Solved

Posted on 2009-02-22

We have a grid of N*N resistors, like this:

http://zlateski.com/static/_media/6/5/1/2/hnybded53ou83bu73n475000000284m350.jpg

And we want to calculate the resistance between A and B (picture).

Each resistor is 1 ohm...

What formula for n can I use? Or what algorithm?

http://zlateski.com/static

And we want to calculate the resistance between A and B (picture).

Each resistor is 1 ohm...

What formula for n can I use? Or what algorithm?

9 Comments

you may be able to convert the grid into one that you can analyze more easily by

adding connections which do not change the resistance of the grid because there will be no current trough the added connections because they connect points with the same voltage.

Take a look at http://www.geocities.com/f

Your problem is find the total resistance across the major diagonal of the entire grid composed of all the mini-grids.

Clue:

Isn't that the sum of the mini-grid diagonals within it?

You already know the resistance across one of the mini-diagonals.

Now you know enough to come up with a simple algorithm for the resistance a n by n grid of 1-ohm resistors as a function of the number "n".

R of the major diagonal for 1-ohm resistors approaches 2 n / pi where n is the number of squares in the side of a n by n grid.

http://www.geocities.com/frooha/grid/node2.html is a different problem

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