Mathematical models of ion transport in a potential field are analyzed. Ion transport is regarded as the superposition of diffusion and migration. The explicit analytical formulaes are obtained for the concentration of the reduced species and the current response in the case of pure diffusive as well as diffusion-migration model, for various initial conditions. The comparitive analysis of these formulaes for current responses and deviation from the classical Cottrellian are derived. The proposed approach can predict an influence of ionic diffusivities, valences, initial and boundary concentrations to the behaviour of current response. In addition to these, the analytical formulaes obtained can also be used for numerical and digital simulation methods for Nernst-Planck equations.