When Electricity Doesn’t Take The Shortest Path

Everyone knows that the path of least resistance is the path that will always be taken, be it by water, electricity or the feet of humans. This is where the PCB presented by [ElectrArc240] on YouTube is rather confusing, as it demonstrates two similarly sized traces, one of which is much shorter than the other, yet the current opts to travel via the much longer trace. If you were to measure this PCB between each path, the shorter path has the lowest resistance at 0.44 Ω while the longer path is 1.44 Ω. Did the laws of physics break down here?

Of course, this is just a trick question, as the effective resistance for an electrical circuit isn’t just about ohmic resistance. Instead the relevant phrasing here is ‘path of least impedance‘, which is excellently demonstrated here using this PCB. Note that its return path sneaks on the back side along the same path as the long path on the front. To this is added a 1 MHz high current source that demonstrates the impact of alternating current, with reactance combining with the resistance.

Although for direct current it’s fair to say that impedance is the equivalent of resistance, once the inductance of a trace has to be taken into account – as in the case of AC and high-frequency signaling – the much higher inductance of the short path means that now the long path is actually the shortest.

When you are doing some impedance matching in your favorite EDA software while implementing an Ethernet RMII link or similar, this is basically part of the process, with higher frequencies requiring ever more stringent mechanisms to keep both sides happy. At some point any stray signals from nearby traces and components become a factor, never mind the properties of the PCB material.

18 thoughts on “When Electricity Doesn’t Take The Shortest Path

  1. Electricity takes ALL paths, it’s just that some allow exponentially more electrons to flow than others. If you had sensitive enough multimeter and noise floor comparable with liquid helium, you could connect LED to a CR2032 in Japan and detect single electrons in Spain. It’s simple dynamic systems, laplace equations etc.

  2. This is where the PCB presented by [ElectrArc240] on YouTube is rather confusing,
    Of course, this is just a trick question,
    No it isn’t. Not confusing and no trick question, just pure 100% unadulterated CLICKBAIT (garbage).
    The electricity is still taking the path of least resistance TO IT!

    Oh nose! A coil with enough henry has almost infinite resistance to HF power? Who would’ve thought HF “ELECTRICITY” doesn’t take a path of negligible resistance to DC.

    I mean this if FUNCKIN HaD and nobody here as ever heard of any type of RF HF antenna… /S

    Aren’t many WiFi Antennas “just” short circuits? Make a fluff video about that and get on HaD

    Please – don’t put this ClickBait shit on HaD (specifically the title of that YT-vid – not sure about the content, only watched a little).

    1. The point is not oh look inductor LOL, the point is to make people understand PCB tracks act as inductors and return path is CRUCIAL at speed. The real valuable lesson of video is at @11:00, is unintuitive and pretty much everyone gets it wrong at first (some never learn).

      Easiest way to get it wrong is stitching tightly routed parallel bus to another layer by placing a bunch of VIAs close together in a neat row. Looks very aesthetically pleasing and neat. Switch PCB editor view to ground plane layer and whats that? a big cut right across it, turns out you just coupled all those tracks.

      1. Beginners like to make “ground islands” where the only way out and back into the power supply is a winding path that dodges and weaves between traces and only connects by a tiny bridge between two vias or component leads.

        It passes circuit continuity and DRC but the board will act erratically. It may even start acting up on DC if the ground return is for any significant current, like a switching transistor.

  3. Okay, let’s try again (hopefully correct formatting this time):

    This is where the PCB presented by [ElectrArc240] on YouTube is rather confusing, …

    Of course, this is just a trick question, …

    No it isn’t. Not confusing and no trick question, just pure 100% unadulterated CLICKBAIT (garbage).
    The electricity is still taking the path of least resistance TO IT!

    Oh nose! A coil with enough henry has almost infinite resistance to HF power? Who would’ve thought HF “ELECTRICITY” doesn’t take a path of negligible resistance to DC.

    I mean this if FUNCKIN HaD and nobody here as ever heard of any type of RF HF antenna… /S

    Aren’t many WiFi Antennas “just” short circuits? Make a fluff video about that and get on HaD

    Please – don’t put this ClickBait shit on HaD (specifically the title of that YT-vid – not sure about the content, only watched a little).

    1. “I mean this if FUNCKIN HaD and nobody here as ever heard of any type of RF HF antenna”

      And surely everyone on HAD has ages of experience building circuits and designing pcbs. There are no beginners here at all! Right?

      1. Personally I’ve never designed a PCB – especially anything with RF.
        But I’ve seen plenty of PCBs with those “wiggly” traces etc. because many if not most or even all modern PCBs with any digital communication on them have those.

        And I’m confident this topic was discussed aplenty on HaD.

        The larger “problem” I have is this:
        A) saying impedance/inductance/capacitance between traces exist doesn’t require a YT vid
        B) proper HaD article about these topics exist: https://duckduckgo.com/?q=site%3Ahackaday.com+PCB+design+inductance
        C) The title of the YT vid featured here is

        Electricity Doesn’t Always Take the Path of Least Resistance

        Perfect clickbait – at least the sub-vid-text contains “Inductance”…

        If people already knowledgeable about the topic can’t tell from the title if the video is even relevant to them it is clickbait.

        Yes, this time I’m that commenter… :-/

        1. You’re still missing the point.

          The value is in giving a concrete demonstration that the loop area matters. Without it, saying PCB traces have impedance is rather academic and meaningless. Just name dropping concepts isn’t teaching.

          1. Teaching a concept is a very valid motivation. But leading with this title is… just… yuck.
            Maybe I’m old (ok, I am old), but one could actually give it a sensible title that tells you what they are discussing. And using this same clickbaity title on HaD is just really wrong. At least tell us what it is about and then we can skip it, because “duh inductance” – or read it because “WTF, inductance? PCB trace geometry?”

            Yeah, I’m feeding the engagement farming.

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