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Two theorems on dissipative energy losses in capacitor systems

This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction of energy dissipated in the resistor depends solely on the ratio of the two capacitances. The values of the original charge and the resistance play no role. In the second case half of the energy supplied by the battery is dissipated and half is stored in the capacitor. The values of the battery emf and the resistance play no role.