What effect does a dielectric have on the capacitance of a capacitor?

Explanation

Introducing a dielectric in a capacitor causes a decrease in the electric field, and hence the voltage. The charge stored on the plate remains unchanged.As C = Q/V,decreasing V causes an increase in capacitance.The capacitance of a parallel plate capacitor is given by:capacitance C = (area of plate) (permittivity of free space) / (distance between the plates) = Aεo/d ..........(1)Introducing the dielectric, the capacitance becomes:capacitance Cm = (area of plate) (permittivity of medium) / (distance between the plates) = Aεm/d .......... (2)The relative permittivity is given by:k = εm/εoor εm = kεoPutting (εm = kεo ) in equation 2:Cm = Akεo/d = Aεo/d x kCm = C x kHence, the introduction of dielectric causes the capacitance to increase by k times.