The distinguishability of a discrete coil induced current electrical impedance tomography system is analysed. The solution methodology of the forward problem of this system is explained. An optimization procedure using this forward problem solution is developed to find optimum currents that maximize the distinguishability. For the concentric inhomogeneity problem, it is shown that the coil currents can be optimized to focus the current density in any desired location, in the field of view. Optimum coil currents under the constraints of limited peak coil currents and limited total power are determined. Examples that demonstrate the performance of the system are presented.