with layer of aluminum. How to calculate the final resistivity along axis?

 

[Hassan2]

There is a method on this but that's related to the radial resistance ( the insulator is consider imperfect).

The resistance along axis seems much simpler to me. Just plug in the cross-sectional area, length and conductivity of both the core and the shield in the related formula ( [itex]R=\frac{l}{σS}[/itex]), and add together the resistance of the core and the shield. Hopefully I'm not missing something!

 

[haruspex]

add together the resistance of the core and the shield.

I don't think you mean add the resistances together. These are in parallel here, so it's the conductances that add.

Btw, in the OP, you mean resistance, not resistivity. Resistivity is a property of the material, independent of shape and size.

 

[jacobier]

Thank you very much. Actually I mean "resistance". I have been looking for solution for this for a long time. Probably the problem is not as complicated as I thought, no one have interest to talked about that.

 

[Hassan2]

I don't think you mean add the resistances together. These are in parallel here, so it's the conductances that add.

Actually what I had in mind is that the two , with a load connected to the end form a series circuit, that's why i added the " resistances" together. (OP asked about resistance along the axis.)

 

[Hassan2]

Thank you very much. Actually I mean "resistance". I have been looking for solution for this for a long time. Probably the problem is not as complicated as I thought, no one have interest to talked about that.

check this for radial resistance:
http://webphysics.davidson.edu/physlet_resources/bu_semester2/c09_resistance_calc.html

 

[haruspex]

Actually what I had in mind is that the two , with a load connected to the end form a series circuit, that's why i added the " resistances" together. (OP asked about resistance along the axis.)

I get the feeling you have the wrong model for the set-up. There's a copper core and an Al coating. The axial current will consist of some current in each, in parallel. At each end there may be some radial flow, but I'm assuming we can ignore that.

 

[marcusl]

Haruspex is correct that the conductances add. To do it with resistance instead, separately calculate the resistance of a length of the copper core and the same length of hollow Al tube. The total resistance is the parallel combination of the two, using the usual formula for resistors in parallel.

 

[Hassan2]

marcusl and haruspex,

In the attached figure, aren't the series resistances of the core and the shield added together to give the cable resistance? Sorry I understand that this is very simple question but I would like to know what I am not getting.

Thanks.

 

[haruspex]

Ah - it was me that had the wrong set-up in mind. Yes, they're in series.

 

[nasu]

marcusl and haruspex,

In the attached figure, aren't the series resistances of the core and the shield added together to give the cable resistance? Sorry I understand that this is very simple question but I would like to know what I am not getting.

Thanks.

But this is a coaxial cable and not what is described in the OP.
The copper core is not "coated with layer of aluminum" but they are separated by insulator. The OP describes a two tightly attached coaxial cylinders.

 

[Hassan2]

You are right nasu. I got it wrong from the beginning. They are parallel then. Many thanks.