In this study, the systematic effect of the dielectric constant of porous material on the performance of capacitive pressure sensors based on circular silicon membranes has been investigated in a multiphysics and nonlinear manner. Unlike previous studies that consider simultaneous changes in several material parameters, in this work only the dielectric constant (κ) is considered as an independent variable at three levels of 3, 40 and 80 and its effect on the static, dynamic and frequency behavior of the sensor has been analyzed, while Young's modulus and other mechanical properties have been kept constant. The modeling is based on the nonlinear governing equations of the classical plate and the compressible behavior of the porous dielectric and has been solved numerically by the Galerkin method. The results show that increasing κ leads to a significant reduction in the pull-in voltage (from 240 V at κ=3 to 50 V at κ=80), an increase in static and dynamic sensitivity, a decrease in settling time, and a decrease in the resonant frequency of the system. These behaviors are due to the increase in electrostatic force and the effective “softening” of the structure. The findings confirm that optimizing the dielectric constant without changing the mechanical stiffness is an effective strategy for designing medical sensors with low operating voltage, high sensitivity, and fast response.