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#1
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Two Cap Puzzle
On Fri, 16 Jul 2010 20:40:26 -0500, flipper wrote:
On Fri, 16 Jul 2010 07:52:47 -0700, Jim Thompson wrote: On Thu, 15 Jul 2010 23:37:35 -0500, flipper wrote: On Thu, 15 Jul 2010 17:59:57 -0700, Jim Thompson wrote: On Thu, 15 Jul 2010 18:45:33 -0500, flipper wrote: On Thu, 15 Jul 2010 13:35:09 -0700, "Paul Hovnanian P.E." wrote: My solution for the missing energy. I'm not sure what inspired the analysis but you don't need two capacitors to express the 'conundrum' as you've got it in the very first term for E in a charged capacitor. From the definition of C, q, V, and E one might expect E, in an 'ideal' capacitor, to be qV or, by substitution, C*V^2 but, as you point out, it's commonly known to be .5*C*V^2. Where did the missing energy go? The answer is the same, dissipated in the R 0, and is inherent to the charging of a capacitor whether it is from a battery or, in your case, another capacitor. Trying to postulate an 'ideal' circuit with R=0 leads to the impossibility of an instantaneous charge of infinite current and with electron mobility limited by the speed of light the universe, as we understand things, simply can't do it. Flipper, _In_the_limit_ as R-0 the exact same amount of energy is lost as with a finite R. Try it, you'll like it :-) I understand your point and one of the endearing things about math is you can calculate the impossible but in this case I think it is more confounding than illuminating as most people will likely have difficulty estimating the dissipation of infinite current through 0 ohms. So why bother confounding the matter with a singularity that cannot exist? ...Jim Thompson I'm just saying that, even with an IDEAL switch, the energy is lost. Perhaps but it doesn't illuminate because the question remains: where did the energy go? And the fact remains that electrons cannot move faster than the speed of light so the condition you mathematically 'solved' cannot exist. I see those as serious problems for 'explaining' the conundrum posited. Otherwise the newbie lurker, and those as ignorant as Larkin, will think it's only lost in the finite resistance case. The problem is that the limiting case you posited cannot exist. Oh, you may make (some) R=0 but you do not have an 'ideal C' nor an 'ideal switch'. Doesn't matter. Something more is going on. Do the due physics. You don't like math ?:-) Why would you ask such a thing with "endearing" being a term of affection? It was a bit tongue in check but it isn't the 'math', its the presumptions of the model one then applies the math to. I picked what I thought would be a simple and obvious limit, the speed of light, and unless we've found a way around that then, Houston we have a problem... with the model. ...Jim Thompson |
#2
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Two Cap Puzzle
On Wed, 21 Jul 2010 02:34:01 -0500, flipper wrote:
Doesn't matter. Something more is going on. Do the due physics. If you think you have a case to make about something then make it. I have been trying. I want to teach you "how to fish", rather than "give you a fish". |
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