A parallel resistance model (PRM), in which the total resistance, Rtotal, is given by a parallel connection of resistance of a filament, Rfila, and that of a film excluding a filament, Rexcl, was proposed to understand DC electric properties of resistive RAM (ReRAM). Here, the relationship of 1/Rtotal = 1/Rfila + 1/Rexcl is satisfied. To prove the validity of this model, the dependence of the relationship between resistance and temperature, R(T), of Pt/NiO/Pt on an area of a top electrode, S, was investigated. It was clarified that R(T) depended on S, which is the result definitely expected by the PRM. It was also clarified that smaller S is crucial to observe intrinsic properties of a filament of ReRAM.