Resistance of a hollow aluminum cylinder

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SUMMARY

The discussion centers on calculating the electrical resistance of a hollow aluminum cylinder with a length of 2.50m, an inner radius of 3.20 cm, and an outer radius of 4.60 cm. The resistance is determined using the formula R=(ρ/2πL)ln(R/r), where R is the outer radius, r is the inner radius, and L is the length of the cylinder. Participants clarify that the resistance should not be assumed to be the same as from end to end, as the current flows radially between the inner and outer surfaces. The correct application of the formula is essential for accurate results.

PREREQUISITES
  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with cylindrical coordinates and geometry
  • Knowledge of logarithmic functions in physics equations
  • Basic principles of equipotential surfaces in electrical circuits
NEXT STEPS
  • Study the derivation and application of the resistance formula R=(ρ/2πL)ln(R/r)
  • Explore the concept of equipotential surfaces in more detail
  • Learn about the properties of hollow conductors and their electrical characteristics
  • Investigate practical applications of resistance calculations in engineering
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Students studying electrical engineering, physics enthusiasts, and professionals involved in materials science or electrical design will benefit from this discussion.

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Homework Statement



A hollow aluminum cylinder is 2.50m long and has an inner radius of 3.20 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface.

At room temperature, what will an ohmmeter read if it is connected between the inner and outer surfaces?

Homework Equations



R=4.60cm
r=3.20cm

R=[tex]\rho[/tex]L/A

and possibly

R=([tex]\rho[/tex]/2piL)*ln(R/r)

The Attempt at a Solution



Well, the first part of the question (not asked here) was to find the resistance from one end of the hollow cylinder to the other (the faces). I found that: 2.00*10-5 [tex]\Omega[/tex]s. The problem does not say that the current is flowing radially through the cylinder though, but is that to be assumed for doing this second part? Or not? I plugged everything into the second equation, but the answer is wrong. Should the resistance be the same as it is from end to end? Is it 0?
*confused*
 
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It is a curious question. Connected exactly how to the two surfaces? Connection at infinitely small points will lead to infinite resistance, so it seems we must assume the contact is spread, equipotentially, across each entire cylindrical surface.

That should mean your second equation is appropriate. See e.g. https://www.miniphysics.com/uy1-resistance-of-a-cylindrical-resistor.html.
Can't say any more without seeing your working and/or answer.
 

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