This is great! xkcd and electronics - infinite 1 ohm resistor grid problem

ELECTRONERD

Joined May 26, 2009
1,146
It's simpler than it seems, you just exclude the surrounding resistors outside the two points and find the total resistance. I'm thinking its going to be 6Ω. On the top, you'll find the original circuit and below you'll find the equivalent circuit.
 

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thatoneguy

Joined Feb 19, 2009
6,349
Oh no. This may be another Airplane on a treadmill...

I can only see a max of 1.5Ω using the eliminate all outside, but there is an infinite number in parallel connected, making the minimum near zero... :D

Sorry for posting this in the wrong area, BeenThere!

When I saw this, I was instantly reminded of you guys and that I haven't been back here in a while.
 

gerty

Joined Aug 30, 2007
1,248
I agree with beenthere, too many parallel paths, and they cannot be ignored.
 

Ratch

Joined Mar 20, 2007
1,068
ELECTRONERD,

It's simpler than it seems,
No its not.

you just exclude the surrounding resistors outside the two points and find the total resistance.
No you don't.

beenthere and gerty,

Gotta be close to 0 with all those paths in parallel.
Faulty reasoning. Those outer paths have increasing resistance.

To the Ineffable All,

See this link http://sites.google.com/site/resistorgrid/node2 . This shows the solution for a single diagonal, but the method can be extended to the "knight's move" nodes. As all you members of the Ineffable All can see, the problem is not trivial.

Ratch
 

ELECTRONERD

Joined May 26, 2009
1,146
I assumed the same current path, but apparently I have the decimal point in the wrong place. Maybe someone can actually construct the seven array of resistors and measure it. I dont have any 1Ω resistors :D
 

beenthere

Joined Apr 20, 2004
15,808
By measurement, 1.42 ohms. .95 ohm corner-to-corner for one square. Those infinite alternate paths cancel their effects.
 

Thread Starter

thatoneguy

Joined Feb 19, 2009
6,349
By measurement, 1.42 ohms. .95 ohm corner-to-corner for one square. Those infinite alternate paths cancel their effects.
How long did it take you to solder together an infinite number of resistors, and how did you get so many?
 

beenthere

Joined Apr 20, 2004
15,808
That was just for 7 resistors. The external paths make it like the Rt should tend towards 0, but every parallel infinity has a series infinity counteracting it
 

Wendy

Joined Mar 24, 2008
21,840
I suspect (without knowing) it resembles calculas, in that it approaches a limit. So if you go 3 or 4 layers out and calculate it you will be very close to the answer.
 

Wendy

Joined Mar 24, 2008
21,840
I remember an engineer telling me about sheet resistors (we were making them for substrates on modules). Basically the measurement on a flat sheet is per square. If you increase the size of the square the resistance stays the same, though the wattage goes up. If you put 2 squares (a rectangle) side by side it's 2X the resistance.
 
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