How do you determine the equivalent capacitance in series?

To determine the equivalent capacitance of capacitors connected in series, the correct formula involves taking the reciprocal of the individual capacitances. This is because, in a series connection, the total capacitance decreases as additional capacitors are added. The relationship is defined by the formula:

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

This equation shows that the reciprocal of the total capacitance is the sum of the reciprocals of each individual capacitance. The reasoning behind this can be understood by considering that in a series configuration, the charge stored on each capacitor is the same, and the total voltage across the capacitors is the sum of the voltages across each individual capacitor. As a result, the overall ability to store charge (i.e., capacitance) diminishes, leading to a total capacitance value that is lower than that of any single capacitor in the series.

This principle is critical for analyzing circuits involving capacitors in series and helps understand how they collectively behave in a circuit. The other provided formulas do not accurately represent the characteristic behavior of capacitors in series and hence do not apply in this context.