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Dielectric spectra of binary composites consisting of equal-sized hard disks of one dielectric dispersed randomly in a matrix of another dielectric are modeled in two dimensions using the finite-element method. The effects of the volume fraction of the disks and difference in the component permittivities and ohmic conductivities on the effective dielectric behavior of the resulting composite are discussed. Numerical results are compared with the results predicted using a few mixture formulas chosen. For this type of composites, the comparison shows, that in the region of compositions and component properties explored, the Brugemann formula is in the best agreement with the numerical results [Ann. Phys. (Leipzig) 24, 636 (1935)]. © 2002 American Institute of Physics.