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A novel method to determine the dispersion of the quadratic electro-optic effect in nonlinear optical materials by using a silicon-on-insulator microring resonator is presented. The microring consists of a silicon slot waveguide enabling large dc electric field strength at low applied voltages. The dispersion of third-order hyperpolarizability of a linear conjugated dye is approximated by using a two-level model for the off-resonant spectral region. As an example, the dispersion of the resonance wavelength of the resonator filled with a dye doped polymer was measured in dependence of the applied dc voltage. The polymer was poly (methylmethacrylate) doped with 5 wt% disperse red 1 (DR1), and the measurements have been carried out at the telecommunication wavelength band around 1550 nm (optical C-band). The described measurements represent a new technique to determine the dispersion of the third-order susceptibility and molecular hyperpolarizability of the material filled into the slot of the ring-resonator.