Suppose the space between the two inner shells of the previous problem is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.

The two capacitors are connected in series, hence the net capacitance is given by

For a spherical capacitor formed by two spheres of radii r_o > r_i is given by

C =

Where,

C: Capacitance

r_i: inner radius

r_o: outer radius

k: relative permittivity or dielectric constant

∈: permittivity of space

Similarly,

And