A slab of material of dielectric constant K has the same area as that of the plates of a parallel - Physics - Electrostatic Potential And Capacitance

Question

A slab of material of dielectric constant K has the same area as
that of the plates of a parallel plate capacitor but has the
thickness d/2, where d is the separation between the plates Find
out the expression for its capacitance when the slab is inserted
between plates of capacitor

Jyoti Pant · Accepted Answer

Capacitance of parallel plate air capacitor is given by,C0=∈0AdCapacitance of capacitor when its plates are partly filled with dielectric of thickness t and same area as the plates,C=∈0Ad-t(1-1K)Here,t=d2So, C=∈0Ad-d2(1-1K)=∈0Ad2+d2K=∈0AdK+d2K=∈0A×2Kd (K+1)=2KK+1∈0AdOr C=2KK+1C0Thus, capacitance becomes 2KK+1times of initial capacitance

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates.Find out the expression for its capacitance when the slab is inserted between plates of capacitor.