A polarized low-coherence interferometer (PLCI) based on a liquid crystal (LC) wedge is designed and an associated demodulation method encompassing the tunability feature is proposed for tunable, standalone optical sensing. The application of an electric field to the LC material effectively decreases the birefringence value and the related dispersion relation, which in turn enhances the resolution of detection. The effect of the electric field on the demodulation of the cavity length is addressed by the successive determination of the centroid positions of the PLCI interferograms. Through a comprehensive study of numerical simulation, the effectiveness of the proposed approach is explored relative to the conventional envelope detection methodology. In order to verify this method, an experiment with Fabry-Perot based fiber optic displacement sensor is investigated using 5CB LC wedge based PLCI setup in presence of electric field. The measurement accuracy of the cavity length is found to be 0.74% of full scale, rendering it to be more precise and robust than the conventional envelope detection method.