Let `A` is the area of plates , `q` is the charge on capacito r at
some instant and the separation between the paltes
Conducting current ,`i_(c) dq / dt`
Electric field between the paltes,
`E = (sigma )/ (epsilon_(0)) = (q//A)/(epsilon_(0)) = (q)/(A epsilon_(0))`
The flux of the elctric field through the given area is
`phi E = EA = ((q)/(A epsilon_(0))) A = q / epsilon_0`
`:. (d phi E)/(dt) = 1/epsilon_0 ((dq)/(dt))`
Displacement current ,
`i_(d) = epsilon_(0)(d phi_(E))/(dt)`
`= epsilon_0 [(1)/(epsilon_(0)).(dq)/(dt)]`
or `i_(d) = (dq)/(dt)`
From Eqs. (i) and (ii), we can see that
`i_(c) = i_(d)` .