What happens to the capacitive reactance of a capacitor as the frequency decreases?

The capacitive reactance of a capacitor is inversely proportional to the frequency of the signal passing through it. This relationship is defined by the formula:

[ X_C = \frac{1}{2\pi f C} ]

where ( X_C ) is the capacitive reactance, ( f ) is the frequency, and ( C ) is the capacitance. As the frequency ( f ) decreases, the denominator of the fraction decreases, which results in an increase in the value of ( X_C).

Therefore, when the frequency decreases, it causes the capacitive reactance to increase, leading to a greater opposition to the alternating current (AC) flowing through the capacitor. This property is crucial in the design and operation of electronic circuits, especially in filtering applications, where the behavior of capacitors at different frequencies directly affects circuit performance.