Using a method introduced by Albano et al (Albano, A. M.; Bedeaux, D.; Vlieger, J. Phys. A 1979, 99, 293. Albano, A. M.; Bedeaux, D.; Vlieger, J. Phys. A 1980, 102, 105), we derive an exact analytic expression for the dipolar coefficient of a charged sphere in an electrolyte as a function of the frequency which is valid for all double layer thicknesses and is given both for low and for high zeta potentials. The expression is found to have the same form as the expression for a sphere surrounded by a multiple of shells of different complex conductivities. One shell can then be attributed to the double layer and another to a diffusion layer. Including a Stern layer in the model subsequently adds another shell with associated complex dielectric permittivity.