Reactance vs Frequency
X_L (linear ↑) and X_C (1/f ↓) crossing at resonance frequency f₀.
Key Notes
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.
Formulas
Inductive reactance
Linear in f; rises without bound at high f.
Capacitive reactance
Hyperbolic in f; rises without bound at low f.
Crossover frequency
Series LCR resonance condition.
RC low-pass cutoff
Frequency at which |V_out| = V_in/√2.
RL high-pass cutoff
Symmetric to RC.
Important Points
X_L and X_C have OPPOSITE behaviour vs f — that's why they cancel at resonance.
Plotting both on log-log axes shows X_L as +slope, X_C as −slope — straight lines crossing at f₀.
Filters exploit this asymmetry: pass certain frequencies, block others.
Tuning a radio = changing C (or L) so f₀ matches the desired broadcast frequency.
RC time-constant τ = RC; RL time-constant τ = L/R. Cutoff f_c = 1/(2πτ).
Both reactances have units of Ω, but unlike resistance they store energy temporarily — no dissipation.
Reactance vs Frequency notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.