Resistance of a fructum-shaped bar

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SUMMARY

The discussion focuses on calculating the electrical resistance of a frustum-shaped bar using the formula R = ρ * (l/A). The user is given the radii of both ends but lacks the length of the bar. They propose calculating the volume of the frustum using V = (π * l / 3) * (r²₂ - r²₁) and treating it as a cube to derive the area A = V/l for resistance calculation. The user seeks clarification on this approach and expresses uncertainty about the frustum's properties.

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  • Understanding of electrical resistance and the formula R = ρ * (l/A)
  • Knowledge of geometric shapes, specifically frustums and their volume calculation
  • Familiarity with mathematical manipulation of formulas
  • Basic principles of physics related to material properties
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  • Study the derivation and application of the volume formula for a frustum
  • Learn how to manipulate resistance formulas in electrical engineering
  • Research the properties of frustums in geometry and their applications
  • Explore numerical methods for solving resistance problems with variable dimensions
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Students and professionals in physics and engineering, particularly those involved in materials science and electrical engineering, will benefit from this discussion.

Icheb
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I have to calculate the resistance of a bar that is shaped like a fructum and I'm only given the radius of both ends, not its length.

The formula to calculate the resistance in general is

[tex]R = \rho * \frac{l}{A}[/tex]

And the formula for the volume of a fructum is

[tex]V = \frac{\pi * l}{3} (r^2_2 * r_2r_1 * r^2_1)[/tex]

My problem is that I have difficulties incorporating the formula for the volume into the formula for the resistance.

Would it be possible to calculate the volume of the fructum (which would be dependent on l) and treat it like it's a cube with the same volume? That way, I could use [tex]A = \frac{V}{l}[/tex], then divide the volume by l and enter it into the formula for R.

Other than that, I have no idea what approach to take.
 
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Sorry, looked as best I can.

No idea what a fructum is.
 
Sorry, I misspelled it. I meant a frustum. It's like a cone, but with the "sharp" end cut off.
 

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