The problem of the electrical discharge in an internally wired capacitor

Abstract

The present work investigates the dynamics of electrical discharges in a capacitor where both plates are internally connected by a conducting wire. A simplifying assumption used to solve the problem is to consider a uniform distribution of the surface charges on the plates. This implies uniform electric fields as well, and allows to calculate the current in the wire as if it were flowing along a simple RC circuit. We show that although the assumption is good if the conductivity of the wire is small, it fails if the conductivity becomes larger than a critical value. The device's behavior beyond this critical value is then analyzed and discussed. The relevance of the problem is discussed in connection to solid-state devices, as well as in problem solving contexts.