Question

You are provided with three identical capacitors, each of capacitance “C”.

If Cp is equivalent capacitance when they are connected in parallel and C, isequivalent capacitance when they are connected in series, calculate the ratio `C_s/C_p`.

Answer 1

When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances:

C_p = C + C + C

= 3 C

When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances:

`1/(C_s) = 1/C + 1/C + 1/C`

= `3/ C`

`C_s = C/3`

Now, we find the ratio of the series capacitance to the parallel capacitance:

`C_s/C_p = (C/3)/(3  C)`

= `(C/3) xx 1/(3  C)`

= `C/(9  C)`

= `1/9`