Final answer:
The impedance of an inductor in the s-domain is represented by the formula Z(s) = sL, where 's' is the complex frequency variable, and 'L' is the inductance of the inductor. In an AC circuit, the inductive reactance can be expressed as XL = 2πfL.
Step-by-step explanation:
The formula for the impedance of an inductor in the s-domain, which is a complex frequency domain used in the Laplace transform method of circuit analysis, is Z(s) = sL. Here, Z(s) is the impedance, s is the complex frequency variable, and L is the inductance of the inductor. This expression accounts for both the reactance and the inertia of the magnetic field associated with the inductance.
In the context of an AC circuit where the frequency is a real number f, the inductive reactance is given by the formula XL = 2πfL. The inductive reactance, XL, represents how the inductor reacts to impede the current due to its inductance and is proportional to both the frequency and the self-inductance value, consistent with its role as an effective resistance in the circuit.