A parallel-plate capacitor with circular plates of radius R is being discharged. The displacement current through a central circular area, p

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?

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Ngọc Diệp 3 months 2021-08-17T01:51:23+00:00 1 Answers 6 views 0

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    2021-08-17T01:53:03+00:00

    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

         

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