Two conducting plates each having area A are kept at a separation d parallel to each other. The two plates are con- nected to a battery of emf V. The space between the plates is filled with a liquid of dielectric constant K. The height (x) of the liquid between the plates increases at a uniform rate from zero to d in a time interval `t_(0)`.
(a) Write the capacitance of the system as a function of x as the liquid beings to fill the space between the plates.
(b) write the current through the cell at time `t`

Answer

(a) `C=(K in_(0)A)/(Kd-(K-1)x)`
(b) `V(K in_(0)Adt_(0)(K-1))/([Kdt_(0)-(K-1)dt]^(2))`