What is "cool", (or a challenge if you design PCB like I do), is that this is not true for alternating current.
For example, if you have a track that does a L on top side, and copper plane on bottom side, with an alternating signal, the return path will follow the L and not go back in a straight line.
It can be explained using the language of basic circuit theory. DC current prefers the path of the least resistance, but AC / RF current (1 MHz and above [0]) prefers the path of the least impedance, which is the combination of resistance and reactance. The main source of reactance in practical circuits is parasitic inductances - all real-world components, like wires, have unwanted parasitic inductance at AC, in the same way that all conductors have unwanted parasitic resistance at DC. The farther two conductors in a loop are located apart, the greater the parasitic inductance. Thus, when you have a big loop and a small loop, current prefers to flow via the smaller loop with lower parasitic inductance - even if the end points of the big loop have a shorter "straight line" distance with a smaller DC resistance. When you have two inductors in parallel, current prefers the smaller one - just like when you have two resistors in parallel, current prefers the smaller one.
Now going from circuit theory to physics, we would see that inductance is not the property of an individual component called the "inductor", but it's the result of the magnetic field of the current around a closed loop of a circuit. Thus, every circuit must have a parasitic inductance. To a first approximation, this inductance is proportional to the loop area enclosed by the circuit. Thus, for high-speed digital / RF signal transmission, we often want to make the return conductor be as close to the signal conductor as possible [1]. This is why ground planes are often used in circuit boards, and why twisted pairs are often used in cables.
[0] The point of transition depends on many factors, including the physical size of the circuit. Sometimes it can be as low in the 100 kHz range.
[1] I ignored the issue of characteristic impedance
There's electric field created by the L-shaped conductor a millimeter away. No wonder that it affects electrons in the larger conductor.
School physics teaches us that metals are perfect conductors of electric field, so the field in the large conductor should be the same across it, and not follow the L shape.
But it's only true for a stationary situation, basically DC. At higher frequencies the fact that the conductor (every part if it!) has some capacitance and inductance starts to play a major role in how a fast-changing signal propagates over it. Both the capacitance and the inductance of the part of the large conductor under the L-shaped conductor on the other side are affected by the L-shaped conductor.
These considerations could help see the result as "more intuitive".
All the basic electric circuit theory is just based on a bunch of simplifications that only apply under certain conditions. You get anywhere outside of assumptions for those simplifications, and all kinds of "weird" things start happening. And they're weird just because you're failing to abandon the simplifications, and start looking at Maxwell equations which are a bit more fundamental.
> With time-varying signals, the return current follows the path of least reactance, which is also the path of least impedance. This means the return current path in your PCB is determined entirely by the impedance of the circuit that carries the return current.
I was also a bit surprised by this. But I do recall doing equations regarding capacitive and inductive reactance. In both cases there is a frequency-dependent effect which alters the shape of the waveform. It being frequency dependent, it disappears in the presence of DC (inductors becoming irrelevant and capacitors becoming nonconductive).
So I can kind of see it. But not enough to turn it into a return-path-is-suprising type example.
Don't think of the path of least resistance (this is the limit case for f = 0 Hz), but about the path of least impedance and a lot of your intuition will translate. Also remember: 50/60Hz is almost zero on a pcb board and you can basically think of it as DC.
To be correct for ac and dc, the title should say “… find the path of least impedance”. Which is resistance and reactance combined (capacitance or inductance). Also to be clear: they are not talking about 50/60 hz ac signal which will follow a path basically exactly like dc on a pcb, but much higher frequencies.
I design sensors, currently for medical applications where I use varying signal to measure properties of a medium. Tiny electrodes in an array that are excited with AC, through different effects (capacitive...), things like density, conductivity... can be deduced from the measure.
> Two players take turns coloring the edges of an arbitrary graph. One player has the goal of connecting two distinguished vertices by a path of edges of their color. The other player aims to prevent this by using their color instead (or, equivalently, by erasing edges). The game is commonly played on a rectangular grid; this special case of the game was independently invented by American mathematician David Gale in the late 1950s and is known as Gale or Bridg-It.
That game, if modeled as an electrical circuit of resistors has the property that the best play is the one with the most voltage across it.
> The game's original incarnation was as a machine built by the game's designer, noted engineer Claude Shannon. The machine would choose its' move by measuring electrical resistance between its' sides of the square and would reportedly win "almost always" when making the first move.
I vaguely remember reading about an impedance matching game, but I can't find it anymore. The goal of the game was moving the projectile to the correct location, and that projectile follows the same kind of curve produced by a reactive load on the Smith chart.
Gravity is the driving force behing the flow of water in this example, and a static electromagnetic field (in a DC circuit at least) is the driving force behind the flow of electrons. The water can do work on physical object (waterwheels, etc), and the electrons can do work on electrical loads (lightbulbs, etc.).
However the static electromagnetic field in the DC circuit propagates through the material at near light-speed once the battery switch is thrown, which is a bit different. I suppose if you could throw a switch and turn gravity on or off it would be a closer analogy, i.e. the idea would be to fill the (sealed) maze with water in a zero-g environment (it would fill everywhere equally, comparable to the electons in the conductor with the power off), then turn on the gravity (or the pressure differential for the pipe version) and see what happened.
> suppose if you could throw a switch and turn gravity on or off it would be a closer analogy
I mean, you could, insofar as you can mechanically control the height difference between the start and end of the maze.
I think the real problem with the analogy was just that the hydrodynamic version wasn't a circuit in the sense that the electrical version was. The water just falls out of the system, so of course you can't control the pressure difference :)
The exit of the hydrodynamic version should have been a (sealed) pipe that flows into an (open) buffer-chamber thatis after the maze; from which a pump operating on a control system then brings pumps water back to the (open) buffer-chamber that sits before the maze.
Additionally, said pump's speed should be determined by the water-level imbalance between the two buffer-chambers, such that it's always trying to bring the two chambers into water-pressure equilibrium. (This pump is then a proper hydrodynamic analogue of a generator: two terminals with a constant height [voltage] differential between them, that pumps faster or slower [= varies current] to maintain the same potential difference in the system, whether the system is loaded or unloaded.)
Then "turning off gravity" would just mean moving everything (the input buffer, maze, output buffer, and pump) from being in a vertically descending sequence (where the pump would be doing constant work to maintain the potential difference despite the "load"), to being on a flat plane (where everything would reach potential equilibrium, and the pump would then turn off.)
And you could then represent AC flow, by just alternatingly raising and lowering the two chambers, and using a bidirectional pump.
I think it’s the same but different rates of propagation. It’s about potential force and gradient descent in the end. It’s also interchangeable. The water moves a physical object which induces a moving magnetic field which induces current in a conductor which moves through the circuit and can induce a magnetic field in a conductor which can move a magnetic which can move water.
The video is interesting, but I suspect, that the author is making some subtle errors at places. Tho I'm not 100% sure, last time I analyzed those subject was at BsC/MsC courses at my uni.
E.g. he says something to the tune of
electrons take a few ns. running around, and then settle down in the maze.
IIRC electron flow in a medium is relatively slow, something on the order of centimeters per second. So it's not electrons which settle some potentials by moving quickly, but the electric potential finds its equilibrium. And it finds its equlibrium by electrons exchanging virtual photons (carries of electromagnetic force)?
I’m actually not sure if that makes his explanation more accurate because it’s informed by that, or more regrettably forced metaphor. But the whole series of videos from different creators is worth watching if you want to understand the whole “electrons are moving” thing.
Here's a good Physics SE answer that addresses this point. The "electrons move slowly in a wire" is a hypercorrection, similar to "light slows down is glass": https://physics.stackexchange.com/a/13568.
Parent didn't say electrons move slowly. Parent said electron flow is slow which is true. The article tries to say that in that average there are fast-moving parts and slow-moving parts. Fine.
No, that's the wrong interpretation. The truth is that there is no such thing as "electron flow". It's not a quantum mechanical concept, just a classical approximation.
I feel that one of the differences is that a wire is "full" of electrons already, and more are reluctant to enter the wire unless there is an exit path, but as soon as there is a path the current/charge/emf flow occurs all along the wire almost simultaneously.
This is not modelled well with the water mazes/analogy.
It can be modelled, but with a slight twist. If in a water analogy we prefill the maze with a water and then connect it to a source and a drain, then water level will raise near the source and fall near the drain. We'll see then how it propagates through the maze, these waves will meet somewhere, then some more hard to describe action will follow and then the system will settle to a dynamic equilibrium.
This way the water level changes probably can propagate faster then water moves. Though probably to get this result we'll need to make a "deeper" maze. I mean make walls higher so a cross section of a path would have bigger area, so a slow flow multiplied by this area would give us a big volume of a water moving. Big enough to raise level of a water fast in a whole section of the maze.
The movement of water molecules is typically much slower than the wave speed of water.
When you turn on flow to a filled pipe, the water is reluctant to enter the pipe faster than other water is leaving the opposite end (mediated by pressure waves).
Mainly because the maze is empty to start with, and the water must flow simultaneously to all points equidistant from the entry until the exit is "found".
The analogy would work better if the maze would start with entrance and exit closed, and filled with water to half height. IIRC the author mentioned this in a comment under the video.
At one point in the video, he appears to splash clear water into the filled maze. You can see the non-moving parts lighten their colour compared to the active path.
the drift speed of electrons in a conductor is, as you say, low, while the fluctuations of the wave travel at near the speed of light, and electrons can be accelerated to near light-speed but I don't think that happens in normal signal transfers.
Even if the electrons move slowly, it can remain true that it only takes a few ns for them to settle down. The time for any of the "wrong paths" to have their current drop to zero after the switch is thrown will be determined by the RC time constant of that path, where C is the stray capacitance and R is the path resistance. That's going to be over pretty quickly.
You are thinking about drift speed of electrons, which is slow. But when the initial voltage is applied, each electron would feel the electromotive force and “jiggle” around a bit which would be nano seconds and then settle.
This begs the question the video is trying to answer. Imagine you have no experience or knowledge of what electricity is or how it works. Then you learn the bare basics. You might have this same question, "how does it 'know' which path has the least resistance?"
The pepper demonstration in the video is a good analogy to show how the resistance information of every possible path (or, really, stub) is "back-propagated" to the branching point. No, it's not a perfect description of what is really going on, but I dare say there's no such thing. Just better and better models.
If I have a wire that connects from (+) to (-) on a battery, and a dozen wires that branch off of (-) and go nowhere, how does the current "know" not to waste time trying each of those stubs? This video explains that.
> This begs the question the video is trying to answer. Imagine you have no experience or knowledge of what electricity is or how it works. Then you learn the bare basics. You might have this same question, "how does it 'know' which path has the least resistance?"
You're still saying "path of least resistance" though.
A very important part of the answer is that it doesn't find it. All paths carry electricity.
So "take all paths" isn't begging the question, it's correcting the question, and "weighted by resistance" isn't begging the question, it's giving a pretty easy answer to anyone that understands the concept of "resistance" in a non-electrical sense that some paths let things through more easily than others.
And if you have a bunch of stubs, the electricity does go onto them. It just gets stuck at the end.
It sounds like you missed the point of what parent was trying to say. As one of those people who was in the exact situation the parent mentioned, your concise and incrementally more correct explanation wouldn't have helped me when I had the same question.
Yeah, I think you're correct here. I'll clarify what I meant:
The title statement is "How electrons find the path of least resistance", and what I replied to said, "They take all paths weighted by resistance".
The underlying question remains: how do the electrons "know" what the weights are? When a new charge carrier enters the maze, how does it "know" that "turning left" will be an easier trip than "turning right"? How do most of them end up taking the express lane?
I guess the original comment wasn't meant to answer this question, but rather rephrase it to be a more accurate question in the first place. I misread it as an answer.
> The underlying question remains: how do the electrons "know" what the weights are? When a new charge carrier enters the maze, how does it "know" that "turning left" will be an easier trip than "turning right"? How do most of them end up taking the express lane?
Question: when you observe water flowing on a flat surface do you see the water droplets freely separating from each other all over the surface until it's kind of evenly distributed or do you find the droplets tend to kind of follow or stick to one another?
For example, imagine you have nice trickling stream of water and that stream comes near a droplet, does the droplet join the stream or does the stream miss the droplet?
Does the new "charge" in the maze join with an existing stream or is it starting with a neutral maze and has to find the exit again?
It doesn't need to know that it needs to turn left or right, it just needs to go with the lazier option which happens to be the less resistant one.
From my point of view, finding the path of least resistance does require some kind of "knowing", but taking every path doesn't take some kind of "knowing".
The electrons just push. Like you can push something across a surface with varied friction. Or you can try to walk down paths with different amounts of obstructions. And when they get through faster, they make room for more faster.
Why resistance exists and varies is a valid question, but it's not one that everyone will have. Some people need that explanation, but some people just need "It takes every path with equal vigor."
So the original comment was an answer to the question. Not the answer everyone needs, but a valid answer for many people.
Also a nice comparison is how lightning does actually find a single path, because the current flow makes the air it touches more conductive in an aggressive feedback loop.
That's analogy is not really correct. Nor is the one in the video. With electrons, or light for that matter you're dealing with wave particle duality and the appearance of "shortest path" is a result of the particle's wave nature. Prof Morales did a good explanatory series in Ars
https://www.google.com/amp/s/arstechnica.com/science/2021/01...
Depends on how you set up the analogy, but sure it's not perfect.
And I put "solve" in quotes precisely because it does no such thing.
But a water molecule interacting with pressure gradients and waves is about the best eli5 or even eli18 that I've seen, with both particle and wave representations.
But maybe that's just because I'm a hydraulics engineer and "get it."
Yea, but we're talking about a 22 min video vs a 2 sentence explainer to grasp the very basics of a concept here.
I love to argue the technical stuff as much as anyone, but the underappreciated aspect and skill of any engineering is eyeballing cost/benefit of any expenditure.
Be it sizing elements of finite analysis, or sizing an analogy.
You're conflating electrons and electromagnetic radiation.
Also light doesn't act like electricity or water, it just bounces at the reflection angle. There is no volume or pressure. Also there is no such thing as a light 'particle'. That is an abstract concept to make simulation easier.
Isn’t that one of the main points of quantum physics?
Do you think quantum mechanics says that light is made up of electrons?
That would be like saying sound and water are the exact same thing because water going through a hose makes sound.
Light does apply pressure.
On the other hand, no it doesn't. If you shine light into a tube, it doesn't fill up with light until the tube blows apart. This is what is being talked about in this thread, so try to understand that context.
Also photon exists?
Are you asking if photons exist? Electromagnetic radiation is magnitude of frequencies over time. There are no individual packets of light just like there are no individual packets of sounds. Photons are a useful idea in simulations because you need to sample specific paths.
> On the other hand, no it doesn't. If you shine light into a tube, it doesn't fill up with light until the tube blows apart. This is what is being talked about in this thread, so try to understand that context.
I don't see what that proves. If you pour water or CO2 or whatever into a normal tube, it doesn't fill up until the tube blows apart, it overflows. And you can easily show those fluids exert pressure.
To blow up a tube you need to have enough pressure at the fill valve. And if you do that, you can blow up a tube with light. It just happens to be hard to concentrate light that much.
Are you sure you are following the context of this thread, where pressure finds the path of least resistance?
you can blow up a tube with light.
Show me an experiment where light exerts itself physically on other light through being constrained to the extent that it finds the path of least resistance.
Really, this is the epitome of a hacker news discussion where there is something reasonable being twisted into absolute nonsense with excessively convoluted arguments.
I really don't understand what you're trying to argue.
You can't just pour electrons into something and blow it up either. So what does it prove that you can't pour photons into a tube to blow it up?
If you want the analogy to electrical flow then it's not trying to blow things up, it's having different sized holes for light to go through, and some scattering in the nodes.
Also my edit to the previous post was late so I'll move it here:
> There are no individual packets of light just like there are no individual packets of sounds. Photons are a useful idea in simulations because you need to sample specific paths.
Sound is carried by individual particles.
Light is quantized (aka packets) unless you happen to have an alternate explanation for the ultraviolet catastrophe?
If you push electrical pressure into a capacitor, it blows up. If you push too much voltage (pressure) into a battery, it blows up.
Sound is carried by individual particles.
Electricity is carried by a conductor like copper, but electricity is not copper and sound is not a particle.
Electromagnetic radiation is magnitude of frequencies over time. There are no individual packets of light just like there are no individual packets of sounds. Photons are a useful idea in simulations because you need to sample specific paths.
This whole thread is about finding the path of least resistance in a pragmatic sense, not some abstract theory that you can't demonstrate. Even the wikipedia article talks about 'light particles' as an 'alternate view with no mass'.
If you have a sufficient strong source that pushes, yes you can blow things up.
That's true of light too.
Not just shining in a weak source indefinitely. You need a powerful source. Just like with electricity or fluids.
They behave the same.
Photons have no rest mass which is extra abstract. They do have mass, and them having mass is not abstract. And you didn't explain how to resolve https://en.wikipedia.org/wiki/Ultraviolet_catastrophe without discrete packets.
I don't have any super thin mirrors on hand, but do you really not believe that solar sails are a real thing? Or do you think a container would act differently from a too-thin solar sail for some reason?
This is about common science that can be done at home, I can show you video of water going through pipes or a capacitor blowing up. You're the one saying that light has volume for some insane reason, so show me. You keep going deeper and deeper into unrelated nonsense just to try to be contrarian.
Your early comments were just a bunch of saying other people were wrong in general. It wasn't just about path of least resistance.
Also if you want to read my other comment chain on this thread, I would not say that electrons do find the path of least resistance. They follow every path, and so would light.
Other people were wrong in general, light doesn't work like electricity. Electricity takes available paths weighted by least resistance. Light bounces at the reflection angle. Not the same. Most people understand this during high school physics. They don't argue that light is the same as electricity and water because of quantum mechanics and solar sails, then not be able to back up anything they say in any way.
This was all about taking the path of least resistance, so show me anything that shows light doing that instead of just bouncing off the reflection angle.
Electromagnetic radiation is magnitude of frequencies over time. There are no individual packets of light just like there are no individual packets of sounds. Photons are a useful idea in simulations because you need to sample specific paths.
This is simply wrong. The energy of light is always an integer multiple of the energy of a photon. It is not a question of simulations, it is a fundamental aspect of nature. The photovoltaic effect, for example, is not explainable with your model.
Simulations are around 50-60 years newer than the discovery of the photon.
Now, in QFT, I believe the photon itself is not fundamental, the electromagnetic field is fundamental. But even then, fluctuations in that field happen only in integer multiples of the energy of the photon.
You can give a name to a small quantity of electromagnetic radiation if you want, but there is no physical particle. Saying the same thing more forcefully doesn't change how things work.
I don't understand your point. If you are coming at this from a QFT perspective, then there are actually no particles at all: the electron is just a fluctuation in the electron field just as much as the photon is a fluctuation in the electromagnetic field (and the same holds true for quarks and thus protons and neutrons etc). If this is the poibt you are making, than I completely agree witht you.
But if you are coming at this from a more old-school QM or even classical mechanics perspective, where fields and particles are different things, then the photon is just as much a particle as the electron and the quark are.
That is, in certain experiments, light behaves like a classical wave (for example, double slit experiment), while in other experiments, it behaves like a classical particle (photoelectric effect [0]).
If your theory is simply that light is a classical wave (EM wave, obeying Maxwell's equations), then you should expect that shining a bright low-frequency light over a surface will eventually dislodge a number of electrons equal to the number of electrons dislodged when a dim high-frequency light is shone on the same surface. However, in real life experiments, this doesn't happen. Instead, no electrons are dislodged by the low-frequence light regardless of intensity, while some electrons are dislodged by the high-frequency light even at very low intensities.
The explanation for this phenomenon is that light consists of individual photons. Each individual photon has an energy that corresponds to the so-called frequency of the light. When a low energy photon hits an electron, nothing happens - so, regardless of how many low-energy photons you generate, nothing will continue to happen. Conversely, when a high-energy photon hits an electron, that electron is dislodged. So, even a sparse beam of high-intensity photons will dislodge some electrons. Even more impressively, you can directly count the number of electrons dislodged and compare to the number of photons contained in the beam, and you will find that they are actually equal, proving even more that the photon is a particle in this type of experiment.
There is no way to explain this phenomenon if you try to explain light as simply a wave in the classical EM field.
No, there aren't. Sound is a classical wave, not a quantum wave, unlike light.
Also, crucially, space isn't quantized, and sound represents the variation of some particles' position in space, so its frequency and so on can take any value - again unlike the EM field.
It's even simpler if you look at parallel resistors by their conductance (more paths), and series resistors by their resistance (steeper path). As usual, more symmetrical math makes the engineering less mysterious.
Not all the electrons follow the path of least resistance. The currents in parallel paths are in inverse proportion to the resistances of the respective branches.
Yeah. I mean neat video but the title baited me a bit. I thought maybe there was some unintuitive insight or interesting physical phenomenon happening that allowed electrons to solve a computationally hard problem better than the naive brute force, but it’s just 100 level physics.
I hope loose your sense of wonder...never settle for path of least resistance... And I hope you still feel small as you stand beside the ocean ..when ever one door closes I hope one more opens I hope you get your fill to eat but always keep that hunger .. ps dance in the reign....challenge has made to the finish line ilevennif I did not pass go. .
Nothing in this video is super groundbreaking if you’ve taken a typical physics class that includes some E&M.
That said, the demonstrations are pretty compelling and well executed. I particularly liked the use of an IR camera to visualize the resistive power loss in the maze. Super cool.
'electricite du magnetisme' would be a nice quadruple-entendre in French
1) electricity of magnetism => electrical side of the electromagnetic force
leads to
2) electricity from magnetism => generating electricity from a magnetic force
leads to
3) edm => electronic dance music
leads to
4) excitement from attraction => the feeling of excitement ('electric' metaphor for excitement) from meeting someone you're attracted to ('magnetic' metaphor for attraction between two people)
Can you solve arbitrary traveling salesman problem with that? There is only a polynomial number of required laser cuts (n nodes, n * (n-1) edges) and the source can be next to sink with a fake 0 edge between them.
No, it would give you the approximate shortest (least resistance) path between the source and sink, which is very different from the traveling salesman problem (which requires finding the shortest path that touches every node).
I say "approximate" because, as has been discussed in this thread, the current actually follows every possible path to some extent, weighted by their resistance. So when there multiple branching paths with similar costs, they will have similar current flow, and the current along each path is not constant. So in general it can be difficult to find the exact minimum resistance path just by measuring the current.
Or.. use non-conductive coated wire to wire up every possible path, with all the wires connected at a start and finish point, and then see which wire gets hot first.
It's not going to save you any time, since wiring up every path is basically the same as brute forcing every path anyway, but it would work.
> Can you solve arbitrary traveling salesman problem with that?
Yes, you can solve TSP in linear time using electricity.
First step is to construct a circuit with a single source, and multiple independent paths -- one for each possible TSP graph traversal. Constructing this circuit can take a bit of time, but after that, finding the shortest path will be extremely fast.
Analog computers set up right can solve very small instances of NP problems extremely fast. However, they do not scale, as the measurement step (which is required to actually obtain the solution) becomes harder and harder with the size of the problem, as you need to distinguish finer and finer details. The energy needed to distinguish between two possible output values becomes prohibitive quite quickly (it may actually be exponential in the size of the problem, I'm not sure).
A (classical) analog computer is not a quantum computer and various conjectures on complexity say that they should all be efficiently (polynomial-time) simulated by a probabilistic Turing machine.
For example, if you have a track that does a L on top side, and copper plane on bottom side, with an alternating signal, the return path will follow the L and not go back in a straight line.
Those links have some explanations:
https://resources.altium.com/p/what-return-current-path-pcb
https://www.nwengineeringllc.com/article/how-to-design-your-...
https://electronics.stackexchange.com/questions/360472/real-...