### Consistent models for electrical networks with distributed parameters

A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form ${L}^{2}(0,T;{H}^{1})$, one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.