Resistance network problem

[Leigh Palmer <palmer@sfu.ca>]

> More on Chris:  Chris has come up with a program for  his TI-85 calculator
> which will find the resistance of any resistor network that you can design
> as long as the memory of the calculator is not exceeded.  Basically, he
> identifies and numbers all the connection points of the resistor network
> and enters the total number into his calculator.  Then the program asks for
> the reciprocal of the resistance between every possible pair of connection
> points.  When finished entering the data, the calculator outputs the total
> resistance.  We've tried his program on all the complicated resistor
> networks we know of where the total resistance was known and it works.

Well, this is not a finite network problem, but Chris might get a kick
out of it. Consider an infinite square lattice of identical resistors
of resistance R. They are wired together like the lines on a go board.

(a) What is the effective resistance of the lattice as measured across
a single resistor?

(b) What is the effective resistance of the lattice as measured across
two junctions diagonally adjacent to one another on the lattice?

The two problems are not of equal difficulty. I read about Chris and I
think you are fortunate to have him around. I don't quite understand
what his algorithm does based on your description, but it sounds like
it might be a version of Thevenin's theorem he's using, if you mean
that he's omitting one resistor at a time.

Leigh