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Veritasium "How Electricity Actually Works"
electrodacus:
--- Quote from: T3sl4co1l on April 30, 2022, 03:14:24 pm ---
Your reaction to the paradox betrays your lack of understanding --
The above is a non sequitur. In the limiting case, two capacitors at equal voltage, connected together, lose no energy. It's not about the absolute energy, it's about where it goes. The zero-full case is as illustrative as any other, and using other ratios or initial conditions just adds more busy work to the problem without making any change to the central fact.
Indeed, one needs only a single capacitor, and some reflection upon what it means to discharge into a short circuit. In this case, we shouldn't expect charge to be conserved (it's shorted out), but you would apparently expect energy to be conserved, while it is not.
The complete answer is this: when inductance is included, then the capacitor(s) resonate with the inductance. If the circuit is later broken precisely at a peak or valley (when I_L = 0), the initial condition is restored and terminal voltage is +/- initial. In this case, energy is conserved, but so is the voltage, and |charge| has not changed. (Or +/- whatever the difference is, for the multiple capacitor case.) There is no state in which the circuit can be stopped, that gives a voltage other than this, that does not result in energy loss somehow (into ESR, switch loss, or it's stored in the inductor).
The case in reality of course always includes resistance, even if it's radiation loss, or poorly understood loss mechanisms of superconductors (example, polished niobium resonators at 2K and 500MHz have a very large Q factor -- indeed somewhat better than quartz crystals, but still far from infinite). In this case, as t --> infty, the difference, the AC / transient component, will always die out, leaving the intermediate case that satisfies charge conservation and not energy conservation (because the energy always finds a way out).
Tim
--- End quote ---
Let me know what part you do not agree with.
a) Energy is transferred from the charged capacitor to the discharged capacitor.
b) Since they are real components they have ESR so during the transfer process exactly half of the energy is lost for two identical capacitors.
c) When capacitors are not equal more or less than half of the energy is lost depending on with of the capacitors is the the charged one at the beginning of the test.
You do not need to include the small amount of inductance (witch is also an energy storage device) to do a correct energy balance.
If you could eliminate the ESR (like using superconductors) then energy at the end of the experiment will be the same with the initial energy.
Assuming you agree with the above do you agree with the fact that energy transfer is done trough wires ?
If you do not agree please be specific.
E63S4Me:
I'm happy that he did acknowledge the issue with units in answer C), which should have been 1 m/c.
Was this just unit laziness or an intentional bit of misdirection? Can't say. I'm inclined to believe laziness given the graphic which show the distances in kelvin mega (KM) rather than kilo meters (km).
A more universal answer for C) would have been d/c. Where d is the distance between the parallel wires.
By using 1/c, one might at first think it is the reciprocal of the speed of light, except for the meter term left unresolved.
If the distance were say 18.5 m, then answer C) would have been a more obvious choice if it were 18.5 m/c.
Still, I thought it was a good follow up video and appreciated his shout outs to many of the other response videos, each of which I'd seen and appreciated.
This is how we advance understanding of the art. Pose a thought and let others have a think and take pot shots at it. If the idea survives it has some merit, if not, well maybe one of the responses will be correct or trigger a new line of thought, and so on. :)
T3sl4co1l:
If you consider this trilemma to be exhaustive, I have a bridge to sell you?
Those are not equivalent to what you claimed above... the confusion seems to be over whether the capacitors have half energy each, or half energy total. Perhaps that post was poorly worded/typoed, I don't know.
Charge conservation dictates the voltage go down by half (again, for the equal case; don't bring other ratios into it, it's beside the point), therefore the energy in each is 1/4 and the total energy is 1/2 initial. This energy is dissipated in the resistance, or is stored in the inductance half the time. In no case will the capacitors have sqrt(2)/2 voltage (half initial energy) in them, which would be a very peculiar ratio indeed to see in a discrete circuit of such simple values.
Tim
electrodacus:
--- Quote from: T3sl4co1l on April 30, 2022, 04:06:45 pm ---If you consider this trilemma to be exhaustive, I have a bridge to sell you?
Those are not equivalent to what you claimed above... the confusion seems to be over whether the capacitors have half energy each, or half energy total. Perhaps that post was poorly worded/typoed, I don't know.
Charge conservation dictates the voltage go down by half (again, for the equal case; don't bring other ratios into it, it's beside the point), therefore the energy in each is 1/4 and the total energy is 1/2 initial. This energy is dissipated in the resistance, or is stored in the inductance half the time. In no case will the capacitors have sqrt(2)/2 voltage (half initial energy) in them, which would be a very peculiar ratio indeed to see in a discrete circuit of such simple values.
Tim
--- End quote ---
They will have half of energy each if you do not have ESR and capacitors have the same capacity.
If capacity is different then energy stored in each will be proportional (still no ESR).
Only in the special case where you have identical capacitors with identical ESR that you end up with half the initial energy as the other half was lost as heat due to ESR.
That is why I mentioned that energy storage should be a more important subject in school and be treated the same way as friction or restive losses.
Both mistakes done by Derek. This one about electricity and the one about faster than wind direct down wind vehicle are related to not understanding what energy storage is and conservation of energy.
T3sl4co1l:
Then you will agree the final voltages will be sqrt(2)/2, not 0.5, or 1 (initial)?
Please provide waveforms showing this.
Tim
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