Xref: utzoo sci.electronics:7998 sci.physics:9841 Path: 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 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 ===================================================================