Micro-structural and impedance analysis of series of insulating polymer/conductor composites (PCC) as a function of frequency and volume fractions of the conductor (f(con)) have been studied. Evidences of conductivity relaxation have been noticed with a correlation with the sample micro-structure. This has been understood and explained in terms of equivalent electrical circuit model of the material established through complex impedance spectroscopy (CIS) across the percolation threshold (f(c)) for all the FCC. CIS analysis confirmed that FCC with f(con) > f(c), exhibit conductivity/interfacial relaxation due to polarization of Maxwell-Wagner-Sillars (MWS) type at f(c) and the relaxation frequency increases with increase of f(con). The modulus spectroscopy analysis suggests the presence of two types of relaxations in different frequency ranges; (i) dipolar relaxation associated with the flipping of dipoles present in the pure polymer for f(con) < f(c) and (ii) the conductivity/interfacial relaxation due to the formation of artificial MWS dipoles at the interface of the two components. A long range dc conductivity appears at f(con) > f(c) and Jonschers universal fractional power law is satisfied for both the regions of f(con) < f(c) and f(con) > f(c) in all PCC. (C) 2014 Elsevier B.V. All rights reserved.