EASA/GCAA Part-66 · Module 3 — Electrical Fundamentals · 3.12 Reactance

Reactance, Phase & Resonance

Objective: reactance is the AC opposition of capacitors and inductors. X_C = 1/(2πfC) falls with frequency; X_L = 2πfL rises. In a series L-C-R they fight: below resonance the capacitor wins (current leads), above it the inductor wins (current lags), and where they cancel is resonance — maximum current, in phase.

Reactance vs frequency

Voltage & current phase

Frequency f 1000 Hz

Capacitance C 1.0 µF

Inductance L 10 mH

X_C capacitive

0Ω

X_L inductive

0Ω

Net X = X_L−X_C

0Ω

Resonance f₀

0Hz

X_C = 1/(2πfC) · X_L = 2πfL · f₀ = 1/(2π√(LC)) · φ = atan(X/R)

A capacitor passes high frequencies and blocks DC, so its reactance X_C is huge at low frequency and shrinks as frequency rises. An inductor does the opposite: it passes DC and chokes high frequencies, so X_L grows with frequency. Plotted together the falling X_C and rising X_L curves cross at the resonant frequency f₀, where they are equal and cancel. In a series circuit (with a little resistance R) the current is largest at resonance and exactly in phase with the voltage. Below f₀ the circuit looks capacitive and the current leads; above f₀ it looks inductive and the current lags.

Try this: Sweep the frequency and watch the phasors: current leads below f₀, lags above it, in phase at f₀.
Try this: At resonance the current waveform grows to its largest — the net reactance is zero.
Try this: Increase L or C — f₀ moves down (f₀ = 1/(2π√(LC))).
Try this: Note X_C and X_L are equal exactly at f₀.