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Reactance vs Frequency

How to Use

  • Inductance L slider — set the inductor value (0.1 µH to 100 mH, log scale).
  • Capacitance C slider — set the capacitor value (1 nF to 100 µF, log scale).
  • Frequency f slider — move the cursor line to read XL and XC at any frequency.
  • The Log Scale button toggles between logarithmic and linear axis display.

What to Observe

  • The red curve (XL = 2πfL) rises linearly on the log-log plot — inductors oppose higher frequencies more.
  • The blue curve (XC = 1/2πfC) falls linearly — capacitors oppose lower frequencies more.
  • The two curves cross at f₀ (the resonant frequency) — the purple dot marks this point.
  • At f₀, XL = XC and the reactances exactly cancel in a series or parallel LC circuit.
  • The resonant frequency f₀ depends on both L and C: changing either moves the crossover left or right.
  • At very low frequencies: XC → ∞ (capacitor = open), XL → 0 (inductor = short).
  • At very high frequencies: XL → ∞ (inductor = open), XC → 0 (capacitor = short).

Key Equations

\[X_L = \omega L = 2\pi f L \quad \text{(increases with frequency)}\]
\[X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} \quad \text{(decreases with frequency)}\]
\[f_0 = \frac{1}{2\pi\sqrt{LC}} \quad \text{(resonant frequency: } X_L = X_C\text{)}\]
Frequency Inductor Capacitor
DC (f=0) Short circuit (XL=0) Open circuit (XC=∞)
f₀ XL = XC XL = XC
High f Open circuit (XL→∞) Short circuit (XC→0)

Key Concepts

  • Inductive reactance XL: Opposition to current by an inductor; proportional to frequency
  • Capacitive reactance XC: Opposition to current by a capacitor; inversely proportional to frequency
  • Resonant frequency f₀: Frequency at which XL = XC; reactances cancel
  • Log-log plot: Both reactance curves appear as straight lines with slopes +1 (XL) and −1 (XC)