Article View: sci.electronics
Article #3252Re: A violation of the law of conservation of energy
From: Andrew Karanicolas
Date: Fri, 29 Sep 1989 00:19
Date: Fri, 29 Sep 1989 00:19
45 lines
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2090 bytes
In article <318@massey.ac.nz> ARaman@massey.ac.nz (A.V. Raman) writes:
>This problem has puzzled me for 2 years
>Can someone please help me out:
>
> ________________
> | |
> V --- ----- C
> --------- -----
> | |
> -----RRRRR------
>
>Consider the RC circuit above.
>
>.......
>That won't be quite as astonishing if not for the following reduction
>of the above circuit. What if R = 0, V = 1 and C = 1 for example?
>....
>Where has the remaining half joule gone?
>Beats me!
>
The capacitor problem once again! The difficulty with what you are asking
is that you are not considering _how_ the voltage is applied. If it is
applied in a step function manner, then you cannot consistently talk about
the energy as you will be implicitly evaluating an integral
E = int(-inf, inf){ v(t)*i(t) }dt
v(t)=V*u(t)
i(t)=C*V*delta(t)
where delta(t) is the Dirac delta function. As a result, the integrand
involves a product u(t)*delta(t) which is not defined. If you want,
I can send you references for more information. It is not a paradox,
it is not E&M radiation, it is a mathematical issue.
--
===================================================================
Andrew Karanicolas MIT Microsystems Laboratory
ankleand@caf.mit.edu MIT EECS Cambridge, MA 02139
===================================================================
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Path: arc1-ca.pugleaf.net!utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!cs.utexas.edu!mit-eddie!mit-amt!mit-caf!ankleand From: ankleand@mit-caf.MIT.EDU (Andrew Karanicolas) Newsgroups: sci.electronics,sci.physics Subject: Re: A violation of the law of conservation of energy Keywords: paradox Message-ID: <3248@mit-caf.MIT.EDU> Date: 29 Sep 89 00:19:14 GMT References: <318@massey.ac.nz> Reply-To: ankleand@mit-caf.UUCP (Andrew Karanicolas) Organization: Microsystems Technology Laboratories, MIT Lines: 45