What is the correct equation for the impedance of a capacitor?

The correct equation for the impedance of a capacitor in the frequency domain is 1/jωC. In this expression, j represents the imaginary unit, ω is the angular frequency (2π times the frequency in hertz), and C is the capacitance in farads.

Impedance is a complex quantity that extends the concept of resistance to AC circuits. For capacitors, the impedance decreases with increasing frequency, which is fundamental to the behavior of capacitors in circuits. The formula demonstrates that as the frequency increases, the impedance of the capacitor goes down, allowing higher frequencies to pass through more easily while blocking lower frequencies, which is a critical characteristic in filtering applications.

The form 1/jωC can be understood as a complex number where the term "1/j" introduces a phase shift of 90 degrees (or -90 degrees when expressed in terms of real and imaginary components), indicating that the current through a capacitor leads the voltage across it by this phase angle.

In summary, the impedance of a capacitor is represented by the equation 1/jωC, which effectively captures how capacitance behaves in response to alternating currents at various frequencies.