# Calculating resistance between two bolts connected to a metal plate

1. Oct 25, 2008

### foges

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

Given is a metal plate with two metal bolts attached to it, the attachement is assumed to be idealy conducting. A current I flows between the two bolts. Find a general formula for the Resistance between the two bolts (depending upon: a) the thickness of the plate (delta) b) the radius of the Bolt (r) c) the distance between the center-points of both bolts (l) d) and the specific conductivity of the metal that the plate is made of (kappa))

Here is what it looks like:

___________________________________
|aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa|
|aaaaaaaaaaaaaaaaaa[COLOR="#black"][/COLOR]l [COLOR="#black"]aaaaaaaaaaaaaaa[/COLOR]|
|[COLOR="#black"]aaaaaa[/COLOR]<----------------------->[COLOR="#black"]aaaaaa[/COLOR]|
|aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa|
|[COLOR="#black"]aaaaaa[/COLOR]O[COLOR="#black"]aaaaaaaaaaaaaaaaaaaaa[/COLOR]O[COLOR="#black"]aaaa[/COLOR]|
|[COLOR="#black"]aaaaa[/COLOR]<>[COLOR="#black"]aaaaaaaaaaaaaaaaaaaaa[/COLOR]<>[COLOR="#black"]aaa[/COLOR]|
| aaaaa2r [COLOR="#black"]aaaaaaaaaaaaaaaaaaa[/COLOR]2r[COLOR="#black"]aaaaa|[/COLOR]
|[COLOR="#black"]aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa[/COLOR]|
|__________________________________|

Edit: ignore the white a's. i tried making them spaces, but the BB removed the spaces

2. Relevant equations

Here is the answer, but how do you get there:

R = ln( 2(l-r)/ (2r) )/( pi * kappa * delta)

3. The attempt at a solution

the ln() must come from integrating one over circumference: 1/( r * 2 * pi) from (2r) to (2(l-r)) but why?

Thanks

Last edited: Oct 25, 2008