AC inductive reactance and current: in a sinusoidal circuit with fixed voltage and frequency, will increasing the inductance reduce the current drawn?

Introduction / Context:
Inductive reactance determines how an inductor impedes AC. Designers often adjust inductance to control current in chokes, ballasts, and filters. This question asks whether increasing inductance decreases current in an AC circuit with otherwise fixed conditions.

Given Data / Assumptions:

• Sinusoidal steady-state at fixed frequency f and RMS voltage V.
• Series circuit whose impedance includes inductive reactance XL = 2 * π * f * L.
• Linear inductor (no saturation), small series resistance for first-order reasoning.

Concept / Approach:
Inductive reactance is proportional to inductance: XL ∝ L. The magnitude of current in a series circuit is I = V / |Z|. As L increases at fixed f, XL rises, increasing |Z| and therefore reducing I. This is the basis for inductive ballasts and chokes that limit current without resistive losses equivalent to brute-force series resistors.

Step-by-Step Solution:

Verification / Alternative check:
Hold f constant and double L; XL doubles, so I approximately halves if R is small compared to XL—consistent with practical choke behavior.

Why Other Options Are Wrong:
Incorrect: contradicts the direct proportionality between XL and L.
“Only true at DC”: at DC, XL = 0, so inductance does not limit steady current; the effect is specifically AC.

Common Pitfalls:
Confusing transient DC behavior (inductor initially resists change) with steady-state DC; overlooking frequency′s role via XL = 2 * π * f * L.

Final Answer:
Correct