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'.

 

[sardar]

Hello, thank you for your question. When calculating equivalent resistance in coated substrate circuits, it is important to consider the properties of each material and how they affect the overall resistance. In this scenario, the substrate material 'B' is poorly conductive while the coating material 'A' is highly conductive. This means that there will be a significant difference in resistance between the two materials.

To answer your first question, yes, you can assume that there are three resistances in parallel in this circuit. The top and bottom coatings, Ra, will have a lower resistance compared to the middle substrate, Rb. However, it is important to note that the overall resistance will also depend on the thickness of the coatings and the material properties of each component.

To calculate the equivalent resistance, you can use the formula for parallel resistors: 1/Req = 1/Ra + 1/Rb + 1/Ra. By combining these three resistances, you can determine the overall resistance of the coated substrate circuit.

In terms of the effective resistivity of the combined coated material, this can be calculated by considering the resistivity of each individual material and the thickness of the coatings. The effective resistivity will be lower than that of the poorly conductive substrate material, as the highly conductive coating materials will reduce the overall resistance.

In conclusion, coating a poorly conductive substrate material with a highly conductive material can reduce the overall resistance of the circuit. However, the specific calculations for the effective resistivity will depend on the properties and thickness of the coatings used. I hope this helps answer your question. Best of luck with your research.