Calculating Equivalent Resistance in Coated Substrate Circuits

[Tanveer Saleh]

Hello I have a question to ask you. Your help will be highly appreciated. Kindly refer to a scenario where a substrate material ‘B’ is coated both side with a coating material ‘A’. The whole thing is then connected to a voltage source. Here B is poorly conductive and A is highly conductive.


If I want to apply Ohm’s law in the above circuit can I assume that there are 3 resistance in parallel (Namely top coating Ra,middle substrateRb,bottom coatingRa)?

And can I further calculate the Req by combining these 3 resistance?

If so then can we conclude that effective electrical resistance can be reduced if it is coated with high conductive material?

How do I calculate the effective resistivity (of the combined coated material)?

Your help would be highly appreciated. Thanks a lot in advance.

 

[AJ Bentley]

I'm not sure I understand your description.
It sounds like a simple 'sandwich' where the electricity is set to flow top-to-bottom.

i.e. in - bread - lettuce - bread - out

In which case, the resistances are in series not parallel and I can't make any sense of the rest of the question.

 

[Tanveer Saleh]

Hello AJ Bentley,
Thanks for the reply.
pls see the attached file for the circuit config.

 

[AJ Bentley]

The final resistance of such an arrangement would depend very strongly on the precise size and shape of each part and on exactly how the connections are made to it.

Very roughly, you can say that there are three parallel paths for the electricity, two passing through the outside materials (All material A) and one passing through the middle (material A then B then A again). But as I said, to calculate resistance values for each path using resistivity would be complicated.

To answer your second question: Putting conductive material round a poor conductor does not change it's intrinsic resistivity, it simply provides a short circuit.
You can't talk about the resistivity of a composite. The concept doesn't make sense in that context. It is a value given to homogeneous materials to allow resistance to be calculated for different shapes and sizes. You could calculate a number certainly - but the number would have no value.
It's like talking about the density of 'water with lumps of lead in it'.