Induced signals in resistive plate chambers

We derive theorems for induced signals on electrodes embedded in a medium with a position and frequency dependent permittivity $\vep(\vx,s)$ and conductivity $\sigma(\vx,s)$ that are connected with arbitrary discrete elements. The problem is treated using the quasi-static approximation of Maxwell's equations for weakly conducting media \cite{melcher}\cite{quasi}. The induced signals can be derived by time dependent weighting fields and potentials and the result is the same as the one given in \cite{gatti}. We also show how these time dependent weighting fields can be derived from electrostatic solutions. Finally we will apply the results to Resistive Plate Chambers (RPCs) where we discuss the effects of the resistive plates and thin resistive layers on the signals induced on plane electrodes and strips.