Reactance is the imaginary part of impedance: the opposition that inductance or capacitance presents to alternating current, expressed in ohms. It stores and returns energy rather than dissipating it, and its magnitude depends on frequency.
Learning objectives
- State the formulas for inductive and capacitive reactance
- Calculate reactance from frequency, inductance or capacitance
- Explain why reactance depends on frequency
- Combine reactance with resistance to find impedance
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
An inductor opposes changes in current, so its reactance rises as frequency rises. A capacitor opposes changes in voltage, so its reactance falls as frequency rises. At 0 Hz, an ideal inductor is a short circuit and an ideal capacitor is an open circuit.
Intermediate How it behaves in a circuit
Reactance is not constant with frequency, which is why a filter can pass one band and reject another. An inductor blocks high frequencies and passes low ones; a capacitor does the opposite.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Reactance | X | ohm (Ω) |
| Inductance | L | henry (H) |
| Capacitance | C | farad (F) |
| Frequency | f | hertz (Hz) |
Worked examples
Inductive reactance at 50 Hz
Problem. A 100 mH inductor is connected to a 50 Hz supply. What is its reactance?
Solution. XL = 2πfL = 2 × 3.1416 × 50 × 0.100.
Capacitive reactance at 50 Hz
Problem. A 100 µF capacitor is connected to a 50 Hz supply. What is its reactance?
Solution. XC = 1/(2πfC) = 1/(2 × 3.1416 × 50 × 0.000100).
Same components at 1 kHz
Problem. Find the reactance of the same 100 mH inductor and 100 µF capacitor at 1 kHz.
Solution. XL = 2π × 1000 × 0.100. XC = 1/(2π × 1000 × 0.000100).
Practical applications
- LC and RC filter design
- Tuning and resonant circuits
- Magnetic ballasts and chokes
- Snubber and damping networks
- Power-factor correction
- Limiting inrush and fault current
Automotive applications
The ignition coil relies on inductive reactance to limit primary current while storing energy. Audio crossover networks use reactive components to send low and high frequencies to the correct speakers, and electric-vehicle inverters must account for the motor winding reactance across the whole speed range.
Industrial applications
Line reactors and dv/dt filters protect variable-frequency drives from high-frequency currents, while capacitor banks and detuning reactors correct power factor without creating resonance with the supply. Reactance also limits fault current in some distribution arrangements.
Measurement procedure
- Use an LCR meter at a stated test frequency; the reading is meaningless without the frequency.
- Measure RMS voltage and current and compute X = V/I when a direct meter is not available.
- Discharge capacitors and short their terminals before measuring, and keep inductors away from sensitive meters.
- Remember that a real component has resistance as well, so the measured impedance is not pure reactance.
Common mistakes
- Using the DC resistance of a coil as if it were its reactance.
- Forgetting that reactance changes with frequency; a value quoted at 50 Hz is not valid at 50 kHz.
- Adding XL and XC arithmetically as positive numbers instead of subtracting them.
- Assuming an ideal component at frequencies where its parasitics dominate.
Safety considerations
- Capacitors can retain a dangerous charge after the supply is removed; discharge and verify before touching them.
- Interrupting current through an inductor produces a high voltage spike; use suppression and rated switching devices.
- Use instruments and probes rated for the voltage and frequency of the circuit under test.