Calculating Equivalent Resistance in Coated Substrate Circuits

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Discussion Overview

The discussion revolves around calculating the equivalent resistance in a circuit where a poorly conductive substrate material is coated with a highly conductive material. Participants explore the implications of this configuration on resistance and resistivity, considering both theoretical and practical aspects.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that the circuit can be modeled with three resistances in parallel: the top coating, the middle substrate, and the bottom coating.
  • Another participant questions this model, suggesting that the arrangement may actually represent a series configuration rather than parallel.
  • A later reply emphasizes that the final resistance is highly dependent on the size and shape of each material and the connection method.
  • It is noted that while conductive material can surround a poor conductor, it does not change the intrinsic resistivity of the poor conductor, merely providing a short circuit.
  • One participant argues that discussing the resistivity of a composite material in this context is problematic, as resistivity is a property of homogeneous materials.

Areas of Agreement / Disagreement

Participants express differing views on whether the resistances should be treated as parallel or series, indicating a lack of consensus on the correct model for the circuit. Additionally, there is disagreement on the applicability of resistivity concepts to the composite material.

Contextual Notes

Participants highlight the complexity of calculating resistance values due to the dependence on the precise configuration of the materials and the nature of the connections.

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

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Last edited:
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'.
 

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