Question

A parallel-plate capacitor with circular plates of radius R is being discharged. The displacement current through a central circular area, parallel to the plates and with radius R/2, is 9.2 A. What is the discharging current?

Answer 1

Answer:

The discharging current is $I_d = 36.8 \ A$

Explanation:

From the question we are told that  

     The radius of each circular plates is  R

     The displacement current is  $I = 9.2 \ A$

      The radius of the central circular area is  $\frac{R}{2}$

The discharging current is mathematically represented as

       $I_d = \frac{A}{k} * I$

where A is the area of each plate which is mathematically represented as

       $A = \pi R ^2$

and   k is central circular area which is mathematically represented as

     $k = \pi [\frac{R}{2} ]^2$

So  

     $I_d = \frac{\pi R^2 }{\pi * [ \frac{R}{2}]^2 } * I$

     $I_d = \frac{\pi R^2 }{\pi * \frac{R^2}{4} } * I$

     $I_d = 4 * I$

substituting values

     $I_d = 4 * 9.2$

     $I_d = 36.8 \ A$