In this paper, we present the design and implementation of a modified parallel-plate capacitor (PPC) and its mathematical derivation, which may well be incorporated as a challenging problem in physics textbooks covering topics on capacitance and dielectrics. The dielectric material under test (MUT) fills the empty space between the plates of the PPC, and a very thin layer of air is trapped between the uneven surfaces of the metallic capacitor plates and the MUT. It has been reported in the literature (Grove T T et al 2005 Am. J. Phys. 73 52–56; Grove T T and Masters M F 2009 The Physics Teacher 47 312) that these air pockets lead to an error in the measured value of the dielectric constant of the MUT. The present work gives a prescription to estimate this value in a smart way so as to bypass the effect of a trapped thin air layer, and it leads to measured values of the dielectric constant similar to what has been reported in the literature (PLEXIGLAS®, Altuglas International and Arkema Inc., 2006 www.altuglasint.com). To the best of our knowledge, this paper is the first to present the design and implementation of a PPC cell of this kind to study dielectric constants. The topic can reasonably be taught in undergraduate laboratory physics coursework.