Exact solutions for debye-like relaxations in multilayered conducting dielectrics

An exact determination of the equivalent dielectric constant of relaxing multilayered dielectrics is derived using Laplace transforms. To highlight in the simplest way the relevant general features, solutions are given in the only case of Debye-like relaxations with superimposed conductivities. Theoretical expressions are found for the equivalent permittivities ¿¿¿¿ and ¿¿s, at infinite and zero frequencies, as well as for the total current I(t), and for the equivalent decay function G(t). It is shown throughout that the usual method of derivation of the equivalent displacement, through calculation of an average value of component displacements, fails when conductivity is present. Possible implications of these results, in domains dealing with composite dielectrics, are indicated.