The first exact solution of the flow of current in a semi-infinite electrolyte bounded by an insulating plane to a finite number of disk electrodes embedded in the plane, when the electrolyte contains a number of spherical or prolate particles, is presented. The method is based on the addition of fundamental solutions of the Laplace equation which conform to the particular geometry of the electrodes and particles. A solution is obtained through the boundary collocation technique. The accuracy and convergence of the method were tested by a detailed analysis of the flow of current in the case of a spherical particle located in front of a disk electrode. The model was used to study the resistance variations of the flow of current to a single electrode induced by particles and, in the absence of particles, the ohmic and concentration interactions of multiple electrodes. Through the solution of the boundary value problem governing the flow of current to a set of electrodes in the presence of particles, the inverse problem is also solved, i.e. an algorithm is developed which finds the position of a particle based on the currents flowing to a set of electrodes. The performance and robustness of this algorithm are illustrated using synthetic data. The algorithm allows the tracking of individual particles, enabling information on the presence, velocity and residence time of particles in the vicinity of surfaces to be obtained from recordings of fluctuations of the electrolyte resistance with time.