Recent developments of local field microscopy allow a considerable
improvement over more traditional techniques (like transmission
electron microscopy) of the knowledge of the actual structure of
composites made of conducting particles dispersed in an insulating
polymer matrix. The Resiscope is an attachment to an AFM microscope
that provides at the same time a classical image of the sample surface
and a new image representative of the local electrical conduction
through the sample, between the tip and the back. Using the thickness
of the sample as an independent variable, we have obtained original
data on the 3D structure of the finite clusters as well as of the
infinite cluster and their relative variations with the particle
concentration in a series of carbon black filled elastomers. These
data are concerned with the geometry and the electrical resistance of
the conducting paths inside the material and provide new conducting
path size and local resistance histograms. The comparison of their
respective behaviors with sample thickness and particle concentration
with classical scaling results of percolation theory turned out to be
difficult due to the particular ``tip-to-bottom'' plane
experimental geometry, that has never been considered in the
literature. We have performed computer simulations on percolation
cubic networks aimed at providing similar data when both the filling
factor $p$ and the sample ``thickness'' (number of planes) are allow
to vary. We have found that in spite of a general agreement between
experimental and calculated data, there exist significant differences
that seem to prove that the actual structure is more complex than the
one predicted by a classical percolation model of random composite.