A capacitor consists of two circular plates each of radius 8.0 cm and separated by 3.0 mm. The capacitor is being charged by an external battery. The charging current is constant and is equal to 0.3 A. Calculate (i) capacitance of capacitor, (ii) the rate of change of potential difference across the plates of capacitor and (iii) the displacement current.

Answer

(i) 59.3pF (ii) `5.06xx10^9Vs^-1` (iii) 0.3A

Explanation

Here, `r=8xx10^-2m , d=3xx10^-3m, I=0.3A`
Plate area of capacitor,
`A=pir^2=pi(8xx10^-2)^2m^2`
(i) Capacitance of capacitor,
`C=(inA)/d=((8.85xx10^(-12))xxpixx(8xx10^-2)^2)/(3xx10^-3)`
`=59.3xx10^(-12)F=59.3pF`
(ii) Charge at any instant on the capacitor plate is,
`q=CV` and `I=(dq)/(dt)=d/(dt)(CV)=C (dV)/(dt)`
or `(dV)/(dt)=I/C=(0.3A)/((59.3xx10^(-12)F)`
`=5.06xx10^9Vs^-1`
(iii) From the property of continuity,
Displacement current=conduction current
`=2mA`