I would like to suggest that if energy dissipation has occurred in the
charging of a capacitor, the amount of energy stored on the capacitor,
alone, cannot be used as evidence of the energy of a distribution of
charges. In the theoretical determination of the energy of (work done
on) a distribution, the assumption is that there is no dissipation of
energy as the distribution is assembled. Therefore, the optimum measure
of the energy of a distribution of charges should be in the absence of
dissipation. But in the case that dissipation occurs, the energy lost in
dissipation should be included in the energy that the distribution would
have had if no dissipation had occurred.
Thus, for a capacitor charged through a resistance, the energy
dissipated by the resistor during charging should be included, along
with the energy of the charges stored on the capacitor, in the energy
of (work done on) the charges. Since the energy dissipated by the
resistor during charging is 1/2 CV^2 and the energy stored on the
capacitor is 1/2 CV^2, I claim that the total energy of the charges,
in the absence of dissipation would have been CV^2. This would seem to
indicate that the energy of a distribution of charges is twice the
conventional value.