# Electrical resistance

• uq_civediv

#### uq_civediv

lets say i have a block of material, measures a,b,c (length width height) and two wires running in from the top, both with circular cross section, radius r, distance d from the edges

Code:
    ____________________
/  d            d   /|
/<--->O       O<--->/ |
/___________________/  |
|                   |  |
|                   |c |
|                   | /
|___________________|/ b
a

if i were to let electrical current through the block, measure the current and voltage i could find its resistance. But how would i calculate it theoretically if i knew the specific resistance of the material? I have no idea how to do that because i can't imagine how the current would go through the block, i mean through what path.

Or, let's create a more general problem:
lets say i have a space filled with material, measurements infinite (fills up all the space), specific resistance known, and two wires (isolated from the material) (sames as before, circular cross section and radius r) running in from infinity with end points at distance L.

Code:
               <---------->
L
--------------|            |----------------------
--------------|            |----------------------

so what i need to know what the path of the current looks like (its diffuse of course but the further away from the shortest path the less current takes that path)

what I'm actually trying to understand is how electric current moves in human body if i would place electrodes on the skin and apply some voltage, but the geometry of this is nontrivial, which i have not seen before while solvin 'find the resistance of blah blah blah' kind of problems

thanks for any hints

Resistance = rho * L / A
rho is the resistivty of the material
L is the distance between the points
A is the cross section area

Is it AC or DC current? Do the wires run through the whole bulk of the material or are they just probes on the surface?

If they are just probes, then I think you could probably estimate them as cylinders or points of potential and solve something like a Poisson's equation to find the voltage field. If you it is an AC current with wires that penetrate through then it could be easily estimated by solving for the fields of a simple twisted pair transmission line in a lossy medium (provided you estimate the bulk to be infinite).

I think it all depends on how you want to model this.