When a certain air-fillled parallel-plate capacitor?

Question

When a certain air-fillled parallel-plate ca-
pacitor is connected across a battery, it ac-
quires a charge (on each plate) of magnitude
95 microC. While the battery connection is main-
tained, a dielectric slab is inserted into the
space between the capacitor plates and com-
pletely fills this region. This results in the ac-
cumulation of an additional charge of 328 microC
on each plate.
What is the dielectric constant of the slab?

Answer 1

Q = CV

C1 = Q1/V (air filled capacitor) Q1 = 95x10^-6

C2 = Q2/V where Q2 = Q1 + 328 x10^-6

V is constant throughout, therefore

Q1/C1 = Q2/C2

C2/C1 = Q2/Q1

The ratio of the capacitors simplifies to epsilon2/epsilon1

Hence epsilon2 = (Q2/Q1)*epsilon1