Inductive reactance units: select the correct SI unit for X_L in AC circuit analysis Assume sinusoidal steady-state and standard definitions.

Introduction / Context:Inductive reactance quantifies an inductor’s opposition to AC. While inductance (L) itself is measured in henrys (H), the reactance (X_L) is the frequency-dependent “resistance-like” term appearing in Ohm’s law for AC magnitudes and phasor analysis. Using correct units avoids dimensional mistakes when calculating current and impedance.

Given Data / Assumptions:

• Definition: X_L = 2 * pi * f * L.
• Frequency f is in hertz (s^-1).
• Inductance L is in henrys (H).

Concept / Approach:Unit analysis: multiply s^-1 by H to obtain ohms. Specifically, 1 H = 1 V·s/A. Therefore, (s^-1) * (V·s/A) = V/A = ohm. Hence, X_L has units of ohms, analogous to resistance but with a phase component (reactive, not dissipative).

Step-by-Step Solution:1) Write formula: X_L = 2 * pi * f * L.2) Insert units: f → s^-1; L → V·s/A.3) Multiply: (s^-1) * (V·s/A) = V/A.4) Recognize V/A as the ohm, confirming the unit of X_L.

Verification / Alternative check:Impedance Z is reported in ohms whether resistive (R) or reactive (X). Since X_L is a component of impedance, the same unit applies.

Why Other Options Are Wrong:“Volts per second” and “amperes per second” are rate units, not impedance. “Henrys” is the unit of inductance L, not of its reactance X_L.

Common Pitfalls:Confusing L (henrys) with X_L (ohms) or forgetting that reactance contributes to magnitude and phase but does not dissipate power in ideal inductors.

Final Answer:Ohm