Electronics
Capacitive and inductive reactance explained
Reactance is how strongly a capacitor or a coil opposes alternating current, in ohms like resistance. A capacitor's reactance, XC = 1 ÷ (2π f C), falls as the frequency rises. A coil's, XL = 2π f L, rises. So capacitors pass high frequencies and coils pass low ones.
Capacitors pass high frequencies
Example: 1 µF at 100 Hz.
Frequency is on the bottom, so ten times the frequency gives a tenth of the reactance: at 10 kHz the same capacitor is only 15.9 Ω. At 0 Hz, steady DC, it's infinite: a charged capacitor blocks DC.
Why? A capacitor's current is set by how fast its voltage changes. A faster wave changes faster, so the same voltage pushes more current through.
Coils pass low frequencies
Now frequency is on top. A 10 mH coil is 6.28 Ω at 100 Hz and 628 Ω at 10 kHz. Compare it with the 1 µF capacitor:
| Frequency | XC (1 µF) | XL (10 mH) |
|---|---|---|
| 100 Hz | 1.59 kΩ | 6.28 Ω |
| 1 kHz | 159 Ω | 62.8 Ω |
| 10 kHz | 15.9 Ω | 628 Ω |
Live experiment
Slide the frequency
One generator feeds two lamps: Pip behind a 1 µF capacitor, Dot behind a 10 mH coil. Slide from 20 Hz to 20 kHz. The capacitor's reactance falls as the coil's rises, and they cross at 1.59 kHz, where both are 100 Ω.
“Reactance” is lesson 2 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 22 before it first.
Ohm's law with X
Reactance goes into Ohm's law like resistance:
Use peak with peak, or RMS with RMS. Example: 3 V RMS across 1 µF at 10 kHz drives 3 ÷ 15.9 ≈ 189 mA RMS.
Unlike a resistor, an ideal capacitor or coil takes no average power. Energy flows in for a quarter of a cycle and back out the next, so it limits the current without getting warm.
Phase
Reactance also shifts the timing. In a capacitor, the current peaks a quarter cycle, 90°, before the voltage. In a coil, it peaks 90° after. "ELI the ICE man" remembers both: voltage (E) before current (I) in a coil (L), current before voltage in a capacitor (C).
Mix reactance with resistance and they don't simply add, because of that 90°: they combine into impedance, |Z| = √(R² + X²).
Where you'll meet it
A speaker's tweeter has a capacitor in series to keep out the bass. Power supplies use coils called chokes to block fast noise, and decoupling capacitors beside chips short fast noise to ground.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Reactance” is lesson 2 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 22 before it first.
Or start from the very first lesson, no account neededWork it out
- Capacitive and inductive reactance calculatorA capacitor's or a coil's ohms at any frequency, the current, and the impedance with R.
- Antenna length calculatorWavelength, quarter-wave and dipole lengths to cut, and the coil for a short whip.
- Capacitive and inductive reactance practice problemsCapacitor and coil reactance, AC current and impedance, with the working.
Practice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: an ideal capacitor. An ideal capacitor stores energy for a quarter of a cycle and hands it all back the next, so it limits the current without getting warm. A resistor or a lamp turns its power into heat and light.
- Why not “a resistor”? A resistor turns its share of the power into heat on every cycle, so it takes plenty on average.
- Why not “a lamp”? A lamp is a resistor that glows. It turns power into heat and light, so it takes power on average.
Show the answer
Answer: 1 ms. T = 1 over f = 1 over 1000 = 0.001 s = 1 ms. A thousand cycles fit in each second.
- Why not “10 ms”? That's the period of 100 Hz. At 1 kHz a thousand cycles fit in a second, so each lasts 1 ms.
- Why not “1 s”? 1 s is the period of 1 Hz. Period is 1 ÷ f, so a higher frequency means a shorter period.
Show the answer
Answer: current. An inductor fights any change in its current. A capacitor is the one that fights changes in voltage.
- Why not “voltage”? Fighting changes in voltage is a capacitor's job, not a coil's.
- Why not “resistance”? A coil's wire has a little resistance, but what a coil opposes is a change in its current.
“Reactance” is lesson 2 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 22 before it first.
Questions people ask
What is the formula for capacitive reactance?
X_C = 1 ÷ (2π × f × C), in ohms, with f in hertz and C in farads. A 1 µF capacitor is about 1.59 kΩ at 100 Hz and 15.9 Ω at 10 kHz. Double the frequency or the capacitance and the reactance halves.
What is the difference between reactance and resistance?
Both are measured in ohms and both limit current. Resistance turns energy into heat and doesn't care about frequency. Reactance comes from a capacitor or coil storing energy and handing it back each cycle, so it wastes nothing, and it changes with frequency.
Does a capacitor block DC?
Yes, once it has charged. At 0 Hz its reactance is infinite, so after the first moment no steady current flows. That's why a coupling capacitor passes an audio signal but blocks a DC level.
What is inductive reactance?
A coil's opposition to AC, X_L = 2π × f × L. It rises with frequency: a 10 mH coil is 6.28 Ω at 100 Hz and 628 Ω at 10 kHz. To DC, an ideal coil is just a wire.
Related topics
- What is impedance?Resistance and reactance combined: why 3 kΩ and 4 kΩ make 5 kΩ, and what phase means.
- How does a capacitor work?Two plates and a gap: how a capacitor stores charge and energy, and why it blocks steady DC.
- How does an inductor work?A coil that fights changes in its current, the high-voltage spike it makes, and how to tame it.
- High-pass filter explainedA capacitor in series that blocks DC and the bass, passes the treble, and couples audio between stages.