Fig. shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0mm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.
(a) Calculate 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 valid at each plate of the capacitor ? Explain.

Explanation

Here, `R=12cm=0.12m, d=5.0mm=5xx10^-3m, I=0.15A, in_0=8.85xx10^-12 C^2N^-1m^-2`
`:.` Area, `A=piR^2=3.14xx(0.12)^2m^2`
(a) We know that capacity of a parallel plate capacitor is given by
`C=(in_0A)/d=(8.85xx10^-12xx3.14xx(0.12)^2)/(5xx10^-3)=80.1xx10^-12F=80.1pF`
Now, `q=CV` or `(dq)/(dt)=Cxx(dV)/(dt)` or `I=C (dV)/(dt) ( :' I=(dq)/(dt))`
or `(dV)/(dt) =I/C =0.15/(80.1xx10^-12)=1.87xx10^9Vs^-1`
(b) Displacement current is equal to conduction current i.e., `0.15A`
(c) Yes, Kirchhoff's first rule is valid at each plate of the capacitor provided we take the current to be the
sum of the conduction and displacement currents.