Reactance vs Frequency

Inductive reactance X_L = ωL = 2πfL — rises LINEARLY with frequency.

Capacitive reactance X_C = 1/(ωC) = 1/(2πfC) — falls HYPERBOLICALLY with frequency.

At low f: X_C is huge (block) and X_L is small (pass) — capacitor blocks DC, inductor lets it through.

At high f: X_L is huge (block) and X_C is small (pass) — inductor blocks high-frequency, capacitor passes it.

The two curves cross at f₀ = 1/(2π√(LC)) — the resonant frequency. At this f, X_L = X_C.

This frequency dependence is the basis of FILTERS: high-pass uses series C, low-pass uses series L, etc.

RC circuits act as low-pass or high-pass depending on which element is in series; RL circuits are dual.