I think I'm on the verge of a breakthrough on this problem, but it's just not coming.(adsbygoogle = window.adsbygoogle || []).push({});

Please tell me where my approach goes wrong or whether I'm correct but don't know how to integrate the resulting equation properly.

The problem reads: A circular disk of radius r and thickness d is made of material with resistivity p. Show that the resistance between the points a and b (a is the front of the curved side of the cylinder and b is the backside) is independent of the radius and is given by R = [pi]p/2d.

I start out with R = pL/A where L is length and A is the surface area perpendicular to the direction of the flow of the charges.

dR = pdx/A

A = d * the width of the rectangular surface area for the little sliver of the cylinder, which is given by the equation of the circle y = 2[squ] (r^2-(x-r)^2).

Is this correct?

I then integrate R = p/2d[inte] dx/[squ](r^2-(x-r)^2) from 0 to 2r?

This gives me R= [pi]pr^2/8d.

Obviously wrong!!!

Any suggestions would be greatly appreciated.

Thanks.

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# Resistance: Non-constant Surface Area

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