Two opposite responses to frequency
A resistor opposes current by the same amount at any frequency, but a coil and a capacitor don't: a coil resists changes in current, so it fights AC harder as frequency rises; a capacitor resists changes in voltage, so it lets AC through more easily as frequency rises. Pick which component you have above to see its reactance at your chosen frequency.
- f — frequency (Hz)
- L — inductance (H)
- C — capacitance (F)
- XL, XC — reactance (Ω)
More detail
Why XL climbs while XC falls
XL = 2πfL grows in direct proportion to frequency — double the frequency, double the inductive reactance — because a faster-changing current induces a larger opposing voltage in the coil. XC = 1/(2πfC) does the opposite: double the frequency and XC is cut in half, because a capacitor charges and discharges faster at higher frequencies, letting more current pass for the same voltage swing. This is why inductors are used to block high frequencies (chokes) and capacitors are used to block low frequencies or DC (coupling/decoupling) while passing the rest.
Where they cancel out. In an LC circuit, XL and XC change in opposite directions as frequency shifts, so there's exactly one frequency where they're equal in magnitude — that's the resonant frequency, where the two reactances cancel and the circuit's impedance is at its minimum (series) or maximum (parallel).
Frequently asked questions
What is the reactance of a 10 mH inductor at 60 Hz?
XL = 2π × 60 × 0.01 = 3.77 Ω. Select "Inductive" above and enter 60 Hz and 10 mH to confirm.
What is the reactance of a 100 µF capacitor at 60 Hz?
XC = 1 / (2π × 60 × 0.0001) = 26.53 Ω. Select "Capacitive" and enter 60 Hz and 100 µF above.
If I raise the frequency 100×, what happens to XL and XC?
XL scales up 100× (it's directly proportional to frequency), while XC scales down to 1/100 of its value (it's inversely proportional). A 10 mH inductor at 6 kHz instead of 60 Hz jumps from 3.77 Ω to 377 Ω; a 100 µF capacitor over the same change drops from 26.5 Ω to 0.265 Ω.
Why does a capacitor block DC but pass high-frequency AC?
DC has a frequency of 0 Hz, and XC = 1/(2π·0·C) is mathematically infinite — no current gets through. As frequency rises above 0, XC drops toward 0, so a capacitor looks increasingly like a short circuit to high-frequency signals — the basis of using capacitors for AC coupling and blocking DC offsets.