Find the capacitance of a system of three parallel plates, each of area A `metre^(2)` separated by distances `d_(1) and d_(2)` metre respectively. The space between them is filled with dielectrics of relatives dielectric constants `K_(1) and K_(2)`. The dielectric constant of free space is `in_(0)`.

Answer

`C = (in_(1) in_(2) in_(0) A)/(in_(1) d_(2) + in_(2) d_(1))`

Explanation

The system is equivalent to two condnesers connected in series as shown in Fig.
`C_(1) = (in_(1) in_(0) A)/(d_(1)) , C_(2) = (in_(2) in_(0) A)/(d_(2))`
`(1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) = (d_(1))/(in_(1) in_(0) A) + (d_(2))/(in_(2) in_(0) A)`

`= (1)/(in_(0) A) ((in_(1) d_(2) + in_(2) d_(1))/(in_(1) in_(2))) = (in_(1) in_(2) in_(0) A)/(in_(1) d_(2) + in_(2) d_(1))`