A computational methodology is presented to simulate d.c. and a.c. transport properties of two-dimensional composites. Using this method, average electrical properties, or, more specifically, d.c. conductivity and a.c. impedance spectra, of macroscopic mixtures of hard spheres which have random or regular arrangements of the components are studied. Numerical results are compared with the calculated results of analytic equations that have generally been used to describe the d.c. and a.c. electrical properties of composites. It is shown in this study that they are sensitive functions of the filling fraction, sample size and the geometrical arrangement of the components. The geometrical arrangement effects, which hardly can be considered in analytical formulae, become more important as the sample size decreases and the filling fraction approaches the effective percolation threshold.