# How to calculate resistivity of coaxial cylinder

1. Jun 18, 2012

### 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?

2. Jun 19, 2012

### 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 ( $R=\frac{l}{σS}$), and add together the resistance of the core and the shield. Hopefully I'm not missing something!

3. Jun 19, 2012

### haruspex

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.

4. Jun 19, 2012

### 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.

5. Jun 19, 2012

### Hassan2

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.)

6. Jun 19, 2012

### Hassan2

7. Jun 19, 2012

### haruspex

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.

8. Jun 19, 2012

### 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.

9. Jun 19, 2012

### 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.

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Last edited: Jun 20, 2012
10. Jun 20, 2012

### haruspex

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

11. Jun 20, 2012

### nasu

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.

12. Jun 20, 2012

### Hassan2

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