Path: utzoo!attcan!uunet!cs.utexas.edu!rutgers!iuvax!watmath!egvideo!timk
From: timk@egvideo.UUCP (Tim Kuehn)
Newsgroups: sci.electronics
Subject: Re: HV Cap Fun!
Summary: Let's get real here...
Keywords: capacitor,energy,paradox
Message-ID: <2027@egvideo.UUCP>
Date: 1 Jun 89 04:00:00 GMT
Reply-To: timk@egvideo.UUCP (Tim Kuehn)
Organization: A Box in the Basement, Kitchener, ON
Lines: 82

In article <349@arc.UUCP> apple.com!arc!steve (Steve Savitzky) writes:
>In article <20772@quacky.mips.COM> vaso@mips.COM (Vaso Bovan) writes:
>>A Paradox of Capacitor Energy Storage
>>

[first part of the original question deleted]

>
>>                                                         Eventually, the
>>voltage across each capacitor will be 5V. Now, there are two equally
>>charged capacitors, each storing (1/2)*CV^2= 25 joules, for a total of
>>of 50 joules.  What happened to the other 50 joules ?
>
>... followed by several unsatisfactory responses from several people
>who obviously didn't think about either the physics or the electronics
>of the situation.

And from looking at your answer I come to the same conclusion about what 
you posted too! :-)

>
>PHYSICS:
>


Analogy deleted....


>
>ELECTRONICS:
>
>We have the following circuit:
>
>       ---------[ Z1 ]---------
>       |                      |
>     -----   C1             -----   C2
>     -----                  -----
>       |          \  S1       |
>       ----------- \-----------
>
>Look familiar?  Those "wires" have inductance and (unless they're made
>of superconductors) resistance, represented by Z1.  

That is true, however we're talking about IDEAL circuits here - no stray 
capacitance, capacitor leakage, resistance or inductance in the line, etc.,
so that the effects you're speaking of don't come into play.

Also the original question didn't mention anything about there being an
inductor in the circuit, and even if you did assume the wires had inductance,
the effect wouldn't be noticible for what we're dealing with here. (after all,
the inductance of a short piece of wire is somewhere in the nH or pH range
which makes the effect of L di/dt *quite* small.)

Again, if the wires had resistance, unless they were a high-resistance wire
or a long piece (couple hundred feet) of normal copper wire the effect would 
be negligable. (Given a normal wire of a short length, we're probably talking 
about 1E-3 or 1E-4 ohms, again  *way* too small to worry about here.)
[explination about oscillating systems with inductors, capacitors, and 
resistive components deleted]

>
>If the wires are resistive, some of the stored energy is converted to
>heat, and the oscillations damp down.
>
>THE TWO EXPLANATIONS ABOVE ARE EQUIVALENT.
>

[more stuff deleted]

>Satisfactory?

Nope. You are to be commended on giving an informative discussion on the nature
of oscillating systems, however you should be slapped on the wrists for making
the error of not making sure of the question and the parameters first, and 
then answer a question that wasn't asked!  (insert many :-)'s here...)

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