Capacitive reactance in an AC circuit generally behaves how with respect to frequency?

Capacitive reactance in an alternating current (AC) circuit is indeed inversely proportional to frequency. This relationship can be understood through the formula for capacitive reactance, which is given by:

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

Here, ( X_C ) represents the capacitive reactance, ( f ) is the frequency of the AC signal, and ( C ) is the capacitance in farads. According to this formula, as the frequency (f) increases, the value of ( X_C ) decreases. This means that higher frequencies result in lower capacitive reactance, allowing more alternating current to pass through the capacitor. Conversely, at lower frequencies, the capacitive reactance is higher, restricting the flow of current.

Therefore, the nature of capacitive reactance with respect to frequency is characterized by this inverse relationship, confirming that it is inversely proportional. This principle is foundational in understanding how capacitors function in AC circuits, particularly in applications such as filtering and tuning.