Three plates of the same size form a system of capacitors. Each plate has an area `alpha`. The intermediate distances between the plates are `d_1 " and "d_2`, respectively. The space between the first two plates is occupied by a dielectric of constant `k_1` and that between the second and third plates by a dielectric of constant `k_2`. Calculate the capacitance of the system.

Explanation

The three plates form two capacitors connected in series. Capacitance of the first capacitor, `C_1=(k_1 in_0 alpha)/(d_1)`
Capacitance of the second capacitor, `C_2 = (k_2 in_0 alpha)/(d_2)`
If C be the equivalent capacitance of the whole system, them
`(1)/(C )= (1)/(C_1)+(1)/(C_2)= (d_1)/(k_1 in_0 alpha)+(d_2)/(k_2 in_0 alpha)= (1)/(in_0 alpha)((d_1)/(k_1)+(d_2)/(k_2))`
`C= in_0 alpha* (1)/((d_1)/(k_1)+(d_2)/(k_2))`.