Library / Electrical / ELE-18
Electrical
Inductive reactance
Opposition of an inductor to alternating current.
- Ref
- ELE-18
- Rev
- v1
- Field
- Electrical
- Result
- XL [Ω]
XL in ohms, f frequency in Hz, L inductance in henries. The impedance of an ideal inductor is ZL = jωL, a purely imaginary value.
An inductor resists changes in current. The faster the current alternates, the stronger the resistance, so inductors pass low frequencies and block high ones.
Calculator
- Angular frequency ω314.2 rad/s
- Current at 230 V RMS7.321 A
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Reactance rises with frequency: an inductor looks like a wire at DC and like an open circuit at very high frequency.
- The voltage across an inductor leads its current by 90°.
- Unlike a resistor, an ideal inductor stores energy (½LI²) rather than dissipating it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| f Frequency | 1 to 1,000,000 Hz | 0.6283 | 628,300 | 628,300 | +10% | +10 % |
| L Inductance | 0.01 to 1,000 mH | 0.003142 | 314.2 | 314.2 | +10% | +10 % |
Sweep of Frequency
| Frequency (Hz) | Reactance (Ω) |
|---|---|
| 1 | 0.6283 |
| 5.623 | 3.533 |
| 31.62 | 19.87 |
| 177.8 | 111.7 |
| 1,000 | 628.3 |
| 5,623 | 3,533 |
| 31,620 | 19,870 |
| 177,800 | 111,700 |
| 1,000,000 | 628,300 |
Sweep one variable
Variables and how each one contributes
Reactance
What the equation gives you. Everything else feeds it.
Frequency
Frequency of the AC signal. Directly proportional.
Inductance
Inductor value. Directly proportional.
Worked example with the values above
- Convert inductance: 100 mH = 0.1 H. ω = 2πf = 314.2 rad/s.
- XL = ωL = 314.2 × 0.1.
- XL = 31.42 Ω.
Assumptions and limits
- Ideal inductor with no winding resistance.
- Sinusoidal steady state.
- Constant inductance (no saturation).
Common mistakes
- Using f in kHz without converting.
- Treating XL as resistance in power calculations.
- Mixing mH and H.
Statistics and uncertainty
Inductor tolerances are typically ±5–20%, and the inductance of iron-cored coils changes with current (saturation). Relative errors combine as δX/X ≈ √[(δf/f)² + (δL/L)²].
Where it is used
- Chokes and filters.
- Motor and transformer analysis.
- Power-factor correction design.
Maths you need
- AC frequency: cycles per second
- Complex numbers: impedance is imaginary