What is the formula for the impedance of an inductor?

The impedance of an inductor in an AC circuit is given by the formula jωL, where j is the imaginary unit, ω is the angular frequency of the AC source, and L is the inductance in henries.

This formula originates from the basic principles of inductive reactance, which describes how an inductor opposes changes in current. When alternating current flows through an inductor, it creates a magnetic field that causes an induced electromotive force (emf) that opposes the change in current. This behavior is frequency-dependent, and the term ωL represents the inductive reactance, which increases with frequency.

The presence of the imaginary unit j indicates that the impedance has a phase shift of +90 degrees, meaning that the voltage across the inductor leads the current through it. This is typical behavior for inductors in AC circuits.

Understanding this concept is critical for analyzing AC circuits, as it highlights the significance of phase relationships in reactive components like inductors. The formula also reinforces the idea of complex impedance, which combines both resistance and reactance, allowing for more comprehensive calculations within AC analysis.