Xref: utzoo sci.electronics:6420 sci.physics:8410
Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!apple!bloom-beacon!think!eplunix!raoul
From: raoul@eplunix.UUCP (Otero)
Newsgroups: sci.electronics,sci.physics
Subject: Re: HV Cap Fun!
Keywords: capacitor,energy,paradox
Message-ID: <747@eplunix.UUCP>
Date: 2 Jun 89 01:29:59 GMT
References: <4924@m2c.M2C.ORG> <3806@mit-amt> <20772@quacky.mips.COM> <8742@fluke.COM>
Organization: Eaton-Peabody Lab, Boston, MA
Lines: 42

In article <8742@fluke.COM>, strong@tc.fluke.COM (Norm Strong) writes:
> In article <8739@fluke.COM> strong@tc.fluke.COM (Norm Strong) writes:
> }In article <20772@quacky.mips.COM> vaso@mips.COM (Vaso Bovan) writes:
> }}A Paradox of Capacitor Energy Storage
> }}
> }}Consider an ideal 2uF (for computational ease) capacitor charged by a 10 volt 
> }}source. Eventually, the energy stored is (1/2)*CV^2=100 joules.
> }}Consider the capacitor to be isolated from the voltage source, and then
> }}directly shorted across an identical (ideal) capacitor. 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 ?
> }
> }The extra energy is dissipated in the form of heat when the current flows
> }though the series resistance of the capacitor.  

What about superconducting materials? No resistive heat dissipation at all.
No, the gentleman who posted about the inductive effects of the wires
connecting the capacitors was much closer. Most real systems will have
heat loss as current travels through them, but even perfect conductors
have electromagnetic radiative losses: current oscillating through space
produces electromagnetic radiation, which can be described as an impedance
of the system. If the net impedance of the system is high enough, more
it damps the system and heat and radiation take up the energy before 
anything oscillates. If the impedance is to low, the system oscillates,
with current and charge oscillating back and forth between the capacitors.

This paradox is almost identical to that of shorting across a charged
capacitor. Where does the energy go?

This sort of problem is also partly why good capacitors are so much
easier to make than good inductors. Capacitors 'only' hold charge, so
they don't have to deal with the losses and problems inductors do.
Capacitors also pretty much contain their fields between their plates,
where inductors' fields project beyond their cores and cause no end
of grief....

-- 
			Nico Garcia
			Engineer, CIRL 
			Mass. Eye and Ear Infirmary
			eplunix!cirl!raoul@eddie.mit.edu