Yes 20.4% -- thanx – fixed. But 20.4% for 1000 mm spacing is mindblowing. I thought that the 2.0% should have been more like 0.2%.
The per-length L and C of a transmission line does not change with end-on scale - 1m spacing and 10mm wires, or 10mm spacing with 0.1mm wires are the same (scale invariant). But remember it is thousands of km long, and since the wavefront travels extremely fast, within almost no time a very long section of cable (compared to spacing) is 'exposed' to electricity. Even in 1 microsecond a 300m length of 1m-spaced wire is involved, and in just 1 millisecond that extends to 300km of 'capacitor'. So it should be no surprise that it is capable of transmitting significant current. In my simulation on p 18 this is enough to light an 8W LED lamp at full brightness off 240V mains (assuming no radiated losses).
I reckon that TL theory & TL models are wrong (physics wise) but give goodish results. This (goodish results) might indeed be so for DC steady state electricity (ie after the non-steady transients have gone), & for AC "steady state" (wall to wall steady transients). And now in the picosecond era we find that proponents of TL models (ie almost everybody) are confident that TL models can predict or postdict the initial stage-1 transients (in the first say 3 nanoseconds), plus stage-2 (say 10 ns) & stage-3 (say 1000 ns) etc.
Nonetheless i do want to learn more about TL & TL models. Partly koz this might help my thinking re Veritasium's gedanken transient question, & re AlphaPhoenix's X pt1 transient (ie to test my new electricity). My new electricity is a work in progress, & so far i think it is ticking all of the boxes. Old electricity seems to be ok, in a limited way in limited cases, but its contradictions are ignored (eg how does insulation on a wire slow the electricity). The Veritasium gedanken & the AlphaPhoenix X pt1 have created a number of wonderful new boxes to tick, & i reckon that old electricity will fail (which i will look at at a later date).
So, we can start with one new old box. How does insulation slow electricity along a wire? In particular, do any TL models allow input for insulation on the wire(s)?
AlphaPhoenix sidesteps this insulation problem, he intentionally refuses to tell us the lengths of his wires (he admits that), he merely says that his half-loops are 1.6 microseconds long. However, his 24AWG copper wires have a heavy enamel insulation, hence the speed of electricity along his wires can't exceed say 2c/3 m/s.
Veritasium sidesteps this insulation problem, he says that his loops are 1 light-second long. However, early on in his youtube he does accidentally say that each loop is 300,000 km, in which case his options should have been 1.5 seconds instead of 1 second, & 3 seconds instead of 2 seconds, but he never corrects his error. We can see that his wires have heavy plastic insulation, but we don’t know whether the remaining 2 light-seconds of wire is similar, which duznt matter koz he has (later in his youtube) specified his loops as being 1 light-second long (if u ignore his earlier accidental error). But he should have corrected his (earlier) error. I suspect that he duznt even realise that his error exists, in which case Veritasium duznt realize that insulation makes a difference. But i feel sure that AlphaPhoenix knows, & that he intentionally sidestepped the issue in his own X pt1. After all, insulation duznt matter in his X pt1, if AlphaPhoenix used bare wires (with zero enamel) he would have got 0.2 V in the first 1,600 ns anyhow. No, wait, if he used the same lengths of wire, but bare, it would have been 0.2 V in the first 1,067 ns. But i suppose that it’s the 0.2 V that counts, the 1,600 ns is a minor side-issue. But it aint a minor issue for old electricity, it is a box that old electricity fails to tick. But no such problem for new electricity.
If Veritasium realized that insulation can make a difference (to the speed of electricity along a wire), then he would have the mother of all electricity topics for the mother of all electricity youtubes. The problem being that his youtube would finish without having an answer (ie re how plastic on the surface can influence conduction electrons slowly drifting along inside)(or re how it can influence the speed of the wavefront created by drifting electrons bumping drifting electrons).
But back to your comment that….
The per-length L and C of a transmission line does not change with end-on scale - 1m spacing and 10mm wires, or 10mm spacing with 0.1mm wires are the same (scale invariant).Yes, i am happyish with that stuff, but i still don’t get it.
Intuitively a 1 mm negatively charged wire with 6248 C/m might induce 1 C/m of positive charge on a parallel 1 mm wire 1000 mm away, based on the circumference at 1000 mm radius being 6248 mm (& based on the electric field diminishing as 1/r).
If i hung the 2 wires on silk threads, while maintaining the 1000 mm gap, & gave the red wire 6248 C/m of negative charge, what charge would be induced on the pink wire. The answer must be zero C/m. All that would happen on the pink is that free surface (conduction) electrons would move to the far side.
If i had an earth connection on the pink wire then yes i would expect to see that it was positive (koz some electrons would exit to earth). If there was an earth connection at each end then a half of the electrons would exit left & a half right. But how positive. Surely not 6248 C/m. If it was 6248 C/m then it would logically still be 6248 C/m if i made the gap 1000 km. I might be told that the wires & gap are taken into account when calculating the characteristic impedance. But i don’t want to worry about that today, except to say that i reckon that the old electricity model of characteristic impedance is bad physics.
I am happy with the old electricity concept that drifting electrons are closer to each other due to the need to push through the resistance of the wire, & that by being closer they give us negative charge.
But back to your comment that….
since the wavefront travels extremely fast, within almost no time a very long section of cable (compared to spacing) is 'exposed' to electricity. Even in 1 microsecond a 300m length of 1m-spaced wire is involved, and in just 1 millisecond that extends to 300km of 'capacitor'. So it should be no surprise that it is capable of transmitting significant current….. Yes, the live wire & a parallel wire act like a capacitor. I see some problems.
Old electricity says that electrons drift along inside a single wire to say the bottom plate (where they accumulate)(the plate becomes negative), & the bottom plate repels electrons from the top plate (& these exit along a single wire), & the top plate becomes positive, & the top plate then attracts more electrons to the bottom plate, which starts a gradual feedback mechanism whereby the bottom plate repels even more electrons from the top plate, etc etc. So, here a TL model should (if it is to have any hope of accurately predicting stage-1 transients) show an initial current that gradually reduces to zero from each pseudo-mini-capacitor (if the leading edge of the primary current in the TL has a vertical step). I will be told that there are standard equations that tell us the charging times (energising times) of capacitors, but i suspect that these do not include an allowance for the gap tween plates (ie they assume 00 mm).
Veritasium has a gap of 1000 mm, & this 1000 mm might in effect have to be crossed 10 more times to give 5 feedbacks (before it is zero), this adds to 11,000 mm (ie 36.7 ns at the speed of light). I suppose that this duznt change Veritasium's 3.3 ns, ie the initial time for a signal to reach across to the other wire (ie to the bulb). But it should show up in the stage-1 of the transient, & even in stage-2.
This kind of delay wont show in the
AlphaPhoenix X pt1 (100 MHz scope) but it might show in the shape of the trace in stages-1 & 2 of the transient in
Howardlong's X (20 GHz scope)(his gap was 24 mm, & initial delay 80 ps)(reply #1042 on page 42)(i will have a look).
AlphaPhoenix got 0.2 V in (say) stage-3 of the transient, which later rose to 1.7 V. This was for say 0.16 km of enamelled wire out (plus 0.16 km coming back), & his stage-3 lasted for 1,600 ns. I suspect that had he used 300.00 km of (enamelled) wire out, plus 300 km coming back, he would have gotten 0.2 V, rising to 1.7 V at 3,000,000 ns. I don’t think that his 0.2 V would increase with length.
All of the above percentages are astonishingly high. But i think i know what happens.
To me and some others here, these results were astonishingly low. For a properly terminated transmission line (which the arms of this circuit can be) and differential drive (which is impossible for the arms because they are driven with a common mode voltage), the initial voltage and current should be 50% of the steady state.
I am surprised that conventional lumped element models for TLs have not yet been proven to umpteen decimals. What happened?
I think that's because there is no need to; they are engineering tools which work adequately for practical purposes, not precision experiments designed to test the limits of QFT. 1% error would usually be good enough. Their first application was sending digital data under the sea in the 1800s, and it and quite a bit of electrical theory grew from there. The need to test the limits for new physics probably never came up.
But this isn't what you're asking. It's as I said: The Veritasium experiment drives the TL models in an unbalanced way; driving one wire and looking for a current out of the other, from the same end. Usually both lines are driven in opposite ways eg +1V and -1V where the current 'through' the send end of the line (ie in one terminal and out the other terminal) is less of a philosophical conundrum. Nothing went wrong. The Veritasium experiment's looped arms are instead an antenna system which radiates power.
I thought that a radio signal (a brief almost immediate spike) would be all that we would ever see (in the first nanoseconds), but the AlphaPhoenix X pt1 opened my eyes. The radio spike must exist (made by the passing of the leading edge of the current along the primary wire) but it might be weak (perhaps less than 1 mA?).
I asked that someone do a TL model for Howardlong's X. Such a model would ideally predict/postdict each of the say 4 stages of the initial transients (of the induced currents)(before the main current arrives). And it could ideally predict/postdict the other say 10 stages of later transients (after the main current arrives)(transients caused by reflexions i suppose). However i suspect that such models were never designed to predict initial transients. I suspect that the models are okish for the later transients. Anyhow i am surprised that today there exist any problems with the application of TL models. Or, are they mainly for amusing skoolkids? ? ? ? ?
Look at all of the pseudo-mini-capacitors joining the top wire to the bottom wire (in TL models). They are drawn with a say 1 mm gap. For the Veritasium gedanken i reckon that they should have 1000 mm gaps. Look at the induced pseudo-current from the pseudo-mini-capacitors, i bet that it is all sent towards the pseudo-bulb, no, i reckon that a half should be sent away from the bulb.
What I just wrote above is one reason why no one took up your request - it has already been determined in this thread. In my kind of tongue in cheek model on page 18, I expected radiation loss, but at the time <10% which is unimportant for lighting an 8W lamp at about the right brightness. It shows the disadvantage of running too far (quantifying) via intuitive feel. The numbers can be orders of magnitude out which is far away from "umpteen decimals". In short, TL models predict everything with 'great' accuracy, but are not an accurate tool to model the Veritasium circuit with, because it works differently.
Schematic capacitors are not intended to depict anything physical so the 1mm gaps are neither here nor there, as I assume you know, but you still want to contrast them with 1000mm to make a point. The point is not lost on the engineers who draw them (Dave, Mehdi, etc), who know the capacitors can take on any value and thus feel no need to draw a 12pF cap with say a page-wide gap on paper. The actual gaps are 1m like you say, the current isn't a pseudo-current (or if it were, there is no means to distinguish it from a real current) and the mini capacitors are real not pseudo (the real distributed capacitance of a TL can be very easily measured between the wires for a defined short length). Yes, half this current does go forward and half back - the transmission line charges with current and delivers to an impedance-matched load in equal amounts. Enough for now, for the night.
I am pleased to see that TL models send the pseudo-mini-capacitor currents half each way.
I agree that the currents from the pseudo-mini-capacitors are real. In that they mimic the real currents arising from the repelling of electrons from (along) the secondary wire. And we need not worry about the old argument whether displacement current is real (it aint).
I agree that a TL has a real (measureable) distributed capacitance. Some call it charge, some call it energy (whatever).
I think that a TL model can give good numbers, even if the theory is wrong. But i suspect that TL models wont or can't account for the stage-1 & stage-2 transients of the Howardlong X. But they might if one included some smart elements etc. But i think that it would take more than some smart elements, it would need the application of my new electricity (& the dumping of the old electricity).