Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Infinite Grid of Resistors

mathpages.com

Post reply on HN
Print view View original

61–70 of 117 posts

Re: Infinite Grid of Resistors

#61

Post by red75prime »

neepi wrote: post #3

I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.

> The electrical engineer suggests it's not measurable unless you apply current and also asks "when"

Just wait infinite time for all the transient responses to die down. The grid to enter steady state and to became true to the schematic.

Re: Infinite Grid of Resistors

#62

Post by kqr »

jfengel wrote: post #24
QuadmasterXLII wrote: post #13

Earlier quoted context omitted.

I think it collapses into a black hole. black hole mass scales with radius, grid mass scales with radius squared

It becomes a black hole, but it doesn't necessarily collapse, at least not at first. A supermassive black hole has very low density and a very gentle gravitational gradient. All of the mass does end up in the singularity, in finite time (at least for any finite subset of the black hole), but it doesn't automatically become super dense just because it's a black hole. It can remain quite ordinary for a very long time.

Wait, can you take this a little slower? I was not aware black holes could have sensible density.

Re: Infinite Grid of Resistors

#63

Post by IronyMan100 »

praptak wrote: post #56

What I never got about the simple symmetry-based solution is "if we accept the idea that we can treat the current fields for the positive and negative nodes separately". Why are the currents in the two node solution (not symmetric) a simple sum of the currents of two single node solutions (symmetric)? Obviously the 2 node solution still has some symmetries but not the original ones that let us infer same current in e…

the Maxwell Equations are linear in the electric and magnetic fields, then you can add Up and subtract fields and Potentials from each other. It's the same Argument for why interfernce works or optical gratings

Re: Infinite Grid of Resistors

#64

Post by divbzero »

neepi wrote: post #3

I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.

An infinite grid of resistors is clearly a toy scenario, but the infinite universe is a reality that astrophysicists try to reason about. I wonder if there are blindspots in astrophysics because we lack intuition about the universe at that scale and are forced to approach it from theory.

Re: Infinite Grid of Resistors

#65

Post by quinndexter »

ordu wrote: post #23
petschge wrote: post #2

See also https://xkcd.com/356/

Why mathematicians are three points? I think it is easier to disable a mathematician. Look at this discussion, for example. EE engineers and physicists are dismissing the problem outright, while mathematicians have no issues thinking about it.

-Why mathematicians are three points?

Possibly based on this ranking. Everything sub-mathematician is 2 points? Maybe there's subdivision of points.

https://xkcd.com/435/

Re: Infinite Grid of Resistors

#66

Post by neepi »

inopinatus wrote: post #16
corysama wrote: post #6

Earlier quoted context omitted.

They say hydrogen is an odorless colorless gas which, in sufficient quantities, given enough time, turns into people. I’m sure the same could be true of resistors.

People are resistors too.

Just checked. Around 1.5Mohms today.

Re: Infinite Grid of Resistors

#67

Post by farhaven »

taneq wrote: post #47
temp0826 wrote: post #33

Earlier quoted context omitted.

I resist that statement

Gee, I hope nobody ever puts you in charge of a train!

Well they can still be a conductor, even if they're not a resistor. Actually they'd be a pretty good conductor. A super-conductor, if you will.

Re: Infinite Grid of Resistors

#68

Post by ohxh »

steamrolled wrote: post #18

I don't get why EE education emphasizes problems of this sort. The infinite grid is an extreme example, but solving weirdly complicated problems involving Kirchoff's laws and Thevenin's theorem was a common way to torture students back in my day... Here, I don't think it's even useful to look at this problem in electronic terms. It's a pure math puzzle centered around an "infinite grid of linear A=B/C equations". Not…

> Here, I don't think it's even useful to look at this problem in electronic terms

I always thought this problem was a funny choice for the comic, because it’s not that esoteric! It’s equivalent to asking about a 2d simple random walk on a lattice, which is fairly common. And in general the electrical network random walk correspondence is a useful perspective too

Re: Infinite Grid of Resistors

#69

Post by TheOtherHobbes »

At infinite scale this reduces to the bulk equation R = rl/A for a rectangular block where r is resistivity, l is length, and A is the area of the block.

Both l and A are infinite. So you get infinity/infinity, which is undefined, proving it's a silly problem and you should go do something useful with your time instead.

Re: Infinite Grid of Resistors

#70

Post by bgnn »

People think this is not relevant to real world problems but it actually is, albeit all the calculations aren't that relevant. Silicon substrate's resistance is basically an infinitely large grid of unut resistances at the distances relevant for a local point of an IC. Note that silicon substrate is often heavily doped (p-type) and all info you get from the fab is it's resistivity (often somewhere between 1 to 100 ohm per cm). For the most advanced tech nodes its often 10 ohm/cm. If you need to develop some intuition about noise coupling via the substrate you have to think that it's a grid instead of just calculating the resustance between point A and B. We need to distribute a grid of substrate contacts to collect the noisy currents too. So the grid shows up again!
Post reply on HN