Additions to concrete may change some of its basic properties in several ways depending on the nature of these additions. The addition of fibers, in particular, has enabled new concrete characteristics, making standard concrete a very modern composite material. If the fibers are electrical conductors, the properties that change in addition to the mechanical ones, are the thermal and electrical conductivities. The results indicate that the arrangement of the electrodes and the electrode-material interface are relevant, because the use of sponges between electrode and concrete prevents the contact between the metallic electrode and the carbon material which ends in different values of electrical resistance with and without sponges. Moisture conditions, that critically influence the electrical resistance of concrete without additions, resulted, also very relevant when conductive substances are present in the matrix. If the proportion of the carbonaceous addition, that lowers significantly the resistivity, is to be quantified, the best procedure seems to measure in dry concrete (0 % relative humidity) with sponges or, alternatively, wet concrete (100 % relative humidity) with silver painted electrodes (without sponges).