- #1

valarking

- 16

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## Homework Statement

http://www.vkgfx.com/physics/p5.gif [Broken]

## Homework Equations

R = rho*l/A

## The Attempt at a Solution

Initially I thought this would be easy. I could just write the surface area A of the trapezoid by its geometric area formula and multiply it by h. I thought about it though and that doesn't really get the resistance from side a to side b.

So my idea now is to design an integral with x representing the width (from a to b) like this:

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

[tex]= \rho{l}\int_a^b{\frac{dA}{A}}[/tex]

[tex]= \rho{l}\int_a^b{\frac{h}{hx}{dx}}[/tex]

[tex]= \rho{l}\int_a^b{\frac{dx}{x}}[/tex]

which obviously comes out to [tex](\rho{l})*(ln(\frac{b}{a}))[/tex]

I sort of went out on a limb here and I'm not sure if it's correct, does anyone here know if that's the right way to approach this problem? Basically I'm saying that due to the way resistors add in series, I'm adding infinitely many infinitesimal resistor cross sections.

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