I am so confused! How do I solve this resistor grid problem I found?

-live wire-

Joined Dec 22, 2017
912
I have tried and am very confused. How does one solve it?

Marley

Joined Apr 4, 2016
387
Thought I recognized XKCD. The answer is all over the internet. Use a search engine!
EDIT: Now after having a look on the internet, I now know the answer. But I'm not telling you!
Clue: Think about the currents flowing into and out of the points.
Another clue: Doesn't matter which two points you use, the answer is always the same!

Last edited:

Analog Ground

Joined Apr 24, 2019
446
The resistor sheet problem is kind of like this from XKCD: Ozymandias

BTW: XKCD reproduction policy:

"Note: You are welcome to reprint occasional comics pretty much anywhere (presentations, papers, blogs with ads, etc). If you're not outright merchandizing, you're probably fine. Just be sure to attribute the comic to xkcd.com."

Marley

Joined Apr 4, 2016
387
It's a bit like that mathematical joke:
An infinite number of mathematicians go into a bar. The first one says "I'll have a pint, please". Second one says "I'll have a half". And so on. How many pints does the barman serve in total?

Janis59

Joined Aug 21, 2017
1,245
Isd this a homework? Then the right place is in another subchapter of this site. But generally, ANY resistor chain may be solved by number of methods studiued at class 11 secondary school, spring semester. It are 1) sequential branch by branch unitions leading to alone equivalent resistance. Method is simple, but long and not universal enough; 2) Y to delta transformation and delta to Y transformation useful specially for inbanaced bridges calculation; 3) Kirhoff (Kirchoff) equation system where one goes around the circuit branch by branch. Method is absolutely universal, however count of separate equations are killingly much thus without of matrix calculus and MatCad one must die instantly. And its enough to make a mistake of sign even in one member then all the job may be condemned; 4) Thevenin equivalent theorem - absolute universal, absolute simple, absolute effective; 5) Northon equivalent theorem - may say the all best about too. Just take a school book and read it about, the example about ethernal grid is one classical task analysed rather in any of physics electricity books.

-live wire-

Joined Dec 22, 2017
912
Isd this a homework? Then the right place is in another subchapter of this site. But generally, ANY resistor chain may be solved by number of methods studiued at class 11 secondary school, spring semester. It are 1) sequential branch by branch unitions leading to alone equivalent resistance. Method is simple, but long and not universal enough; 2) Y to delta transformation and delta to Y transformation useful specially for inbanaced bridges calculation; 3) Kirhoff (Kirchoff) equation system where one goes around the circuit branch by branch. Method is absolutely universal, however count of separate equations are killingly much thus without of matrix calculus and MatCad one must die instantly. And its enough to make a mistake of sign even in one member then all the job may be condemned; 4) Thevenin equivalent theorem - absolute universal, absolute simple, absolute effective; 5) Northon equivalent theorem - may say the all best about too. Just take a school book and read it about, the example about ethernal grid is one classical task analysed rather in any of physics electricity books.
No it's not homework, just something I found interesting. I don't really know much calculus, and have not heard of these equations/fomulas.

Thought I recognized XKCD. The answer is all over the internet. Use a search engine!
EDIT: Now after having a look on the internet, I now know the answer. But I'm not telling you!
Clue: Think about the currents flowing into and out of the points.
Another clue: Doesn't matter which two points you use, the answer is always the same!
I googled it and all of the results seem to use calculus.

It's a bit like that mathematical joke:
An infinite number of mathematicians go into a bar. The first one says "I'll have a pint, please". Second one says "I'll have a half". And so on. How many pints does the barman serve in total?
If you are saying it's an infinite geometric series, then that kind of helps. But how do I figure out which way the current would flow and start simplifying? Also, the approaches on the internet use calculus, not an infinite geometric series. So what would the solution be?

ci139

Joined Jul 11, 2016
1,696

Tonyr1084

Joined Sep 24, 2015
5,568

Analog Ground

Joined Apr 24, 2019
446
Small quibble. The original diagram asks "what's the equivalent resistance between the two marked nodes?". Equivalent to what? Shouldn't it be "what's the resistance between the two marked nodes?"?

Joined Jul 18, 2013
22,049
It's a bit like that mathematical joke:
An infinite number of mathematicians go into a bar. The first one says "I'll have a pint, please". Second one says "I'll have a half". And so on. How many pints does the barman serve in total?
Depends if it is Imperial or US measure!
Max.

Joined Jul 18, 2013
22,049
I have tried and am very confused. How does one solve it?
Reminds me of the old one we were often posed.
A cube made up of 1 ohm resistors, what is the resitance between diagonal corners of the cube?
Max.

Mark Hughes

Joined Jun 14, 2016
409
Reminds me of the old one we were often posed.
A cube made up of 1 ohm resistors, what is the resitance between diagonal corners of the cube?
Max.
That one's a lot easier to solve -- it's just a series of linear equations.

You basically sketch out a schematic with a virtual voltage source (just make one up, it'll cancel out later) and then use Kirchoff's laws to generate the series of equations. (Loop rule - delta V in a loop is 0, Current rule -- current in = current out of a point)