Inductive reactance formula derivation and calculation

Inductive reactance (XL) is a measure of the opposition to current flow in an inductive circuit. It is caused by the magnetic field that is generated around the conductor when current flows through it. The mathematical expression for inductive reactance is given by the following equation:

XL = 2πfL

where: XL = inductive reactance (Ω)

f = frequency of the current (Hz)

L = inductance of the circuit (Henries)

π = pi (approximately 3.14)

The derivation of this equation is based on Faraday’s law of electromagnetic induction. According to Faraday’s law, a change in magnetic flux induces an electromotive force (EMF) in a conductor. In an inductive circuit, the current flowing through the conductor creates a magnetic field, and any change in the current level will cause a change in the magnetic flux.

The relationship between flux and current can be expressed mathematically as:

Φ = L * i

Where: Φ = magnetic flux (Webers) L = inductance of the circuit (Henries) i = current flowing through the circuit (Amperes)

The induced EMF in the circuit can be related to the rate of change of flux by: E = – dΦ / dt

Where: E = induced EMF (Volt)

Substituting the equation for flux into this equation and rearranging, we get: E = – L * di / dt

The induced EMF can also be related to the current flowing in the circuit through Ohm’s law (E=IR). Applying the above in an AC circuit with V = Vmsimωt