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.
.

Explanation

Here, R = 12 cm = 0.12 m,
`d = 5.0 mm = 5 x10^(–3)1 m.,`
`I = 0.15 A`,
`in_(0)=8.85xx10^(-12)C^(2)N^(-1)m^(-1)`
`therefore "Area, "A = piR^(2) - 3.14xx(0.12)^(2) m^(2)`
(a) We know that capacity of a parallel plate capacitor is given by
`C=(in_(0)A)/d=(8.85xx10^(-12)xx3.14xx(0.12)^(2))/(5xx10^(-3))`
`= 80.1xx 10^(-12) F = 80.1` pF
Now q = CV
or `(dq)/(dt)=Cxx(dV)/(dt)`
or` I=C (dV)/(dt) (therefore I = (dq)/ (dt))`
or ` (dV)/(dt) =I/C = (0.15)/(80.1xx10^(-12))= 1.87 xx10^(9)Vs^(-1)`
(b) Displacement current is equal to conduction current i.e.` 0.15 `A.
(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.