Inductor behavior with alternating current The opposition offered by an ideal inductor to alternating current (AC) is quantified by inductive reactance. Inductive reactance is directly proportional to which parameter in steady-state sinusoidal analysis?

Introduction / Context:
Inductors behave differently under DC and AC. At DC an ideal inductor looks like a short (after transients), but in AC it resists current changes. The measure of this opposition is called inductive reactance, a frequency-dependent quantity essential for filters, matching networks, and resonant circuits.

Given Data / Assumptions:

• Linear inductor with inductance L (henry).
• Sinusoidal steady-state at frequency f (hertz).
• Parasitics like winding resistance and self-capacitance are neglected.

Concept / Approach:
The inductor voltage-current relationship is v = L * di/dt. Under sinusoidal excitation, i and v are sinusoidal; in phasor form, Z_L = j * 2π * f * L. The magnitude of this impedance is X_L = 2π * f * L. Hence, X_L scales linearly with frequency f and also with inductance L. When f increases, X_L increases proportionally; when f decreases toward zero, X_L tends to zero.

Step-by-Step Solution:

Verification / Alternative check:
Measure current through a fixed inductor driven by a fixed-amplitude source at two frequencies, f1 < f2. Since I ≈ V / X_L, current at f2 is smaller by the ratio f2/f1, confirming linear dependence on frequency.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing X_L (reactance magnitude) with the complex j operator; forgetting that at very high frequency, parasitics can shift behavior from ideal.

Final Answer:
frequency