College Physics 10th Edition by Raymond Serway,Chris Vuille

Exercise 5

A parallel-plate capacitor with a plate separation d has a capacitance C 0 in the absence of a dielectric. A slab of dielectric material of dielectric constant k and thickness d/ 3 is then inserted between the plates as in Figure P16.57a. Show that the capacitance of this partially filled capacitor is given by
Hint: Treat the system as two capacitors connected in series as in Figure P16.57b, one with dielectric in it and the other one empty.