Journal of Statistical Physics, Vol. 24, No. 1, 1981. p. 215-233.
An exactly solvable model of the ballast resistor is considered. Analytic expressions are obtained for the nonuniform stationary temperature distributions and the corresponding I-V characteristics. A bifurcation point for Neumann boundary conditions is found and its analytic properties are discussed. It is found that the infinite wire limit plays a role analogous to the thermodynamic limit in statistical mechanics for equilibrium phase transitions.