Complete Guide to Reactance: XL, XC, and Circuit Behavior
The Reactance Calculator computes inductive reactance (XL), capacitive reactance (XC), and total reactance in series or parallel circuits. Essential for AC circuit analysis, power factor correction, and filter design.
What is Reactance?
Reactance is opposition to current flow in AC circuits due to inductance or capacitance. Measured in ohms (Ω). Unlike resistance, it causes phase shift but no power loss.
- Inductive Reactance (XL): XL = 2πfL
- Capacitive Reactance (XC): XC = 1/(2πfC)
Our Reactance Calculator handles single, series, and parallel combinations with frequency in Hz.
Why Calculate Reactance?
Critical for:
- Impedance Calculation: Z = √(R² + (XL - XC)²)
- Resonance: XL = XC → minimum impedance
- Power Factor Correction: Add capacitors to cancel XL
- Filter Design: High-pass, low-pass, band-pass
Use with Impedance Calculator and Resonance Frequency.
Formulas
| Type | Formula | Behavior |
|---|---|---|
| XL | 2πfL | Increases with f, L |
| XC | 1/(2πfC) | Decreases with f, C |
| Series | XL - XC | Net inductive if XL > XC |
| Parallel | 1/(1/XL + 1/XC) | Always < min(XL,XC) |
Reactance vs Frequency
XL rises linearly with frequency. XC falls hyperbolically. At resonance, they cancel.
Series L-C Circuit
X_total = XL - XC. If XL > XC → inductive. If XC > XL → capacitive. At resonance → X = 0.
Parallel L-C Circuit
X_total = (XL × XC) / (XL + XC). High impedance at resonance (tank circuit).
Calculation Steps
- Convert Units: mH → H, μF → F
- Compute XL: 2πfL
- Compute XC: 1/(2πfC)
- Combine: Series: XL - XC; Parallel: product over sum
Example: 60 Hz, L=100 mH, C=100 μF
Series circuit.
- XL = 2π×60×0.1 = 37.7 Ω
- XC = 1/(2π×60×100e-6) = 26.5 Ω
- X_total = 37.7 - 26.5 = 11.2 Ω (inductive)
Resonance Frequency
f_res = 1/(2π√(LC)). Use Resonance Calculator.
Inductor Q Factor
Q = XL / R. Higher Q → sharper resonance. Typical 50–200.
Applications
- Power Systems: Capacitor banks reduce reactive power
- Audio: Crossovers separate frequencies
- RF: Tuned circuits in radios
- Motors: Starting capacitors
Common Units
| Unit | Symbol | Conversion |
|---|---|---|
| Henry | H | 1 H |
| milliHenry | mH | 10⁻³ H |
| microHenry | μH | 10⁻⁶ H |
| Farad | F | 1 F |
| microFarad | μF | 10⁻⁶ F |
Practical Tips
- Frequency Accuracy: Use exact 50/60 Hz
- Tolerance: L, C ±5–20%
- ESR/ESL: Real components have resistance
- Safety: Discharge capacitors
Common Mistakes
- Forgetting 2π: XL ≠ fL
- Unit Errors: μF as F
- DC Reactance: XL = 0 at DC
- Parallel Formula: Not XL || XC = XL + XC
Advanced Topics
- Complex Impedance: Z = R + j(XL - XC)
- Phasor Diagrams: Current lags voltage in L
- Bandwidth: f2 - f1 = f_res / Q
- Skin Effect: Increases XL at high f
FAQs
Is reactance frequency dependent? Yes — XL ∝ f, XC ∝ 1/f.
Can reactance be negative? XC is often treated as negative in series.
How to reduce XL? Lower inductance or frequency.
Conclusion
Reactance governs AC circuit behavior. Our Reactance Calculator simplifies XL, XC, and combination analysis. Design efficient circuits with Impedance, Resonance, and Construction tools. Master AC theory with 1000 Calculators.