Question

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

• A. $nC$
• B. $\frac{n}{C}$
• C. $(n+1)C$
• D. $(n-1)C$

Answer 1

The correct option is D $(n-1)C$

If $n$ equally spaced plates are stacked alternatively then its diagramatic representation can be shown as follows:

Upon furthur simplication, the above figure can be rearranged as
We can see that the number of capacitors formed due to 4 plates alternatively are 3. Therefore, if $n$ number of plates are to be stacked alternatively the the number of capacitors formed in parallel will be $(n-1)$.
$⟹C_{eq}=(n-1)C$