Figure shows a capacitor made of two circular plates each of radius `12 cm`, and separated by `5.0 cm`. the capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to `0.15 A`
(a) Calcuate the capacitance and the rate of change of potential difference between the plates
(b) Obtain the displacement current across the plates
(c) Is kirchhoff's first rule(junction rule) vaild at each plate of the capacitor ? Explain.
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Explanation

(i) As displacement current across the plates
`I_(d) = (d)/(dt) (epsi_(0)phi_(E)) = epsi_(0)(dphi_(E))/(dt)`
where `phi_(E)` = electric flux across the loop `= int_("loop") E.dS`
`phi_(E) = EA= (q)/(epsi_(0))`
`:. I_(d) = epsi_(0)((q)/(epsi_(0))) = (epsi_(0))/(epsi_(0)).(dq)/(dt) = I = 0.15 A`
i.e., displacement current is equal to condution current.
(ii) Yes, Kirchhoff's first rule is valid at each plate of the capacitor. Net current is equal to the sum of the condution current and the displacement current.