Abstract The dielectric properties of suspensions are usually calculated from the quasi-static solution of the Laplace equation for the potential around a single particle in the continuous phase. The results are only straightforward for the static conductivity and for the high frequency permittivity, since these expressions only involve the potentials which are in phase with the applied field. The static permittivity and the high frequency conductivity, are much more difficult to evaluate, since they strongly depend on the limiting behaviour of the out of phase terms, which actually vanish in these two limits. Using arguments based on the stored energy and on the dissipated power, it is shown how the expressions for the static permittivity and the high frequency conductivity, can be calculated using only the in phase terms of the potential. The results are much easier to derive than using the classical procedure, and they contribute to a better understanding of the meaning of the relaxation amplitudes. A further advantage of this method, is that it permits one to obtain the limiting solutions for the dielectric properties in some systems (e.g. ellipsoidal particles surrounded by a layer of uniform thickness) for which an analytical solution of the Laplace equation does not exist for all frequencies.