Electrochemical processes taking place in an electrodialysis chamber packed with the granulated ion-exchange resin, when a dilute solution of a heavy metal salt is flowing through it, have been studied. The influence of the quantity of electricity transferred through such a system on the value of surface electrical resistance of the electrodialysis chamber and the limiting current value was experimentally determined. A mechanism for current transfer in such a system is presented. It allows for some unusual relationships between process parameters: current-voltage curves, the limiting current, the specific surface resistance, the quantity of transferred electricity and the solution flow rate.