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Question

Seven identical large conducting plates are placed parallel to each other. The separation between any two consecutive plates is a. The area of each plate is S. The effective capacitance of the system between A and B is 2x11ϵ0Sa. Then the value of x is :

74274_f3b51fccea0342a895d40b846fbddba2.png

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Solution

There are (71)=6 capacitors and the capacitance of each capacitor is C=Sϵ0a.
Above 2 capacitors are in parallel and below 3 capacitors are in parallel and these two groups and middle one capacitor are in series as shown in the figure below.
The total effective capacitance of the system is
1Ceff=1(C+C)+1C+1(C+C+C)=116C

or Ceff=6C11=611.Sϵ0a.

thus, 2x11=611x=3

199124_74274_ans_d2bc052cd1644679a4045477f8b889b9.png

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