There is an infinite ladder-shaped grid of 1Ω resistors connecting adjacent nodes as follows:

What is the electrical resistance between (a) and (b)? Note: in the image, every resistor is 1Ω.

Let Q_n be the equivalent resistor of the
finite ladder of n R_0 (1 ohm) resistors.
Clearly, Q_1 = 3 ohms and the following
relation holds,

              3*Q_n + 2
   Q_(n+1) = ----------- 
               Q_n + 1

As n approaches infinity, Q_n approaches

         2.73205080756888 ohms

Posted by Bractals on 2006-11-03 10:00:46