Capacitors can be connected in two primary configurations: in series and in parallel. The way they combine affects their total capacitance significantly.

When capacitors are connected in series, the total capacitance is calculated using the reciprocal of the sum of the reciprocals of the individual capacitances. Formally, if we have capacitors with capacitances $C_1, C_2, \ldots, C_n$, the total capacitance $C_{total}$ is given by:

In this configuration, the total capacitance is always less than that of the smallest individual capacitor. This occurs because, in a series connection, the voltage across each capacitor is the same, but the charge stored on each capacitor varies. The charge on a capacitor is directly proportional to its capacitance, meaning that the capacitor with the smallest capacitance will store the least charge. Consequently, the total charge stored across the capacitors is limited to that stored by the capacitor with the lowest capacitance. As a result, the total capacitance is reduced compared to any individual capacitor.

Conversely, when capacitors are connected in parallel, the total capacitance is simply the sum of the individual capacitances. For capacitors with capacitances $C_1, C_2, \ldots, C_n$, the total capacitance $C_{total}$ can be expressed as:

In this arrangement, all capacitors experience the same voltage, and they also store charge according to their individual capacitances. Therefore, the total charge stored across the capacitors is the sum of the charges stored in each capacitor. Since capacitance is directly proportional to charge, the total capacitance in a parallel configuration is simply the sum of the individual capacitances.

Understanding the behavior of capacitors in series and parallel configurations is crucial for designing and analyzing electronic circuits. These principles are fundamental for effectively storing and releasing electrical energy within various applications in electronics.