When two capacitances of equal size are connected in series, how does their equivalent capacitance compare?

When two capacitances of equal size are connected in series, the formula for calculating the equivalent capacitance (C_eq) is given by:

1/C_eq = 1/C1 + 1/C2

For two capacitors of equal capacitance (let's say each has a capacitance of C), this equation simplifies to:

1/C_eq = 1/C + 1/C = 2/C

Rearranging this, you find:

C_eq = C/2

This means the equivalent capacitance is half the size of one of the individual capacitors. Thus, when capacitors are in series, the total or equivalent capacitance is always lower than the smallest capacitance in the group. Therefore, the assertion that the equivalent capacitance is half the size of one capacitor is accurate.

In contrast to this correct understanding, the equivalent capacitance being equal to one capacitor of twice the size mistakenly suggests a mathematical addition of capacitance rather than the need to consider the inverse relationship present in capacitors in series. The idea that it would remain unchanged contradicts the fundamental properties of capacitors in series, as their effective capacitance must always decrease. The claim about being one-fourth of the original size is also incorrect because it