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From: ARaman@massey.ac.nz (A.V. Raman)
Newsgroups: sci.electronics,sci.physics
Subject: A violation of the law of conservation of energy
Keywords: paradox
Message-ID: <318@massey.ac.nz>
Date: 26 Sep 89 04:21:43 GMT
Reply-To: ARaman@massey.ac.nz (A.V. Raman)
Organization: Massey University, Palmerston North, New Zealand
Lines: 45

This problem has puzzled me for 2 years
Can someone please help me out:

                       ________________
                      |                |
                   V ---             ----- C
                  ---------          -----
                      |                |
                       -----RRRRR------

Consider the RC circuit above.

The aim is to determine an equation for the energy expended in the resistor
R at t = infinity.

If we denote the energy at t = infinity by E, then
E = integral from t = 0 to t = infinity (power (t) dt)
where power = R * square (i)
since i = f(t) = V/R exp (-t/RC)
E = integral from t = 0 to t = infinity (square (V) / R exp (-t/RC))

which implies E = C * square(V) / 2
which is perfectly logical considering the fact that E = total energy -
energy stored in the capacitor.

But note that the energy expended in R does not depend on R itself.

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?

On creation of such a circuit, the charge that will flow out of V into C
is 1 coulomb.
By definition then, the energy transferred from V to C is
charge * pressure = 1V * 1C = 1 joule
But what is the energy stored in the capacitor?
It is half C*square(V) = half * 1 * square(1) = half joule.
Where has the remaining half joule gone?
Beats me!



-- 
/*----------------------------------------------------------------------*/
Anand Venkataraman - Systems group, Computer Center, Massey University,
Palmerston North, New Zealand
INTERNET: A.Raman@massey.ac.nz  Ph: +64-63-69099 x7943  NZ = GMT + 12