What is effective conductivity?

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Discussion Overview

The discussion revolves around the concept of "effective" conductivity, particularly in the context of electrical signals in conductors and materials. Participants explore the differences between conductivity and effective conductivity, especially at higher frequencies and in specific materials.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the difference between conductivity and effective conductivity, seeking clarification on the concept.
  • Another participant explains that at higher frequencies, the skin effect limits the depth of penetration of a signal into the conductor, leading to a calculation of effective conducting area based on skin depth.
  • There is a repeated mention of the effective conducting area being less than the total conductor area due to the skin effect.
  • Several participants inquire about the context of the problem, specifically whether it involves AC or DC signals and the type of materials involved (simple or composite).
  • A later reply confirms that the context involves a wave traveling through a lossy dielectric medium, indicating that it is an AC scenario.
  • One participant asserts that if the situation were DC, the considerations would differ.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definitions and contexts of effective conductivity, with some agreement on the implications of the skin effect in AC scenarios. However, the discussion remains unresolved regarding the broader definitions and applications of effective conductivity.

Contextual Notes

The discussion lacks clarity on the assumptions regarding material properties and the specific conditions under which effective conductivity is defined. There are also unresolved questions about the implications of AC versus DC in this context.

Xyius
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What is "effective" conductivity?

In one of my homework problems (This ISNT a homework help question! It is conceptual) It says to find the "effective" conductivity.

What is the difference between conductivity and effective conductivity? Is there any difference?
 
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At higher frequencies, the depth of penetration of a signal into the center conductor of a coaxial cable is limited to the skin depth δ. See http://en.wikipedia.org/wiki/Skin_effect. So if the radius of the center conductor is r, then the effective conducting area is 2 πrδ, which is less than the total conductor area πr2.
 


Bob S said:
At higher frequencies, the depth of penetration of a signal into the center conductor of a coaxial cable is limited to the skin depth δ. See http://en.wikipedia.org/wiki/Skin_effect. So if the radius of the center conductor is r, then the effective conducting area is 2 πrδ, which is less than the total conductor area πr2.


Thanks a lot!
 


Is this AC or DC? Is this in simple or composite materials? What is the context.
 
Vanadium 50 said:
Is this AC or DC? Is this in simple or composite materials? What is the context.

I was given a wave traveling though a lossy dielectric medium in a transmission line. So this is AC.
 


Then Bob's answer is right. If it were DC, it would have been something else.
 

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