🚀 go-pugleaf

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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