[SI-LIST] FEM/BEM/MoM
- From: Abdulrahman Rafiq <arafi001@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Thu, 28 Aug 2003 12:07:50 -0700
Gary,
Ok that makes sense, 1/4 Joules of Energy being dessipated as
heat, as to the Paradox that Geoff is talking about, I think
he is trying to illustrate the fact that a circuit analysis
alone doesn't give one the full picture of what physically is
going on in the circuit. As from a purely circuit analysis
prespective you find that the Initial energy is 1/2 Joule,
and after the switch is closed you find it to be 1/4 Juoles.
Intutively, or from experimentally you could probably figure
out that there is some energy being desipated as heat.
However if one views the circuit from from a more "physical"
or "geometric" perspective one can explictly account for the
energy, thus satisfying the conservation of energy laws.
Thanks,
A. Rafiq
---------------------------------
The quarter-Joule turns into heat when the switch is
vaporized into a
cloud of smoke.
Whats the paradox?
Gary L. Pratt, P.E.
Product Manager
High-Speed Design Kits
Mentor Graphics
(503) 685-1177
gary_pratt@xxxxxxxxxx
Geoff,
Could you ellaborate on this a little more, as I am afraid i
can't quite see what happened to the 1/4 Joule of energy.
Perhaps if you could do a quick back of the envelope
calculation as an example.
-----------------
Just a little diversion to show the error in a schematic:
An old example often quoted is the problem of connecting two
one farad
capacitors together by a switch; one is at 1V potential, the
other zero.
The initial energy is 1/2 CV**2 =3D 0.5 joule. After closing
the switch th=
ere
is charge distribution, and energy =3D 1/8 +1/8 =3D 0.25
joule. Where did =
the
missing 0.25 joule go? If you did an electrical degree,
you'd see the
paradox. If you studied high frequencies, you'd know the
answer. (I did a
Physics degree, then built RF circuits, so for me a capacitor
is not a
capacitor.)
The answer is
1) it's not physically possible to put two capacitors
together at one point
2) therefore they are separated by a distance
3) therefore on closing the switch, the discharge current
travels a distance
4) the conductors have finite conductivity
5) therefore there is a varying electromagnetic field and
energy is
dissipated and radiated
6) please don't talk about too much about inductance because
it's only an
approximation.
-------------------
---------------------------------------
Abdulrahman Rafiq
Department of Physics
University of California
Riverside, Ca. 92521
Email: arafi001@xxxxxxx
URL: www.geocities.com/arafiq786
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-----------------------------------
---------------------------------------
Abdulrahman Rafiq
Department of Physics
University of California
Riverside, Ca. 92521
Email: arafi001@xxxxxxx
URL: www.geocities.com/arafiq786
--------------------------------------
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