A group of identical capacitors is connected first in series and then in paralle

Question

A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in parallel is 49 times larger than for the series connection. How many capacitors are in the group?

Suppose we have n identical capacitors, each with capacitance C. If these capacitors are connected in parallel, we have

Cp = C1 + C2 + . . . + Cn = nC.

For these identical capacitors connected in series, we have

=

+

+ . . . +

=

.

We have the following ratio.

=

= n2

So for the factor given in this problem,

Explanation / Answer

total capacitance when connectd in parallel Cp= nC

total capacitance when connected in series Cs= C/n

Cp/Cs = nC/( C /n)

n = sqrt(Cp/Cs) = sqrt(49/1) = 7 { Cp = 49 Cs}

n= 7

no of capacitor = 7

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