TN-LCDs particularly doped with the metal nanoparticles of Ag-Pd composite, which are protected by chemical covering with nematic liquid crystal, 5CB (K-15, Merck) as a ligand, are shown to exhibit a long term stability in the electro-optical (EO) effect featured by a frequency modulation with short response times of ms or sub-ms order. This device is called FM-LCD. The unique electro-optical characteristics of the FM-LCD were clarified in terms of the Maxwell-Wagner effect of a heterogeneous dielectrics, where the analysis is done using an equivalent circuit model rather than the conventional potential theory; and we derived the formulae of the dielectric strength and the dielectric relaxation time. The former is used to explain the FM-LCD effect and also to evaluate the effective electrical conductivity of the metal nanoparticle that will be 4.4 x 10(4)S/m, which is about 1 x 10(-3) times smaller than that of metal Ag, and the latter is expressed to demonstrate that the relaxation time decreases with increasing the concentration of metal nanoparticle for the first time.