How does frequency impact the impedance of a capacitor?

Impedance in a capacitor is given by the formula ( Z = \frac{1}{j \omega C} ), where ( Z ) is the impedance, ( j ) is the imaginary unit, ( \omega ) (omega) represents angular frequency in radians per second, and ( C ) is the capacitance in farads. This equation shows that the impedance of a capacitor is inversely proportional to the frequency: as the frequency increases, the value of ( \omega ) increases, which in turn decreases the impedance.

This property is essential in AC circuits, as it indicates that capacitors allow more current to flow through at higher frequencies, making them effective in filtering applications, where high frequencies are allowed to pass while low frequencies are impeded. This characteristic is why capacitors are often used in audio systems and signal processing.