What is the formula for X_L (inductive reactance)?

What is the formula for X_L (inductive reactance)?

• A. pi f L
• B. f L
• C. 2 pi f L
• D. 2 f L

Answer: (C)

Inductive reactance shows how an inductor opposes AC current and it grows with frequency and inductance. In phasor form, the impedance of an inductor is Z_L = j ω L, where ω is the angular frequency. The magnitude of that impedance is X_L = |Z_L| = ω L. Since ω = 2π f, the magnitude becomes X_L = 2π f L. This is why the correct expression includes both 2 and π together with f and L. The other options miss either the 2, the π, or both, leading to incorrect values as frequency changes. For a quick check, if f = 60 Hz and L = 0.1 H, X_L = 2π × 60 × 0.1 ≈ 37.7 Ω.

Inductive reactance shows how an inductor opposes AC current and it grows with frequency and inductance. In phasor form, the impedance of an inductor is Z_L = j ω L, where ω is the angular frequency. The magnitude of that impedance is X_L = |Z_L| = ω L. Since ω = 2π f, the magnitude becomes X_L = 2π f L. This is why the correct expression includes both 2 and π together with f and L. The other options miss either the 2, the π, or both, leading to incorrect values as frequency changes. For a quick check, if f = 60 Hz and L = 0.1 H, X_L = 2π × 60 × 0.1 ≈ 37.7 Ω.