The mystery of the missing joules

A liquid dielectric exhibiting Debye behavior can be represented by a series RC circuit. It is evident that if this circuit is energized by a constant DC source, when the capacitor is fully charged the amount of energy stored in it is equal to the amount of energy expended as heat in the resistor. Nevertheless, the variation of power with time delivered to each element is not the same. In his analysis, Debye ignores the inertia of the molecular dipoles, and it follows that the total torque acting on each of them must always be zero. He therefore equates the driving torque on each dipole created by the applied field to the retarding torque, proportional to dipolar angular velocity, caused by inner molecular friction. However, it is evident that following DC charging, the energy which is returned on discharge must have been stored in the dielectric. It is shown that this energy storage can be attributed to the work done against another retarding torque in addition to the frictional torque. Although such a torque was not introduced explicitly by Debye into his analysis, his method produces the same result that he would have obtained if he had done so.