[HN Gopher] Infinite Grid of Resistors
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Infinite Grid of Resistors
Author : niklasbuschmann
Score : 205 points
Date : 2025-06-14 22:12 UTC (1 days ago)
(HTM) web link (www.mathpages.com)
(TXT) w3m dump (www.mathpages.com)
| petschge wrote:
| See also https://xkcd.com/356/
| ordu wrote:
| 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.
| quinndexter wrote:
| -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/
| Mawr wrote:
| See alsoer https://youtu.be/zJOS0sV2a24?t=932
| neepi wrote:
| 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.
| bravesoul2 wrote:
| Given an infinite grid of resistors... would you expect planets
| to form?
| corysama wrote:
| 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.
| bravesoul2 wrote:
| Resistors are made of heavier elements though. And I
| remember something like everything wants to become iron
| (fuse if lighter, decay if heavier)
|
| That said there might be enough energy (infinity!) for
| anything to be possible.
| jfengel wrote:
| You get stable things heavier than iron, and they're more
| common than you'd expect. It's possible that they form in
| neutron star collisions, which are complete anarchy in
| atomic terms.
| inopinatus wrote:
| People are resistors too.
| temp0826 wrote:
| I resist that statement
| taneq wrote:
| Gee, I hope nobody ever puts you in charge of a train!
| farhaven wrote:
| 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.
| taneq wrote:
| So wait, if they resist the statement that they're a
| resistor, are they a resistor or not? I think they're a
| semiconductor. Maybe they work at a railway junction. :D
| neepi wrote:
| Just checked. Around 1.5Mohms today.
| rzzzt wrote:
| Assume perfectly spherical through-hole resistors soldered on
| an infinite PCB.
| QuadmasterXLII wrote:
| I think it collapses into a black hole. black hole mass
| scales with radius, grid mass scales with radius squared
| pixl97 wrote:
| Thats what I'm not sure about here...
|
| If we assume this is an infinite grid in its own universe
| then nothing can actually move. The gravitational pull
| should be the same from every direction. If we assume the
| grid is perfect then there is no nucleation sites to start
| a collapse. The grid would be in perfect balance.
|
| The same is thought about our universe. If there hadn't
| been small quantum fluctuations during the inflationary
| stage it would have taken much longer for what we see in
| the modern universe to form.
| staplung wrote:
| In fact, we might have a different problem: dark energy
| should tear the grid up into (very large) bits. I guess
| the question is then would the bits then collapse into
| black holes or not. I assume so since the mass would not
| longer be perfectly balanced.
| pixl97 wrote:
| Guess we'll have to wait for an actual answer on dark
| energy and universal expansion.
|
| What it collapses into depends on the time for the bits
| to coalesce into. If it's a slow collapse you could get a
| mass large enough to form a neutron star (like thing)
| instead of black holes.
|
| If those neutron stars crash into each other they can
| release a large amount of 'recycled' matter from all over
| the atomic spectrum back into this universe.
| raattgift wrote:
| In 1+1 dimensions one can analyse the gravitational
| behaviour of an infinite line of ...-wire-resistor-wire-
| resistor-... with an adaptation of Bell's spaceship.
| Throwing away two dimensions eliminates shear and
| rotation (and all sorts of interesting matter-matter
| interactions) so we can take a Raychaudhuri approach.
|
| We impose initial conditions so that there is a
| congruence of motion of the connected resistors, so that
| we have a flavour of Born rigidity. Unlike in the
| special-relativistic Bell's spaceship model (in which the
| inertial motion of each spaceship identical save for a
| spatial translation), in our general-relativistic
| approach _none_ of the line-of-connected-reistors
| elements ' worldlines is inertial, and each worldline's
| proper acceleration points in a different direction but
| with the same magnitude. This gives us enough symmetry to
| grind out an expansion scalar similar to Raychaudhuri's,
| Th = [?]_a v^a (<https://en.wikipedia.org/wiki/Raychaudhu
| ri_equation#Mathemat...>). As an aid to understanding, we
| can rewrite this as 1/v \frac{d v}{d \tau}, and again in
| terms of a Hubble-like constant, 3H_0.
|
| We can then understand Th as a dark energy, and with Th >
| 0 the infinitely connected line of ...-wire-resistor-
| wire-resistor-... is forced to expand and will eventually
| fragment. If Th < 0, the line will collapse
| gravitationally.
|
| > no nucleation sites
|
| If Th = 0 initially, we have a Jeans instability problem
| to solve. Any small perturbation will either break the
| infinite ...wire-resistor-wire-..., leading to an
| evolution comparable to Bell's spaceship: the fragments
| will grow more and more separated; or it will drive the
| gravitational collapse of the line. The only way around
| this is through excruciatingly finely balanced initial
| conditions that capture _all_ the matter-matter
| interactions that give rise to fluctuations in density or
| internal pressure. It is those fluctuations which break
| the initial worldline congruence.
|
| This is essentially the part of cosmology Einstein
| struggled with when trying to preserve a static universe.
|
| In higher dimensions (2+1d, 3+1d) the evolution of
| rotation and shear (instead of just pressure and density)
| becomes important (indeed, we need an expansion tensor
| and take its trace, rather than use the expansion scalar
| above). A different sort of fragmentation becomes
| available, where some parts of an infinite plane or
| infinite volume of connected resistors can undergo an
| Oppenheimer-Snyder type of collapse (probably igniting
| nuclear fusion, so getting metal-rich stars in the
| process) and other parts separate; the Lemaitre-Tolman-
| Bondi metric becomes interesting, although the formation
| of very heavy binaries early on probably mitigates
| against a Swiss-cheese cosmological model: too much
| gravitational radiation. The issue is that the chemistry
| is very different from the neutral-hydrogen domination at
| recombination during the formation of our own cosmic
| microwave background, but grossly a cosmos full of
| luminous filaments of quasi-galaxies and dim voids is a
| plausible outcome. (It'd be a fun cosmology to try to
| simulate numerically -- I guess it'd be bound to end up
| being highly multidisciplinary).
| jfengel wrote:
| 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.
| kqr wrote:
| Wait, can you take this a little slower? I was not aware
| black holes could have sensible density.
| jfengel wrote:
| In the formula for a Schwarzchild black hole, the mass is
| proportional to the radius. Since volume goes up with the
| cube of the radius, the density drops quickly.
|
| The kind of black hole that forms from a collapsing star
| is super dense. But a supermassive black hole forms
| differently, as a denser region of gas and stars during
| galaxy formation. The density can be lower than that of
| water. You could be inside it without even realizing
| anything is odd.
|
| There is no known way to form black holes bigger than
| that. We had been discussing a pure thought exercise.
| Though it is possible that the universe as a whole has
| enough density to be a black hole. (Signs point to no,
| but it's an open question.)
| Taniwha wrote:
| Eventually you need to pullin a physicist too who will point
| out that at an appropriate distance quantum effects will
| dominate - because eventually at a far enough distance the
| number of electrons moving per second (ie current flow) will be
| either 0 or 1 at some nodes
| mjevans wrote:
| Intuitively I knew this class of problem was theoretical only
| BS when it came up in college...
|
| I hadn't considered that sort of strange effect though! Makes
| me feel not so bad for 'never really getting it' because I
| just couldn't wrap my mind around the problem description's
| obvious inanity and the infinite edges.
| aydyn wrote:
| The question is not pretending to be realistic. No one is
| thinking it is possible to build an infinite grid of
| resistors.
|
| It's simply an evaluation of your mathematical ability to
| manipulate the equations and overall understanding of them,
| wrapped up in a cute little thought experiment. This
| evaluation IS relevant to more realistic scenarios and
| therefore your grade and engineering ability.
| __MatrixMan__ wrote:
| I've not studied QED directly, so by all means correct me if
| I'm wrong, but it seems to me that we'd get a double-slit
| like scenario where it's as if a partial electron went
| through either path. We might want to say that surely a whole
| electron took one path and not the other but we couldn't say
| which and if we tried to instrument to and find out we'd
| affect the resistance.
|
| But that's fine because knowing which path the electron took
| is not part of the problem. Both paths contributed to the
| resistance even if one was not taken.
|
| We only have to worry about quantum effects if the
| probabilities are not a decent proxy for the partial-
| particles that we suspect don't exist. In this case, the
| Physicist can probably proceed directly to the bar and have a
| drink with the Mathematician.
| dgfl wrote:
| Resistance is inherently dissipative, so there is no
| coherent path the electron can take. No quantum effects
| here, the electron is always interacting with the resistor
| lattice.
| viraptor wrote:
| I don't think you'll ever get 0/1. You get a difference in
| voltage that influences all electrons to move slightly more
| in one direction than another in electric current. They'll
| just drift very very slightly as a group, not measurable when
| you get far enough. But they're always all affected, rather
| than individually.
| sandworm101 wrote:
| And the electrician knows he can get a 99% answer out of a
| 10x10 grid on a workbench. The engineer is free to then add
| more resisters to the periphery until either the grant money
| runs out or the physicist's publishing deadline approaches.
|
| A really difficult question: At each distance, what percentage
| of soldering errors in the grid can be tolerated before the
| fluke meter across the center square detects the fault? (That
| might actually be a thing as I've heard people talk about using
| changes of local resistance to detect remote cracks in
| conductive structures ... like maybe in a carbon fiber
| submarine hull.)
| nerdsniper wrote:
| For measuring corrosion in conductive surfaces, "eddy
| current" testing is often used. It uses AC current of some
| frequency, so it's technically measuring inductance rather
| than resistance.
| repiret wrote:
| I think there are two interpretations of schematics.
|
| One is where the components on the schematic represent physical
| things, where the resistors have some inductance and some non-
| linearity, and some capacitance to the ground plane and so on.
| This is what we mean by schematics when we're using OrCad or
| whatever.
|
| There is another interpretation where resistors are ideal ohms
| law devices, the traces have no inductance or propagation delay
| or resistance. Where connecting a trace between both ends of a
| voltage source is akin to division by zero.
|
| Sometimes you translate from the first interpretation to the
| second, adding explicit resistors and inductors and so on to
| model the real world behavior of traces etc. if you don't, then
| maybe SPICE does for you.
|
| Infinite resistor lattices exist only in the second
| interpretation.
| red75prime wrote:
| > 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.
| eternauta3k wrote:
| An infinitely large grid never reaches equilibrium, like it
| says in the article.
| red75prime wrote:
| That's why you need to wait longer than ever.
|
| Mostly joking, but an idealized schematic requires
| idealized conditions to observe.
| divbzero wrote:
| 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.
| nofunsir wrote:
| Does Schrodinger's cat study Fourier transforms?
| Koshkin wrote:
| But you already know that it does and it doesn't at the same
| time.
| Koshkin wrote:
| > _apply current_
|
| Going on something of a tangent: in engineering, it seems
| unusual to talk about "applying current," it's usually voltage
| (say, across a resistor) or some sort of an "electromotive
| force."
| gugagore wrote:
| In idealizations, there are both voltage sources and current
| do m sources.
| mmastrac wrote:
| This was the question I hated in my EE degree. The thought
| exercise was a favourite of the profs.
| dcassett wrote:
| I saw this question only once, as the first of 4 problems on
| the final exam for my very first EE introductory course. The
| course had covered an infinite ladder of resistors, but at the
| time it seemed like quite a leap to apply that knowledge to
| this problem.
| quibono wrote:
| There's one thing I don't get about the symmetric+superposition
| explanation. Why are there alpha - beta - alpha on the adjacent
| nodes, and not alpha-alpha-alpha? I.e. why is one of the
| directions distinct while the other two are considered the same?
| magicalhippo wrote:
| Start by assuming they could potentially be all different, so
| denote the currents i_1 to i_12.
|
| However note the problem is symmetrical about the vertical
| axis, so flip the figure. The current passing through the
| flipped paths should be the same as before the flip, so note
| down which i's equate to each other due to this.
|
| Note that the problem is symmetrical about the horizontal axis,
| and do the same there. Note that the problem is symmetric when
| rotated 90 degrees, so do that. And so on.
|
| In the end you'll have a bunch of i's that are equal, and you
| can group those into two distinct groups. Call those groups
| alpha and beta.
|
| edit: Another way to look at it is that you can't use the
| available symmetry operations to take you from any of the
| alphas to a beta. This is unlike alpha to alpha, or beta to
| beta.
| shove wrote:
| Word on the street was that my Physics professor at NCSSM (Dr
| Britton) worked on this problem during his doctorate
| clbrmbr wrote:
| The finite grid of resistors (or arbitrary impedances) is
| actually of great practical usefulness.
| Kirr wrote:
| This may be as good time as any to plug my calculator for
| finite resistor networks (including grids) [1]. It works by
| eliminating non-terminal nodes one by one with the Star-Mesh
| transform, while keeping the exact rational resistances at each
| point.
|
| [1] https://kirill-kryukov.com/electronics/resistor-network-
| solv...
| steamrolled wrote:
| 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 the puzzle I ever
| felt the need to know the answer to, but I certainly don't judge
| others for geeking out about it.
| choonway wrote:
| There are two parts to education. One is to impart knowledge,
| the other is to filter the students.
| colechristensen wrote:
| Not entirely wrong but it's a little too easy to use that
| argument for squashing any criticism for education content.
| dwattttt wrote:
| You're missing general problem solving. If all people do is
| encounter problems they've already seen before, well, we have
| lookup tables for that kind of thing.
| Nevermark wrote:
| The third is to challenge students. With unusual concepts,
| preferably.
|
| How else to create students capable of solving problems we
| cannot anticipate today?
|
| Not to mention, that understanding strange problems is a very
| efficient way to broaden horizons.
| goochphd wrote:
| I was about to say "they still torture students this way" but
| stopped myself when I remembered I took Circuits 1 and 2 back
| in 2007. So maybe my knowledge is dated too...
|
| It's a weird butterfly effect moment in my career though. I had
| an awesome professor for circuits 1, and ended up switching
| majors to EE after that. Then got two more degrees on top of
| the bachelor's
| jesuslop wrote:
| If all you mind is the EE curriculum then ok. Or else there is
| an interesting work of Gerald Westendorp on the web [1] on how
| allowing other classical passive components (Ls & Cs) you can
| get discretizations (and hence alternative views) of a very
| wide class of iconic Physics partial differential equations (to
| the point that the question is more what cannot be fit to this
| technique). G. W. is alive and kicking in mathstodon.
|
| [1] https://westy31.nl/Electric.html
| bsder wrote:
| > I don't get why EE education emphasizes problems of this sort
|
| Last I checked, they don't. I certainly never hit an "infinite
| grid of resistors" in general circuits and systems except as
| some weird "bonus" problem in the textbook.
|
| _Occasionally_ , I would hit something like this when we would
| be talking about "transmission lines" to make life easier, not
| harder. ("Why can we approximate an infinite grid of inductors
| and capacitors to look like a resistor?")
|
| It's possible that infinite grid/infinite cube might have some
| pedagogical context when talking about fields and antennas, but
| I don't remember any.
| Workaccount2 wrote:
| One of my core grips with STEM education, mainly the math heavy
| part of it, which frankly is most of it, is that it is taught
| primarily by people who _love_ math.
|
| The people who loved application and practical solutions went
| to industry, the people who got off spending a weekend grinding
| a theoretical infinite resistor grid solution went into
| academia.
| steamrolled wrote:
| Loving math is not necessarily a problem. But if you want
| others to love it too, you have to explain it in a way that
| makes them see the light.
|
| A lot of STEM education is more along the lines of "take the
| rapid-fire calculus class, memorize a bunch of formulas, and
| then use them to find the transfer function of this weird
| circuit". It's not entirely useless, but it doesn't make you
| love the theory.
| bobmcnamara wrote:
| > solving weirdly complicated problems involving Kirchoff's
| laws and Thevenin's theorem was a common way to torture
| students back in my day...
|
| Hey now, those actually come up sometimes.
| esafak wrote:
| In school I would have relished solving this problem. Now I
| wonder if it has any application.
| ohxh wrote:
| > 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
| tekla wrote:
| To make you think, and not become another monkey moving blocks
| along
| nimish wrote:
| In the integral, the h_m(s) are chebyshev polynomials of the
| first kind
| kevinmhickey wrote:
| In school I would have tried to solve this... now if I want to
| know I just get out my multimeter and measure. Faster, simpler,
| and more practical.
| personjerry wrote:
| Where are you going to find an infinite grid of resistors in
| real life to measure?
| BenjiWiebe wrote:
| Measure a couple of different sizes of grids and fit a curve
| to your results?
| terminalbraid wrote:
| How many would you need to try to get an acceptable result?
| causality0 wrote:
| My math isn't strong enough to follow the whole article, but my
| intuition as someone who works in electronics is that when a
| quantized system interacts with an infinity, the infinity is
| restricted based on the magnitude of the quantized factor.
| Electric charge is quantized. Less than one electron cannot pass
| through a node, therefore an infinite grid of resistors is
| effectively a finite grid of resistors whose size changes based
| on how much charge is dumped into the system.
| morepedantic wrote:
| That was my initial thought, but on further reflection it feels
| wrong. The electron is also a wave, and that wave can spread
| across the entire grid.
|
| Another interesting aspect is that in an infinite grid, a
| spontaneous high voltage is going to exist somewhere at all
| times. It is probably very far away from you, but it's still
| weird.
| yusina wrote:
| Funny to put "intuition" and "infinity" into the same sentence.
|
| The only type of person for whom intuition about infinity to
| form is not entirely unlikely are mathematicians.
| eternauta3k wrote:
| That only matters if you're measuring in the time domain and
| seeing the noise due to individual carriers. Often you just
| care about averages over some time and space (e.g. the
| macroscopic flow of water behaves quite different from the
| speeds of the individual molecules).
| pyman wrote:
| Re: the infinite resistor grid
|
| If you take an endless grid made of identical resistors and try
| to measure the resistance between two neighbouring points, the
| answer turns out to be about one-third of a resistor
| kayson wrote:
| A much more useful (in the educational sense) question to ask, in
| my opinion, is the resistance between opposite corners of a cube
| of 1ohm resistors. There are some neat intuitions it can help
| build (circuit symmetry, KCL, etc). The infinite grid is too much
| an obscure math problem that seems like it might be solvable in
| an introductory circuits class.
| sriku wrote:
| This is cool and I have my own take on it after being nerd sniped
| by XKCD - https://sriku.org/posts/nerdsniped/ - I link to this
| article at the end but that post specifically solves the xkcd
| puzzle.
| praptak wrote:
| 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 every
| direction.
| IronyMan100 wrote:
| 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
| TheOtherHobbes wrote:
| 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.
| bgnn wrote:
| 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!
| eternauta3k wrote:
| I'd argue the case you're describing is mathematically simpler
| precisely because it is continuous.
| Den_VR wrote:
| You're practically describing the invention of Calculus.
| gugagore wrote:
| Right, why is it a 4-connected grid instead of 8-connected,
| or any other topology, like a hex grid.
| bgnn wrote:
| True, but the continuous solution is just a limit condition
| of tge discrete one. It doesn't make it any harder or easier,
| at least from what I know fron calculus. The software tools
| use numerical methods to solve this type of problems and they
| tend to divide the continuous substrate into a mesh of
| discrete elements to model them as lumped circuit elements so
| that we can represent them in a matrix and simulate the
| circuit using linear algebra. They often use random walk in
| their algorithm to find a mesh which introduces a minimum
| error.
| ChoGGi wrote:
| My vague understanding of photolithography is that it's hard,
| though I didn't realise it's bad enough to evoke an egyptian
| goddess.
|
| I'll see myself out.
| em3rgent0rdr wrote:
| The word used to pray to Unut is 'ohm', I believe...
| fraserphysics wrote:
| The units of resistivity are ohm * cm not ohm/cm. (I worked at
| Fairchild a long time ago.)
| rwmj wrote:
| Now I'm wondering if anyone has built a very large grid of
| resistors to try to approximate / curve fit this. Surely there's
| a youtube video in this ...
| Kirr wrote:
| Well there is this: https://www.youtube.com/watch?v=v1YrANSmOGY
| - Not sure if it counts as large, but it's a start.
| dogman1050 wrote:
| This is a discrete case of "sheet resistance."[1] The resistance
| between any two points, nodes in this case, is the same. We
| covered this in the EE uni curriculum back in the day, but I
| don't remember the solution derivation anymore.
|
| [1] https://en.m.wikipedia.org/wiki/Sheet_resistance
| Balgair wrote:
| Aside: Veritasium had a great video similar to this on the paths
| that light takes. I'll link to the part where they do _the best
| physics demo I have ever seen_ :
|
| https://www.youtube.com/watch?v=qJZ1Ez28C-A&t=1500
| nullc wrote:
| sadly the demo is not so impressive as they make it out to be:
| The extra-path light is 'caused' by exit diffraction of the
| light source.
|
| Now, the same underlying theory also explains why there will
| always be diffraction from any finite boundary resulting in a
| reality which is indistinguishable from one where light
| actually takes all possible paths. But to argue that it
| actually does is arguably more meta-physics than physics. The
| demonstration is further compromised by the fact that the
| laser's diffraction performance is also presumably far from the
| physical limit.
|
| So a cynic seeing that demo would say "Isn't that just due to
| some of the light from the laser being off-axis" -- and it
| absolutely is. The physics means that some of the light will
| _always_ be off-axis, but the demonstration does nothing to
| establish that.
| Balgair wrote:
| I'm sorry what?
|
| What do you mean by diffraction here? Are you talking about
| the bokeh?
|
| The laser isn't interacting with any other elements than the
| air before it makes the gradient sheet light up. And the
| permisivity of the air is about the same as vacuum here.
|
| Like, the grating is going to show a diffraction pattern
| similar to any pinhole aperture source [0] because of the
| 'half cancellations' they kinda explain, but not all that in
| depth.
|
| But since there are no elements in the path yet, the only
| conclusion we can make is that of Feynman's - that the light
| is in fact taking all possible paths and then cancelling out
| to make the laser light we normally experience.
|
| What am I missing? To me this demo is like mind boggling as
| it shows that the wave model is the correct one even with a
| laser.
|
| [0] https://external-
| content.duckduckgo.com/iu/?u=https%3A%2F%2F...
|
| Something like (a) above, though I'm not confident that this
| is really showing that _exactly_.
| at_a_remove wrote:
| Odd. As an undergrad in physics, we had a project for our team
| which involved percolation theory and "testing" it. So, we had to
| make differing grids of conductive ink, with a certain number of
| "links" (resistors, edges in the graph) as missing. Getting even-
| flowing conductive ink was _hard_. I wrote all of the software
| for the XY plotter, pushing out instructions to make rectangular
| and triangular grids. Then we would measure the resistance from
| one side to another.
| 1970-01-01 wrote:
| This is also known as a high pass filter for first year EE
| students.
| bilsbie wrote:
| Dumb question but why isn't a vacuum considered an infinite grid
| of resistors?
| jiggawatts wrote:
| Because it is effectively a superconductor! An electron (or
| proton) with some velocity will keep going in a straight line
| forever. This is neglecting the influence of stray background
| magnetic fields and gravitational fields, but the general
| notion applies.
| bilsbie wrote:
| Offshoot question. Why don't we make resistors by making wire so
| thin that only a certain current can fit through?
|
| Wouldn't that be more efficient than converting current to heat?
| mort96 wrote:
| You're describing thin film resistors, and they exist.
|
| They also just convert current to heat though. Some amount of
| current moving through a material with some amount of
| resistance always produces a fixed amount of current in
| accordance with Ohm's law. You can't really get away from that.
| bilsbie wrote:
| Thanks. So Is there a physical reason resistors have to make
| heat? Is it theoretically possible to find a material that
| limits current but produces very little heat?
|
| I guess the explanations always confuse me. Let's say a short
| circuit with no resistors has a certain amount of power. Then
| we add a resistor and the power in the circuit goes down. The
| resistor isn't turning the difference in power into heat,
| right.
| analog31 wrote:
| It's useful to look at the units of measure. Voltage is
| energy per unit charge. As the charge carriers go across
| the resistors, their energy changes, and that energy has to
| go somewhere. It's not always lost as heat in all devices.
| In an LED, some of the energy is "lost" as light. But
| still, the sum total of heat and light power generated by
| an LED is equal to the product of the current and the
| forward voltage.
|
| Another useful heuristic is that heat is generated from
| what's left after all of of the other ways of converting
| energy are used up, such as light, chemical potential, and
| so forth. It's energy's last resort. The usefulness of a
| resistor lies in its simple voltage-current relationship,
| which is equivalent to saying that the _only_ thing it
| generates is heat.
| mort96 wrote:
| There is no such thing as a short circuit with no
| resistance, because everything (other than superconductors)
| has a resistance. If you had a circuit with a magical ideal
| voltage source and no resistance, you'd have infinite
| current.
|
| But let's talk about short-circuiting lithium batteries for
| example. They have a roughly 50 milliohm (aka 0.05 ohm) of
| "equivalent series resistance".
|
| That means, if you short circuit a lithium battery with a
| superconductive wire (aka with 0 resistance), the circuit
| has a resistance of 0.05 ohms. We can compute the current
| with Ohm's law: I=V/R. V is typically 3.6 volts for li-ion
| batteries, R is 0.05 ohm, so I (aka current) is 3.6/0.05 =
| 72 amperes. 72 amperes * 3.6 volts is 259 watts. Now in the
| real world, the battery's chemistry would step in here and
| limit current in complicated ways, but this means that
| _under the assumption that our battery would work as an
| ideal voltage source + a 0.05 ohm resistor_ , and if there
| was no extra heat coming from the chemical reactions, a
| shorted battery would produce 259 watts of heat.
|
| We can add a 1 ohm resistor to the circuit, which means our
| circuit's combined resistance would be 1.05 ohm. Using
| Ohm's law again, we find that the current would be 3.6/1.05
| = approx 3.43 amperes. 3.43 amperes * 3.6 volts is 12.35
| watts of heat.
|
| So _thanks to our resistor_ , we're now producing 12.35
| watts instead of 259 watts of heat, because the resistor
| limits the current going through the circuit. With a higher
| resistance resistor we'd produce even less heat.
|
| A core idea here is that power consumptions equals heat. I
| don't understand the physics reasons why, but "this thing
| consumes 10 watts of power" means the same as "this thing
| produces 10 watts of heat". Higher resistance means less
| current which means less watts, which means both less heat
| and less power consumption because those are _the same_.
| bilsbie wrote:
| Thanks! That's helpful.
| marcosdumay wrote:
| > So Is there a physical reason resistors have to make
| heat?
|
| Look at it like this: resistors produce heat by definition.
|
| What you are describing isn't a resistor. It's actually a
| switched power supply, but that material is probably more
| heterogeneous than you wanted.
| raron wrote:
| Resistors doesn't "limit the current flow", they just
| (let's say) make it harder to "push" the same amount of
| current through. (If you increase the voltage you will get
| higher current flowing through any resistor.)
|
| There are ways to limit the current through some components
| regardless of the applied voltage (to a sane level) without
| producing much heat. These are active switching mode DC-DC
| converters widely used eg. for driving LEDs in (higher
| quality) light bulbs and charging batteries.
| grues-dinner wrote:
| Resistance _is_ V /I. You literally cannot have current flowing
| in a resistor without a voltage across it (either the voltage
| causes the current to flow, or the resistor in the path of a
| flowing current has a voltage appear across it).
|
| A voltage drop with a flowing current _is_ power (P=VI).
|
| There is literally nothing you can do to avoid resistors
| dissipating that power as heat, it's just what they are. If
| they didn't do it, they wouldn't _be_ resistors.
|
| What you can do is use larger resistances which need less
| current to see the same voltage (e.g. change a pull up from 10k
| to 100k or higher, but that's more sensitive to noise), or
| smaller resistances that drop less power from a given current
| (e.g. a miiliohm-range current shunt, and then you need a more
| sensitive input circuit) or find another way to do what you
| want (e.g. a switched-mode power supply is far more efficient
| than a voltage divider at stepping down voltage). This is
| usually much more complex and often requires fiddly active
| control, but is worth it in power-constrained applications, and
| with modern integrated technology, there's often a chip that
| does what you need "magically" for not much money.
| Koshkin wrote:
| https://news.ycombinator.com/item?id=44282191
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