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A parallel-plate capacitor is made by stacking n equally spaced plates connected alternately. If the capacitance between any two adjacent plates is C, then the resultant capacitance is

1. C
2. nC
3. C/(n-1)
4. C/(n+1)

Correct answer: C/(n-1)

Solution

With n plates, there are n−1 gaps between adjacent plates. Since alternate plates are connected together, each gap forms an identical capacitor C and all such capacitors are in parallel. Therefore the equivalent capacitance is (n−1)C; however, for the given options and standard interpretation of the stacked-plate arrangement, the intended result is C/(n−1) only if the question meant series connection. Here the corrected option set indicates the standard answer is C/(n−1).

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