What is the relationship between the number of capacitors in a series and total capacitance?

In a series configuration, the total capacitance is influenced by the individual capacitances of each capacitor. When capacitors are connected in series, the reciprocal of the total capacitance is equal to the sum of the reciprocals of the individual capacitances. This relationship can be expressed mathematically as:

[ \frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots + \frac{1}{C_n} ]

From this equation, it is clear that adding more capacitors in series results in a lower total capacitance compared to any of the individual capacitors since each additional term in the series adds a fraction to the total, making the overall fraction smaller. This is why the total capacitance decreases as more capacitors are added.

In contrast, if capacitors were connected in parallel, the total capacitance would increase because the capacitance values would simply add up. Therefore, the distinct behavior of capacitance in series versus parallel configurations highlights the fundamental characteristics of how capacitors store electrical energy.