n equal capacitors are first connected in series and then in parallel. The ratio of capacitances in series and parallel arrangements will be :

The capacitance of a capacitor is a measure of its ability to store charge. When capacitors are connected in series, the total capacitance (C_series) is given by the reciprocal of the sum of the reciprocals of the individual capacitances. In this case, since all the capacitors are identical and have a capacitance of C, the total capacitance when connected in series is:

1/C_series = 1/C + 1/C + 1/C + ... (n times) 1/C_series = n/C C_series = C/n

When capacitors are connected in parallel, the total capacitance (C_parallel) is simply the sum of the individual capacitances. So in this case, the total capacitance when connected in parallel is:

C_parallel = C + C + C + ... (n times) C_parallel = nC

The ratio of the capacitance in series to the capacitance in parallel is therefore:

C_series / C_parallel = (C/n) / (nC) = 1/n^2