Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Calculating resistance



How to solve this problem? Find the resistance R between
two small silver-painted dots separated by a distance L on
an infinite sheet of a carbon-impregnated paper. The uniform
thickness of the paper, d, and its conductivity, rho, are given.
Ignore the contact resistance of silver dots.

R(L,d,rho) = ????

My first idea was to think about the rim-to-rim resistance
when the sheet is circular and when one dot is in the center
while another "dot" is painted along the circumference. The
radius of the central dot is r1 while the radius of the outer
"dot" (the radius of the sheet) is r2. This problem is likely
to be less complicated and I know how I would start
solving it. But how can this help me to find the resistance
R between the two dots in the central region of a very
large circular sheet?

This problem has probably been solved somewhere. But
I have no idea how to begin solving it. One doesn't need
calculus to find the resistance for a long narrow strip of a
specified length L and of a constant width w<<L. But the
problem of an infinite sheet (many parallel resistors between
the two small dots) seems to be much more complicated.
Ludwik Kowalski