In the present paper, we formulate a mathematical theory for dielectric anisotropy and threshold voltage of the nematic liquid crystal (NLC). We have also observed the influence of zinc oxide nanoparticles (ZONPs) on the threshold properties of the nanonematic suspension. Nanonematic suspension show changed threshold properties in comparison to the pure nematic liquid crystals. In addition to this, the effective dielectric displacement vector of composite material is calculated. We have proposed a theoretical formula for the effective dielectric anisotropy of nanonematic composite material. The equilibrium energy condition under the given constraints gives the modified threshold voltage formula and the calculated threshold voltage by this formula is found to be in accord with the experimental results.