Inductive reactance formula — evaluate the statement: the magnitude of inductive reactance is given by XL = 2π f L for a linear inductor at frequency f (hertz) and inductance L (henry).

Introduction / Context:Inductive reactance quantifies how an inductor impedes alternating current due to the changing magnetic field. It plays a central role in AC analysis, filter design, resonance calculations, and impedance matching. The standard relationship ties reactance to frequency and inductance linearly in magnitude.

Given Data / Assumptions:

• L is the inductance in henry (H).
• f is the signal frequency in hertz (Hz).
• The inductor is linear over the operating range (no core saturation, negligible parasitics).
• Steady-state sinusoidal analysis is assumed.

Concept / Approach:For a sinusoidal steady state, the inductor voltage-current relation is v(t) = L * di/dt. In phasor form, this becomes V = j ω L * I, where ω = 2π f is the angular frequency. The impedance of the inductor is therefore Z_L = j ω L. The magnitude of this impedance is |Z_L| = ω L = 2π f L, which is by definition the inductive reactance, X_L. Thus, X_L grows linearly with frequency and inductance; at DC (f = 0), X_L = 0 Ω, behaving as a short in ideal form.

Step-by-Step Solution:

Verification / Alternative check:Example: L = 10 mH at f = 1 kHz → X_L = 2π * 1000 * 0.01 = about 62.8 Ω. A measurement with an LCR meter at 1 kHz would read a similar reactance (ignoring ESR and parasitics).

Why Other Options Are Wrong:

Common Pitfalls:Forgetting units (henry and hertz) leading to numeric errors; confusing reactance magnitude X_L with the complex impedance j ω L; neglecting nonidealities like winding resistance and self-resonance at very high frequencies.

Final Answer:Correct