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Veritasium "How Electricity Actually Works"
electrodacus:
--- Quote from: ejeffrey on May 04, 2022, 07:29:17 am ---
--- Quote from: electrodacus on May 04, 2022, 06:30:29 am ---Like the fact that a 20nF capacitor has a very small capacity and so even a relatively short wire will have an inductance large enough that you form a resonant circuit.
--- End quote ---
Any indicance and capacitance will (at least in an ideal situation) form a resonant circuit.
--- Quote ---If you use a few mF then even with fairly long wires the inductance is super negligible and it is not a problem.
--- End quote ---
Only to the extent that the parasitic L and R of a real world 1 mF capacitor are likely to be larger. But an ideal 1 mF capacitor plus a 10 nH inductor will resonate at about 50 kHz. A more realistic 100 nH inductance will lower the frequency to 15 kHz.
--- Quote ---The DC-DC converter is fairly easy to do but likely not for last few people that replayed to me.
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Everybody here agrees that the DC DC converter will do exactly as you have described. Nobody is trying because there isn't any disagreement on this topic so no point arguing. Our contention is that simply shorting a capacitor out will do something different and Tim did experiments to demonstrate that the circuit either oscillates or decays to V/2.
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All are good points but you likely did not read all the earlier replays.
People did not understood that doing a test with superconductor materials is not trivial unless they work at some large university lab and even then it will be expensive. And did not got the idea that all the elements in the circuit will need to have zero resistance in order for all of the energy to remain in the two capacitors at the end of the test.
You are the first to mention that the DC-DC converter will do what I described. The others before where either not convinced as they where confusing charge with energy and thinking that everything is already conserved just with two normal capacitors.
And some others suggested that adding instructors and active components will somehow add energy from exterior.
The circuit will always decay to V/2 in a real setup (not ideal without resistance) as it was demonstrated in a video posted earlier.
But he concluded that energy was conserved as he confused charge with energy.
Exactly half of the energy was lost as heat in the circuit resistance and that will always be the case as long as resistance is different from zero no matter the resistance value.
The main point is that a transmission line is a capacitor or the other way around a capacitor is a transmission line and what Derek observed in his experiment as current trough that 1.1Kohm load resistor is just due to transmission line capacitance.
There will be a current trough the 1.1kOhm resistor because is in series with the supply the switch and two smaller value capacitors formed by the transmission line.
So his claim that energy travels outside the wires is false in all instances not just DC but even at initial transient when switch is closed or in AC
The electric field will only be present after charges are present.
Also the fact that half of the energy is lost as heat (heat in the conductors) should be clue enough that energy was transferred trough wires.
Electrons are those that transfer the energy from source to load and not as Derek claims electric field.
I'm also a bit rude and I apologies for that. I feel frustrated trying to explain this and I still have PTSD from a few months ago when I tried unsuccessfully to explain how the faster than wind direct down wind vehicle works and there the exact same type of mistake was made and energy storage was not considered.
The short answer to that problem is that energy is stored in pressure differential (air is a compressible fluid) while vehicle was well below wind speed and that stored energy is what allowed the vehicle to temporarily exceed wind speed. All experiments end before that stored energy is used up and so they concluded that vehicle will continue to accelerate basically forever.
Seeing people with phd in physics not understanding energy conservation was hard.
T3sl4co1l:
--- Quote from: electrodacus on May 04, 2022, 03:03:39 pm ---All are good points but you likely did not read all the earlier replays.
People did not understood that doing a test with superconductor materials is not trivial unless they work at some large university lab and even then it will be expensive. And did not got the idea that all the elements in the circuit will need to have zero resistance in order for all of the energy to remain in the two capacitors at the end of the test.
--- End quote ---
I have just one more question. You've seen the waveform; I ask you: after one half-cycle, where is the energy? How much of it? After one full cycle, where is the energy? How much of it? And this repeats on, ad infinitum; it is, as you say, an oscillator.
Where does the energy remain at the end of the test?
Tim
electrodacus:
--- Quote from: T3sl4co1l on May 04, 2022, 03:39:45 pm ---
--- Quote from: electrodacus on May 04, 2022, 03:03:39 pm ---All are good points but you likely did not read all the earlier replays.
People did not understood that doing a test with superconductor materials is not trivial unless they work at some large university lab and even then it will be expensive. And did not got the idea that all the elements in the circuit will need to have zero resistance in order for all of the energy to remain in the two capacitors at the end of the test.
--- End quote ---
I have just one more question. You've seen the waveform; I ask you: after one half-cycle, where is the energy? How much of it? After one full cycle, where is the energy? How much of it? And this repeats on, ad infinitum; it is, as you say, an oscillator.
Where does the energy remain at the end of the test?
Tim
--- End quote ---
Your was a normal circuit with resistance so it will not oscillate forever as energy will all be dissipated as heat after just a few oscillation cycles.
You seemed to have an almost matched resonant circuit meaning the capacitor and inductor energy storage capacity was almost identical thus the large fluctuation.
If you had order of magnitude larger capacitance than inductance then you will not even notice any oscillation unless you had super high vertical resolution oscilloscope.
If you had the means to build a superconductor experiment then you will have build the capacitors as in one of my earlier examples as below
____________________________
____________/ ______________
this sort of physical setup will have extremely low inductance relative to capacitance (very small distance between plates and a good dielectric material between) then you will not see any oscillation unless you had super high vertical resolution equipment as oscillation amplitude will be some infinitesimal small value around the 0.707 Vi so maybe 4'th or 5'digit type fluctuation that will remain forever as there is no resistance for the energy to be dissipated as in non superconductor circuits.
An inductor opposes the change in current flow so the opposite of a capacitor that opposes the change in voltage.
The capacitor creates a electron imbalance between the plates that in turn result in an electric field inside the capacitor.
With the inductor an magnetic field is generated in the space surrounding the inductor and that field is where energy is stored (stored not dissipated).
So at constant current you will have a constant magnetic field (same as you have on a permanent magnet) but if the current reduces the magnetic field will reduce but the energy stored in that magnetic field is converted back to current flow.
The best analogy I can came up with will be a flexible stretchy hose where the elastic force represents the magnetic field.
If you flow water trough a long flexible hose (hose is already filed with water but not under any pressure) then when you open a valve connected say to a barrel filled with water (barrel the analogy for capacitor) the hose if super stretchy (high inductance) will oppose the flow of water as it will start to stretch before it allows water to flow on the other end and so at constant water flow (constant current flow) the hose is stretch is maintained at some level but if you increase the flow the hose will stretch even more storing even more energy (it is not lost) and then that energy can be recovered as the flow drops as the hose will put pressure on the water trying to maintain the earlier flow.
Do not try to push this analogy further as there are differences beyond this. It is just an analogy for the inductor as an energy storage device.
T3sl4co1l:
So you propose a superconducting resonator? Yeah, those resonate too. :)
Examples that come to mind are the cavities used in particle accelerators, with Q factors up to 10^8 (it's not quite infinite because there's always some loss at AC), and superconducting qubits which, being small enough and cold enough that quantum mechanics is quite relevant, have ground states that are effectively resonators in perpetual motion (and for which, bulk measures like Q aren't so meaningful).
The bulk metal forms of these resonators might not be called high inductance, but the fact that they resonate at 100s or 1000s of MHz makes that irrelevant.
Low inductance is not no inductance!
The permeability of free space has units of per-length. Anything that has nonzero physical size, must necessarily have inductance! Even free space itself, or else waves wouldn't propagate (that, or some wierd causality shit that would be even more bonkers if true..).
It seems your gap in knowledge comes down to magnetic aspects:
- Length corresponds to inductance (notice I hinted earlier that the waveform and capacitance were sufficient to solve for the wire length -- evidently around 71m. Hm, it's quite a bit less than that actually, I think; I was lazy and just coiled it up on a spool, magnifying the effect.)
- Energy is stored in the magnetic field, proportional to current flow.
- Energy conservation is true, AND charge conservation is true. Both must be true jointly. However, it happens to be a hell of a lot easier to lose energy to dissipation or radiation into the surroundings, than charge into the surroundings!
- We can assess the behavior of a series RLC circuit (which this is, necessarily: see points above) based on the ratio of Zo = sqrt(L/C) to R. When Zo > R, some oscillation will be evident; when Zo = R, critically damped; Zo < R, overdamped (RC dominant).
- This is a continuum relationship and no distinction appears for R --> 0.
- As a special case, for R = 0, any combination of L and C will resonate; the damping factor is 0 regardless!
So I maintain that my waveform was obtained from a superconducting apparatus until proven otherwise. ;D
I mean, how would you know? Given the above information, can you solve for the resistance (if any) in my circuit?
And there's nothing wrong with the waveforms; half the time, the energy difference (the "missing" 0.5 Ei) is stored in the inductance as current flow. The other half it's in one or the other capacitor, hence the voltages alternate between 0 and Vi. Energy is always conserved! And charge is always conserved too, which is why this process averages 0.5 Vi during the wave, and as the AC transient decays (when R > 0), the energy difference is dissipated as heat. The fact that the capacitors end with 0.25 Ei each, 0.5 Ei total, is also no coincidence; perhaps less satisfying than having no dissipation, but the dissipation itself is a necessity (for such simple circuits; else, we must go to great lengths if we wish to avoid it -- such as DC-DC converters!) and so this is the result, no sqrt(2) to be found.
As for the sqrt(2), there is a separate chain of logic which should sound immediately. Such special ratios are EXTRAORDINARILY rare from simple systems. Impossible even, for suitable definition of "simple systems". Such ratios are more likely to be found in, say, properties of signals -- take the peak to RMS ratio of a sine for example, or its integral which picks up a factor of pi -- but not from such simple, finite, geometric relationships like two capacitors rubbed together. This is ultimately a deep truth about numbers themselves, you can't get an irrational (like sqrt(2)) from a rational (like 1/2) without going to some lengths first (sqrt(2) is an algebraic number).
Or, if we could easily construct such ratios -- it would certainly make transformer design easier. We could easily and accurately match 50 to 75 ohms, for example: a 1.5:1 impedance ratio. But we cannot: a 1.22474... turns ratio is needed. We can only get arbitrarily close. (The continued fraction representation of this ratio goes [1; 4, 2, 4, 2, ...]; large numbers in the continued fraction are desirable as they represent points of especially good (but still not perfect!) fit, but repeating sequences like this don't give any especially good stopping points.)
Tim
electrodacus:
--- Quote from: T3sl4co1l on May 04, 2022, 05:37:13 pm ---So you propose a superconducting resonator? Yeah, those resonate too. :)
Examples that come to mind are the cavities used in particle accelerators, with Q factors up to 10^8 (it's not quite infinite because there's always some loss at AC), and superconducting qubits which, being small enough and cold enough that quantum mechanics is quite relevant, have ground states that are effectively resonators in perpetual motion (and for which, bulk measures like Q aren't so meaningful).
The bulk metal forms of these resonators might not be called high inductance, but the fact that they resonate at 100s or 1000s of MHz makes that irrelevant.
Low inductance is not no inductance!
The permeability of free space has units of per-length. Anything that has nonzero physical size, must necessarily have inductance! Even free space itself, or else waves wouldn't propagate (that, or some wierd causality shit that would be even more bonkers if true..).
It seems your gap in knowledge comes down to magnetic aspects:
- Length corresponds to inductance (notice I hinted earlier that the waveform and capacitance were sufficient to solve for the wire length -- evidently around 71m. Hm, it's quite a bit less than that actually, I think; I was lazy and just coiled it up on a spool, magnifying the effect.)
- Energy is stored in the magnetic field, proportional to current flow.
- Energy conservation is true, AND charge conservation is true. Both must be true jointly. However, it happens to be a hell of a lot easier to lose energy to dissipation or radiation into the surroundings, than charge into the surroundings!
- We can assess the behavior of a series RLC circuit (which this is, necessarily: see points above) based on the ratio of Zo = sqrt(L/C) to R. When Zo > R, some oscillation will be evident; when Zo = R, critically damped; Zo < R, overdamped (RC dominant).
- This is a continuum relationship and no distinction appears for R --> 0.
- As a special case, for R = 0, any combination of L and C will resonate; the damping factor is 0 regardless!
So I maintain that my waveform was obtained from a superconducting apparatus until proven otherwise. ;D
I mean, how would you know? Given the above information, can you solve for the resistance (if any) in my circuit?
And there's nothing wrong with the waveforms; half the time, the energy difference (the "missing" 0.5 Ei) is stored in the inductance as current flow. The other half it's in one or the other capacitor, hence the voltages alternate between 0 and Vi. Energy is always conserved! And charge is always conserved too, which is why this process averages 0.5 Vi during the wave, and as the AC transient decays (when R > 0), the energy difference is dissipated as heat. The fact that the capacitors end with 0.25 Ei each, 0.5 Ei total, is also no coincidence; perhaps less satisfying than having no dissipation, but the dissipation itself is a necessity (for such simple circuits; else, we must go to great lengths if we wish to avoid it -- such as DC-DC converters!) and so this is the result, no sqrt(2) to be found.
As for the sqrt(2), there is a separate chain of logic which should sound immediately. Such special ratios are EXTRAORDINARILY rare from simple systems. Impossible even, for suitable definition of "simple systems". Such ratios are more likely to be found in, say, properties of signals -- take the peak to RMS ratio of a sine for example, or its integral which picks up a factor of pi -- but not from such simple, finite, geometric relationships like two capacitors rubbed together. This is ultimately a deep truth about numbers themselves, you can't get an irrational (like sqrt(2)) from a rational (like 1/2) without going to some lengths first (sqrt(2) is an algebraic number).
Or, if we could easily construct such ratios -- it would certainly make transformer design easier. We could easily and accurately match 50 to 75 ohms, for example: a 1.5:1 impedance ratio. But we cannot: a 1.22474... turns ratio is needed. We can only get arbitrarily close. (The continued fraction representation of this ratio goes [1; 4, 2, 4, 2, ...]; large numbers in the continued fraction are desirable as they represent points of especially good (but still not perfect!) fit, but repeating sequences like this don't give any especially good stopping points.)
Tim
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Maybe I was not clear enough.
If you have orders of magnitude larger capacity than inductance then you will not even be able to measure the signal (and I'm referring to amplitude not frequency).
So a sine wave with 0.001 Vi amplitude and a 0.707 Vi DC offset. An 8 bit scope will not be able to measure that and even with a 12bit scope the signal will be in the noise so you will read a DC voltage of abut 0.707 Vi
The setup that you build was something like 0.9 Vi waveform amplitude so an almost perfectly tuned LC oscillator due to using almost equal L and C in therms of energy storage.
Also all this is irrelevant as energy is conserved in LC vs the RLC where half of the energy ends up as heat when energy is transferred from one identical capacitor to another. This is a fact both if you do the calculations using appropriate equations and if you measure the temperature rise of the conductors.
Now that I think about you can not get a perfect capacitor as there is no perfect dielectric (as far as I know) so there will be losses there and energy from this super conductor made capacitor will slowly dissipate over time as heat due to leakage in dielectric.
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