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Complex dielectric constants of binary-phase random composites are simulated for a three-dimensional structure consisting of cubic grains using the Monte Carlo-finite element method. Numerical results are fitted using Maxwell–Garnett, Bruggeman symmetrical, and general effective media formulas, and the fitting efficiencies of the formulas are quantitatively evaluated. The general effective media formula gives the best fitting to our simulation results and its accuracy is better than 3.7%. The effects of frequencies on the spatial distribution of electrostatic potentials in dielectric composites are discussed. The distribution of potential contours drawn in the low-frequency region and the high-frequency region show great variation, because of different lengths of time for charge to accumulate near the interphase boundaries. Dielectric spectra are drawn by varying volume fraction and lossy property of one phase in binary-phase composites. General properties of the dielectric spectra are discussed and the characteristics of the dielectric spectra caused by the differences in the lossy properties of the two phases at certain volume fractions are analyzed. © 2004 American Institute of Physics.