Apparent Nonconservation of Energy in the Discharge of an Ideal Capacitor

An "ancient chestnut" of circuit theory is the energy loss in switched circuits made up of lossless storage elements. For example, a charged capacitor, short-circuited by an ideal conductor, loses all of its initial stored energy. This can be explained as a limiting case problem, which could not be physically carried out in any experiment, where the dissipated energy has the indeterminate form (0·¿). This paper gives a pedagogical treatment of this problem, bringing out the distinctions between the mathematical and physical problems. Energy is not necessarily "radiated" during this transient, as is sometimes claimed. For specially chosen geometry of the structure, the true radiation can be made vanishingly small. Furthermore, when radiation is present it can be accurately represented in circuit terms by introducing a circuit resistor to represent the radiation resistance of the structure acting as an antenna.