Cylindrical Shell Resistor

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Homework Statement



A copper resistor has the shape of a cylindrical shell. What is the resistance of this resistor if its length is 1m, its inner radius is 0.1cm, and its outer radius is 0.2 cm? What is the radius of a solid wire of circular cross section with the same length and the same resistance?

The Attempt at a Solution



R = int(dR)
dR = (rho)dr / (2(pi)Lr)

R = int((rho)dr / (2(pi)Lr), from r1 to r2)
R =(rho)dr / (2(pi)L) * ln(r2/r1)

With the given info, I came to a resistance R of 1.8 x 10^-8 ohms, equivalent wire radius 0.55m, but apparently the correct answer is 1.8 x 10^-3 ohms, equivalent wire length 0.17 cm. I'm not sure what I'm doing wrong.

Thanks for the help again, guys!
 

Answers and Replies

  • #2
haruspex
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Your equations don't look right for this problem at all. Maybe they're for current flowing out radially? This problem is much simpler: the current is flowing along the cylinder. (I admit that could be made clearer.) The resistance per unit length should be ρ/A, where A is the cross-sectional area.
 
  • #3
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I had assumed that the current was flowing out radially. Apparently this textbook is notorious for being very vague on what exactly it wants. Thanks for the quick response!
 

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