We introduce a definition of 'best' currents to apply to an electrode array on the surface of a body in order to distinguish between the conductivity inside the body and a conjectured conductivity. Using these 'best' currents, we illustrate with a simple example the general fact that a single current applied between a pair of electrodes, loses its ability to distinguish between different conductivities as the size of the region over which the current is applied goes to zero. We next introduce approximations to the best currents on systems having L electrodes, and calculate the ability of these systems to distinguish between conductivities as L goes to infinity and the electrode size goes to zero. We conclude with a simple example that illustrates a process for producing the 'best' currents without a previous knowledge of what is inside the body.
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