What is the formula for the impedance of an inductor in the s-domain?

The formula for the impedance of an inductor in the s-domain is expressed as sL. In the s-domain, which is used for analyzing systems in the Laplace transform framework, the relationship between current and voltage across inductive elements becomes more straightforward.

Impedance, which combines resistance and reactance, is mainly determined by the inductive reactance in the case of an inductor. The general form of impedance for an inductor can be derived from the Laplace transform of its differential equation.

For an inductor, the voltage-current relationship is defined by the equation V(s) = sL * I(s), where V(s) is the voltage across the inductor, I(s) is the current through it, and L is the inductance. Rearranged, this gives us the expression for impedance: Z(s) = V(s)/I(s) = sL.

This formulation indicates that the impedance of the inductor increases linearly with frequency (indicated by 's'), highlighting that inductors resist changes in current. In analysis and design of electrical circuits involving inductive loads, this relationship is essential for understanding the behavior of circuits in response to various inputs.