A Circuit-Theoretic Anomaly Resolved by Nonstandard Analysis

Abstract

An anomaly in electrical circuit theory is the disappearance of some of the 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 enregy that had disappeared, and that all but an infinitesimal amount of this dissipation occurs during an infinitesimal initial time period.