Motivated by the interest that microelectrolytic systems are gaining in the development of the so-called lab-on-a-chip systems, i.e., miniature microfluidic devices for biochemical analysis, we present an analytical study of Ohmic conduction in rectangular charged microchannels filled with electrolytic solution. The study complements a previous one [M. Campisi et al., J. Chem. Phys. 123, 204724 (2005)], concerning ac electro-osmosis. The problem is framed within the theory of nonequilibrium thermodynamics and is based on the solution of the incompressible Navier-Stokes equation with an electrical body force due to the interaction of the applied electric field with the charged electric double layer (EDL) which forms at the solid-liquid interface. We analyze in detail the dependence of the system complex conductance on the ratio linear dimensions over Debye length with an eye on finite EDL effects, and compare its scaling properties with those of electrokinetic and hydraulic complex conductances.