Topology of thin film RC circuits

Integrated RC circuits can be made by depositing exceedingly thin metallic and dielectric films in suitable patterns on an insulating substrate. Resistors are strips of conductor; capacitors are patches on which conducting, dielectric, and conducting layers are superimposed. Since conductors can cross at capacitor patches, RC networks need not be strictly planar to be realizable in thin film. Determining which RC circuits are realizable poses new problems in topology which are remarkably simple to state but are as yet unsolved. The results reported here are fragmentary, but they do cover some cases of small order that may be of practical interest.