Need to determine resistance of an object

1. Feb 12, 2009

Kruum

1. The problem statement, all variables and given/known data

A material of resistivity p is formed into a solid, truncated cone of height
h and radii r_1 and r_2 at either end. Calculate the resistance of the cone
between the two flat ends.

You can find my awful sketch as a thumbnail.

2. Relevant equations

R=pL/A ,where p is resistivity.

3. The attempt at a solution

I know I need to calculate dR=(p*dy)/(pi*r^2). But I don't know what is r as a function of y.

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Last edited: Feb 12, 2009
2. Feb 12, 2009

Mapes

Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r1 to r2.

Where does the 4 come from in the denominator?

3. Feb 12, 2009

Kruum

Thank you. I'll try your tip. And the 4 was just a typing mistake.

I uploaded the image. It can be found here: http://www.aijaa.com/v.php?i=3584252.jpg

Last edited: Feb 12, 2009
4. Feb 12, 2009

Kruum

This is what I came up with:

r = r2+y*(r1-r2)/h

If I integrate dR, it gives me (p*h)/(pi*r1*r2).

Does that look okay?

Last edited: Feb 12, 2009
5. Feb 12, 2009

Mapes

Looks good.

6. Feb 12, 2009

Kruum

Thanks for the help, Mapes!