Re: Computing current between two points from a given resistivity map

On Wed, 16 Apr 2008 20:28:16 -0700 (PDT), Gradient <hmobahi@xxxxxxxxx>
wrote:

Hello Folks,

I am coming from a non-physics discipline, so this might be a naive
question. Given some function f which determines the eletrical
resistance of a body. For example, in 2D, consider a plane having
different resistance at each point x,y and f(x,y) determines the value
of this resistivity.

Now given two points P1=(x1,y1) and P2=(x2,xy). If a unit voltage is
established between these two points, I am interested in knowing the
current passing through these points. Is there any way to come up with
a mathematical function g(u,v,s,t) that for any two given points P1
and P2, g(x0,y0,x1,y1) returns the value of this current for a fixed
given f?

Obviously, if there is no conductivity path, i.e. P1 and P2 are
trapped in a regions with infinite resistance, the current must be
zero. Similarly, if there is a perfect conduction path connecting the
two points, then g must be infinity.

Ultimately, I am interested in n-dimensional instance of this problem,
e.g. a hypercube or whatever shape in a n-dimensional space, for which
f(x1,x2,...xn) determines the resistance at a point in that space and
again two points P1 and P2 are given and g must be computed.

Your help would be highly appreciated.

H.M.
Google "infinite grid of resistors
for a start
w.
.

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