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I have a few questions regarding my task of calculating AC and DC resistances:

  1. If a cylindrical conductor is made of two different materials, would the conductor's effective resistance be the parallel combination of two resistors? Or do I just add up both resistances that each material provides?

  2. For finding the Impedance \$Z = R + jX\$ (with \$j = \sqrt{-1}\$) do I use \$R_{dc}\$ or \$R_{ac}\$ for \$R\$ in this equation?

  3. I see in some previous questions on the internet that people are saying that AC resistance is always greater than DC resistance due to the Skin Effect. What happens when we factor in the Proximity Effect too? Does this inequality still hold?

I would greatly appreciate any input for these questions. I seem to be confused with the differences between AC Resistance and Impedance. Thank you in advance!

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  • \$\begingroup\$ Think about it. How can we possibly answer this without knowing how the materials are arranged in the cylinder and between what two points you are measuring resistance. This is not a real question. \$\endgroup\$ Nov 16 '12 at 20:43
  • \$\begingroup\$ Yes the first part of the question required more information, but I don't think this question should be down voted because of it, just request more information. \$\endgroup\$
    – Samuel
    Nov 16 '12 at 22:48
  • \$\begingroup\$ @OlinLathrop It seems someone is completely lost and trying to figuring it out. \$\endgroup\$
    – Kortuk
    Nov 16 '12 at 22:54
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1) If you don't know the arrangement, you cannot calculate this.

2) The same equation applies to both AC and DC, in the DC case frequency is zero so the additional component is zeroed. The R in the impedance equation is the real part, the DC resistance. So, at DC, "impedance" = "resistance".

3) Skin effect and proximity effect both depend on the frequency. You can't say AC resistance (impedance) will always be greater. It will depend on the circuit, for instance if there are capacitors in a circuit, impedance can be much lower than DC resistance.

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  • \$\begingroup\$ For 1) the arrangement is basically a circle with the upper 1/4th of its cross sectional area as material1 and bottom 3/4's of it is material2 \$\endgroup\$ Nov 16 '12 at 21:02
  • \$\begingroup\$ They are welded onto each other, thought that would create a parallel combination of 2 resistors. \$\endgroup\$ Nov 16 '12 at 21:05
  • \$\begingroup\$ Do you mean like a pie where a quarter of it has been replaced by a different kind? If that's the case and the voltage is being uniformly applied to the top and bottom of the pie, then yes, those conductors are in parallel. \$\endgroup\$
    – Samuel
    Nov 16 '12 at 22:29
  • \$\begingroup\$ @user1197993 We really need a picture of what you mean, you statement is not very clear. \$\endgroup\$
    – Kortuk
    Nov 16 '12 at 22:56

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