Sorry, but I believe half of the energy used to charge your empty capacitor is lost in heat inside the resistance between them+electromagnetic energy.
Just for Joe.
Scott asked about energy which is 0.5xCxVxV . Connect two identical capacitors and half the energy vanishes although charge (CV) is conserved.
Simple question as to why. Yet you decide to get all defensive and quote Feynman.
Scott asked about energy which is 0.5xCxVxV . Connect two identical capacitors and half the energy vanishes although charge (CV) is conserved.
Simple question as to why. Yet you decide to get all defensive and quote Feynman.
The Feynman quote was not defensive at all, rather the other way around. It is a fair descriptor of what happens.
But fair enough, a Joule calculation is what I should have done and that would have revealed it. Fair cop.
But I shan't exactly lose a lot of sleep over it. Can we move on from child's play, please.
These academic questions that involve infinities get on my tits. Supercilious.
It may be easier to grasp by considering the charged cap draining in to the empty one through a constant current source until both have the same charge/voltage. The work done in this transfer is the integral wrt time of voltage across the CCS times the current. This work done is the energy that is lost.
Magically infinite current/superconduction is not required.
It may be easier to grasp by considering the charged cap draining in to the empty one through a constant current source until both have the same charge/voltage. The work done in this transfer is the integral wrt time of voltage across the CCS times the current. This work done is the energy that is lost.
Magically infinite current/superconduction is not required.
Fair point.
In what electronic circuit would you do this? Maybe such a circuit does exist and for good reason, but I shall not waste much time trying to find it. 😀
Too complicated.
Get a capacitor and charge it from a battery. The energy stored in the capacitor is CV^2/2=QV/2 while charge conservation says that the batery delivered an energy of QV. Where is half of the battery energy?
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Took a few seconds. A full answer would describe the problem with the question and how it would turn out in reality including as JN might see it. An undergraduate EE degree should be more than enough for the gist of it, but don't know what percentage would give a good answer.
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Wright brothers - Wikipedia
You might want to do some serious research about the context of that quote. You might find that it actually invalidates the "naive" approach you seem to champion versus "conservative". The Wright Brothers were very thorough and not willy-nilly about how they went about their business. Notice the part about them building a wind tunnel to develop airfoils? And the very people the quote is admonishing weren't exactly working from empirically validated bases. You're at least 100 years late on a huge portion of the electronics theory that you're fighting against in terms of when it was empirically validated.
Also, "Not making S*** up" is not being "conservative", it's about knowing where the boundary between what is well understood and where we don't know. I'll let you in on a little secret about how discoveries are made nowadays: a team of bright folk will accumulate all the things we really do know well and then take that background (which requires pretty insane levels of diligence) and use it to push into the unknown. Notice I wrote "team"? Yeah. And depending on the discovery those teams are multi-billion dollar endeavors.
Futzing around with audio circuits isn't pushing into the unknown. Perhaps one's own lack of knowledge, which makes it a great learning pursuit.
Question was where did the difference in energy go, wasn't it? Won't say more now.
Okay, it turns to heat in resistance that wasn't mentioned, it it still there sloshing around back and forth between the plates because of inductance that wasn't mentioned, it radiated away due to sloshing around, or some combination of the above. Our idealized models that capacitors can exist without resistance or inductance is probably an over simplification.
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Well Tournesol mentioned the heat a load of posts ago, but first law of thermodynamics works for this (hence the calculus comment).
The same general problem. My favorite answer involves the work done to move charge so what the work does does not matter. The classic sometimes considered wrong solution involves assuming a resistance in the connection and the integrated power dissipated is always 1/2 the energy and the integral has that limit even as R goes to 0. But that does not account for the fact that the time for the charge to get from one place to another approaches 0 also. The recent paper I mentioned does a full EM solution to the paradox.
Haven't seen the paper, but in addition to unstated conditions in the problem as given, there is presumably an unstated assumption of system linearity (i.e. that boundary conditions are unchanging as the process transpires).
It's probably the fact that's it's 1/2 no matter you do to the parameters, that trips people up. If it was anything besides 1/2, they might start thinking about all kinds of things.
It is designed to be misleading, like many such interview questions. DIY IQ testing and personality inventory, all in one.
I disagree, finding out how someone thinks when faced with a paradox is hardly a "personality inventory". Physics supersedes in this case, work is put into the system and is taken out nothing has to be solved conservation of energy and charge are all you need. The problem here often is that the most basic principles of physics are considered inadequate for audio reproduction.
I find the same beauty in this problem as the T-line speaker cable issue.
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