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Obtain the formula for the effective capacitance of the series combination of different n capacitors. |
Answer» Solution :Figure shows n CAPACITORS of capacitance `C_(1) , C_(2), C_(3) cdots, C_(n)` are arranged in series.  The characteristics of series combination sudthat the charges on two plates are the same each capacitor and potential difference of eacl capacitor is DIFFERENT . Suppose the potential difference `V_(1), V_(2),cdots, V_(1)` of capacitor of capacitance `C_(1), C_(2),cdots, C_(1)` respectively . The total potential difference of SERIE combination, `V= V_(1)+V_(2)+V_(3)+cdotsV_(n)` `:. V=(Q)/(C_(1))+(Q)/(C_(2))+(Q)/(C_(3))+ cdots (Q)/(C_(n))` `:. (V)/(Q)=(1)/(Q)+(1)/(C_(2))+(1)/(C_(3))+cdots (1)/(C_(n))` If charge Q and potential difference V are of the combination then effective capacitance of a series combination of n capacitors, `(1)/(C) = (1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3))+cdots (1)/(C_(n))` Hence the value of effective capacitance is even smaller than the smallest value of the capacitors which are CONNECTED series combination . The reciprocal of the effective capacitance of capacitors coMected in series is the sum of the reciprocals of the individual capacitances. |
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