For an inductor of fixed inductance L, what happens to the inductive reactance when the operating frequency is doubled (f → 2f)?

Introduction / Context:Inductive reactance governs how strongly an inductor impedes AC. Designers frequently assess how changes in frequency alter circuit impedances for filters and resonant networks.

Given Data / Assumptions:

• Ideal inductor with inductance L.
• Steady-state sinusoidal operation.
• Frequency doubled from f to 2f.

Concept / Approach:Inductive reactance is X_L = 2 * pi * f * L. If frequency doubles, X_L(2f) = 2 * pi * (2f) * L = 2 * (2 * pi * f * L) = 2 * X_L(f). Thus, reactance doubles when frequency doubles.

Step-by-Step Solution:

Verification / Alternative check:Numerical example: If X_L = 100 Ω at f, then at 2f it becomes 200 Ω, confirming the doubling behavior.

Why Other Options Are Wrong:

Common Pitfalls:Mixing inductive with capacitive reactance (which halves when frequency doubles).

Final Answer:doubles the amount of inductive reactance.