Electrothermal breakdown: Solutions for the case of thermal resistance in the electrodes

An exact solution is found for the critical voltage at a thermal instability corresponding to a particular model of a dielectric under high applied voltage and with thermal resistance in the electrodes. Other models that require approximate or computed solutions yield results that are very close to the analytic solution when appropriate dimensionless variables are chosen. The dimensionless critical voltage as a function of dimensionless critical thickness is shown to be almost independent of electrical and thermal conductivity parameters. It is also found that the solution for the thick limit applies in most cases of physical importance.