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(c) Derive the expression for the affective capacitance of a series combination of n capacitors. |
Answer» Solution : Let `V_(1),V_(2),V_(3).......V_(n)` be the potential DIFFERENCE across the PLATES of n capacitors. Then, `V=V_(1)+V_(2)+V_(3)+.......V_(n)` `V=(q)/(C_(1))+(q)/(C_(2))+(q)/(C_(3))+......(q)/(C_(n))=q[(1)/(C_(1))+(1)/(C_(2))+(1)/C_(3)+......(1)/(C_(n))]......(i)` Let C be the equivalent capacitance of series combination, Then, `V=(q)/(C)""....(iii)` From (i) and (ii) `(q)/(C)=q[(1)/(C_(1))+(1)/(C_(2))+(1)/C_(3)+......(1)/(C_(n))]implies(1)/(C)=(1)/C_(1)+(1)/(C_(2))+(1)/C_(3)+......(1)/(C_(n))`. |
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