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Mister Resistor (Posted on 2006-11-03) Difficulty: 2 of 5
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.

See The Solution Submitted by Larry    
Rating: 3.5000 (2 votes)

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Solution Solution | Comment 1 of 7

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
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