There is an infinite laddershaped 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 20061103 10:00:46 