What happens to the equivalent capacitance when equal capacitances are connected in series?

When equal capacitances are connected in series, the equivalent capacitance decreases. This phenomenon can be understood through the relationship that governs capacitors in series.

For capacitors connected in series, the total or equivalent capacitance, C_eq, is given by the formula:

1/C_eq = 1/C1 + 1/C2 + ... + 1/Cn

In the case of equal capacitances, let's say each capacitor has a value of C. The formula simplifies to:

1/C_eq = n/C

where n is the number of capacitors. Therefore, we can rewrite the equation to find C_eq:

C_eq = C/n.

This shows that the equivalent capacitance is directly inversely proportional to the number of capacitors connected in series. As the number of equal capacitors increases, C_eq will obviously decrease. Thus, the compelling result is that when multiple capacitors of equal value are placed in series, the overall capacitance will always be less than the individual capacitance of each capacitor.

This is in contrast to situations where capacitors are connected in parallel, where the equivalent capacitance increases with the addition of more capacitors. In summary, when equal capacitances are connected in series, the equivalent capacitance