Inductive reactance is the opposition that an inductor presents to alternating current (AC), measured in ohms, which increases proportionally with both the frequency of the AC signal and the inductance of the coil. Unlike standard DC resistance, which dissipates electrical energy as heat, inductive reactance temporarily stores energy in a magnetic field and returns it to the circuit. This fundamentally changes a real circuit by limiting AC current flow without burning real power (watts), while simultaneously shifting the current phase behind the voltage by up to 90 degrees. Beginners and even seasoned technicians commonly confuse inductive reactance with DC resistance (which causes thermal losses) or capacitive reactance (which behaves inversely, dropping as frequency rises).
The Core Formula and a Worked Numeric Example
To calculate the exact opposition an inductor will present to an AC signal, we use the standard formula:
XL = 2 π f L
- XL = Inductive reactance in Ohms (Ω)
- π = Pi (approximately 3.14159)
- f = Frequency of the AC signal in Hertz (Hz)
- L = Inductance in Henrys (H)
You are designing an EMI filter for a 2026-era GaN (Gallium Nitride) power supply and need to evaluate a 47 mH (0.047 H) common-mode choke, such as a Würth Elektronik 744824 series part.
Scenario A: 60 Hz Mains Hum
XL = 2 × 3.14159 × 60 Hz × 0.047 H = 17.7 Ω
At line frequency, the choke presents very little opposition, allowing the 60 Hz power to pass through with minimal voltage drop.
Scenario B: 100 kHz Switching Noise
XL = 2 × 3.14159 × 100,000 Hz × 0.047 H = 29,530 Ω (29.5 kΩ)
At the high-frequency switching node, the reactance skyrockets, effectively choking off the high-frequency noise and preventing it from back-feeding into the AC mains.
Reference Table: Reactance Across Frequencies and Inductances
The table below provides pre-calculated inductive reactance values for standard inductor sizes across common frequency domains. This is highly useful for bench troubleshooting and quick component selection without needing to run the math every time.
| Inductance (L) | 60 Hz (Mains) | 1 kHz (Audio) | 10 kHz (SMPS Low) | 100 kHz (SMPS High) |
|---|---|---|---|---|
| 1 mH (0.001 H) | 0.38 Ω | 6.28 Ω | 62.8 Ω | 628 Ω |
| 10 mH (0.01 H) | 3.77 Ω | 62.8 Ω | 628 Ω | 6.28 kΩ |
| 100 mH (0.1 H) | 37.7 Ω | 628 Ω | 6.28 kΩ | 62.8 kΩ |
| 1 H (1.0 H) | 377 Ω | 6.28 kΩ | 62.8 kΩ | 628 kΩ |
Note: These values assume an ideal inductor. In reality, parasitic winding capacitance will cause the actual impedance to deviate from these numbers as you approach the component's Self-Resonant Frequency (SRF). Always verify high-frequency behavior using manufacturer tools like the Coilcraft Inductor Finder.
Where You Meet This in Practice
Understanding the inductive reactance definition is not just an academic exercise; it dictates how you select components and troubleshoot failures on the bench and in the field.
1. AC Motor Starting and Inrush Current
When a large AC induction motor (like a 5 HP HVAC compressor) starts, the rotor is stationary. The effective inductance of the stator windings is relatively low at this locked-rotor state, meaning the inductive reactance is low, and the motor draws a massive inrush current (often 6 to 8 times the full-load amp rating). As the motor spins up, back-EMF is generated, the effective reactance rises, and the current drops to normal running levels. If you are sizing a breaker or a motor-start capacitor, you must account for this temporary low-reactance state to avoid nuisance tripping.
2. Switch-Mode Power Supply (SMPS) Output Filtering
In a modern buck converter stepping 12V down to 3.3V for a microcontroller, the output inductor smooths the PWM switching ripple. If your controller switches at 500 kHz, a 10 μH inductor yields an XL of roughly 31.4 Ω to the AC ripple component, heavily attenuating it, while presenting near-zero reactance to the DC output current (limited only by the wire's tiny DC resistance). If you substitute a smaller inductor, XL drops, and your 3.3V rail will be plagued by high-frequency ripple that can reset your ESP32 or corrupt ADC readings.
3. Audio Crossover Networks
In passive speaker crossovers, inductors are used as low-pass filters for woofers. Because XL increases with frequency, high-frequency audio signals (tweeter range) face high reactance and are blocked from entering the woofer, while low-frequency bass signals pass through easily. A 2 mH air-core coil paired with an 8 Ω woofer will create a crossover point at approximately 636 Hz.
Imagine a heavy water wheel placed inside a pipe. If water flows steadily in one direction (DC), the wheel eventually spins up to match the water speed, offering almost no resistance. But if you rapidly slosh the water back and forth (AC), the heavy wheel's inertia resists every change in direction. The faster you try to slosh the water (higher frequency), or the heavier the wheel is (higher inductance), the harder it is to push the water through the pipe. That 'sloshing resistance' is inductive reactance.
Common Confusions and FAQ
Even experienced makers sometimes mix up the different types of opposition in AC circuits. Here is a quick comparison to lock in the concepts.
| Parameter | DC Resistance (R) | Inductive Reactance (XL) | Capacitive Reactance (XC) |
|---|---|---|---|
| Frequency Response | Constant (ignoring skin effect) | Increases as frequency rises | Decreases as frequency rises |
| Energy Handling | Dissipates as heat (Real Power) | Stores in magnetic field (Reactive) | Stores in electric field (Reactive) |
| Phase Shift | None (Voltage and Current in phase) | Current lags voltage by 90° | Current leads voltage by 90° |
Frequently Asked Questions
Does inductive reactance apply to DC circuits?
No. In a steady-state DC circuit, the frequency (f) is 0 Hz. Plugging 0 into the formula XL = 2πfL results in 0 Ω of reactance. The only opposition to DC in a real coil is its parasitic DC Resistance (DCR), which is the resistance of the copper wire itself. For deeper reading on how inductors behave in mixed-signal environments, Electronics Tutorials offers excellent AC/DC breakdowns.
Why does my inductor get hot if reactance doesn't burn power?
Ideal inductive reactance is 'wattless'—it borrows energy from the source during one half-cycle and returns it during the next. However, real-world inductors get hot due to two factors: DCR losses (I²R heating from the wire's physical resistance) and core losses (hysteresis and eddy currents in the magnetic core material, which scale heavily with frequency). If your inductor is burning up in a high-frequency SMPS, you likely need a core material rated for higher frequencies, like powdered iron or specific ferrite mixes, rather than just a higher inductance value.
How do I measure inductive reactance with a multimeter?
You cannot measure XL directly with a standard multimeter's ohms setting; that will only read the DCR. To find the reactance, you must apply a known AC voltage at a known frequency, measure the resulting AC current, and use Ohm's law (XL = V / I). Alternatively, use an LCR meter (like a UNI-T UT612 or a Keysight benchtop model), which injects a test signal and calculates the inductance, allowing you to derive the reactance for your target frequency mathematically. Fluke's guide on inductance provides solid field-measurement practices for motor windings and transformers.
