Introduction:
When identical capacitors are connected in series, their capacitances combine in a way that results in a reduced effective capacitance. However, when the same capacitors are connected in parallel, their capacitances add up, resulting in an increased effective capacitance.

Explanation:
To understand why this happens, let's consider the capacitance formula for capacitors connected in series and parallel.

Capacitors in Series:
When capacitors are connected in series, the total capacitance (C_total) can be calculated using the formula:

1/C_total = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn

Where C1, C2, C3...Cn are the individual capacitances of the capacitors connected in series. Since the capacitors are identical (N identical capacitors), we can rewrite the formula as:

1/C_total = N * (1/C)

Simplifying the equation, we get:

C_total = C/N

This means that the effective capacitance when capacitors are connected in series is equal to the capacitance of a single capacitor divided by the number of capacitors.

Capacitors in Parallel:
When capacitors are connected in parallel, the total capacitance (C_total) can be calculated by simply adding up the individual capacitances:

C_total = C1 + C2 + C3 + ... + Cn

Since the capacitors are identical, we can rewrite the formula as:

C_total = N * C

This means that the effective capacitance when capacitors are connected in parallel is equal to the capacitance of a single capacitor multiplied by the number of capacitors.

Conclusion:
In summary, when identical capacitors are connected in series, the effective capacitance is reduced and given by C/N. However, when the same capacitors are connected in parallel, the effective capacitance is increased and given by N*C. This behavior arises from the way the capacitances of the individual capacitors combine when they are connected in different configurations.