I would like to respond to David Rutherford's argument that energy is associated with both the heat gained by the surroundings (via what he calls the transverse component velocity) and the kinetic energy associated with the current (which he relates to the longitudinal component velocity).
This is actually a common source of confusion for my students and so I would like to see it better addressed than it has. DR is right that, at any given time, only part of the energy (associated with the kinetic energy of the electrons) will be converted to heat as measured by the calorimeter experiment. However, the key point that I think my students (if not DR) miss is that eventually the current will stop. At that point, all of the energy will be dissipated to the calorimeter. Consequently, the calorimeter should be measuring *all* of the energy dissipated by the resistor (which, in turn, must be equivalent to the initial energy stored by the capacitor since the final current in the circuit is zero).
Of course, this only addresses the question of how to measure the energy. It doesn't address the original question of why we can't double-count the stored energy.
I may be totally misinterpreting DR's question but let me rephrase it in a way that I think my student's would ask it. If we have two balls connected by a spring and we compress the spring by holding one ball stationary while moving the other ball toward it, haven't we done work on*both* balls?
After all, our muscles are working to keep the stationary ball steady. Where does that energy go if not into the stationary ball or at least the two-ball configuration?
Note: To address this, I find that JG's terminology is helpful. I also find it helpful to compare two situations. In one situation, one ball is held stationary while the other is brought toward it. In the other, both balls are brought toward each other. Compare the stored energy in both cases.
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Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301