A Circuit-theoretic Anomaly Resolved by Nonstandard Analysis

An anomaly in circuit theory is the disappearance of some of the stored energy when two capacitors, one charged and the other uncharged, are connected together through resistanceless wires. Nonstandard analysis shows that, when the wires are taken to have infinitesimally small but nonzero resistance, the energy dissipated in the wires equals that substantial amount of energy that had disappeared, and that all but an infinitesimal amount of this dissipation occurs during an infinitesimal initial time period. This provides still another but quite simple model of what is in fact a multifaceted physical phenomenon. It also exemplifies the efficacy of at least one application of nonstandard analysis to circuit theory.