Re: [Phys-l] Infinite net resistors expression deduction

[Philip Keller <PKeller@holmdelschools.org>]

The method that solves this does not require infinte series sums.  It is reminiscent of the method used to evaluate continuing fractions.

Assign the circuit an equivalent resistance, X.  

Then, notice that the circuit can be though of as (starting from the left) as the two R1 resistors in series with a parallel combination of R3 and the original circuit repeated!

So this:

--R1 ----|----R1----|----
         R3         R3         ...................>>>>
--R1 ----|----R1----|----

Becomes this:

--R1 ----|-------|
         R3         x      
--R1 ----|-------|



Then, the equivalent resistance x = 2R1 + (parallel combination of R3 and x)

which gives:  x = 2R1 + (R3 times x)/(R3 +x)


That will yield a quadratic equation with the solution you stated.



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