# Infinite array of resistors

1. Nov 20, 2004

### DrKareem

... |
... R
... |
-R- --R
... |
... R

Suppose you have an infite array (2by2) of resistors, each of value let's 1k.

If you place the an ohmeter accres one resistor, what resistance will the ohmeter read?

2. Nov 20, 2004

### TenaliRaman

::
Its a pretty old one and this one probably is the simplest of them all.
Simply applying superposition principle gives 1/2 ohm.
::

A much harder one,
What is the resistance across opposite vertices of the 2x2 array?

People have ofcourse extended this to many different dimensions and its all spread across the net at different places.

-- AI

Last edited: Nov 20, 2004
3. Nov 21, 2004

### vsage

This wouldn't have anything to do with google would it?

4. Nov 22, 2004

### TenaliRaman

Google in its interviews hasnt asked for anything like this, if u meant it that way.

The version i gave is really hard , i dont know of elementary techniques to solve it , and the one found on the net was too complex .... i just posted it in the hope that maybe someone has some bright ideas for a simple proof for my version of the question ...

-- AI

5. Nov 22, 2004

### DrKareem

hehe, just the same reason of me posting this. I got it off a magazine, and i didn't even get the solution :P

I'd give a hint though, he injected a current at one node, and then he tried to collect another current accress another node (no the same current) and then see the voltage across that resistor, and of course he already knows the current passin through it so he knows the R :)

6. Nov 24, 2004

### TenaliRaman

Dr Kareem,
Whatever u found in that article was the thing i did tho in a more sophisticated manner its called the superposition principle. I put across voltages across the terminals , calculate closed circuit voltages and then find the effective resistance.

Do u know the superposition principle?

-- AI

7. Nov 30, 2004

### Cosmo16

We did this on a computer simulation in digital electronics. (Of course we used a fixed amt. of resistors) We kept adding a box of resistors around it anoter and another and another. Can't remember t he answer though.