What Resistance Does an Ohmmeter Read in an Infinite 2x2 Resistor Array?

[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?

 

[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

 

[vsage]

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

 

[TenaliRaman]

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

And if u are asking abt the answer being spread on the net , then yes google will be helpful to find the answer to this question ...

The version i gave is really hard , i don't 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

 

[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 :)

Tenali, can you explain how you got your answer?

 

[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

 

[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.