  Electrical and optical properties of binary inhomogeneous media are currently
modelled by a random network of metallic bonds (conductance $\sigma_0$,
concentration $p$) and dielectric bonds (conductance $\sigma_1$, concentration
$1-p$). The macroscopic conductivity of this model is analytic in the complex
plane of the dimensionless ratio $h=\sigma_1/\sigma_0$ of the conductances of
both phases, cut along the negative real axis. This cut originates in the
accumulation of the resonances of clusters with any size and shape. We
demonstrate that the dielectric response of an isolated cluster, or a finite
set of clusters, is characterised by a finite spectrum of resonances, occurring
at well-defined negative real values of $h$, and we define the cross-section
which gives a measure of the strength of each resonance. These resonances show
up as narrow peaks with Lorentzian line shapes, e.g. in the weak-dissipation
regime of the $RL-C$ model. The resonance frequencies and the corresponding
cross-sections only depend on the underlying lattice, on the geometry of the
clusters, and on their relative positions. Our approach allows an exact
determination of these characteristics. It is applied to several examples of
clusters drawn on the square lattice. Scaling laws are derived analytically,
and checked numerically, for the resonance spectra of linear clusters, of
lattice animals, and of several examples of self-similar fractals.
