Library / Electrical / ELE-19
Electrical
Capacitive reactance
Opposition of a capacitor to alternating current.
- Ref
- ELE-19
- Rev
- v1
- Field
- Electrical
- Result
- XC [Ω]
XC in ohms, f frequency in Hz, C capacitance in farads. The impedance of an ideal capacitor is ZC = 1/(jωC).
A capacitor passes fast-changing current easily and blocks slow-changing current. Its opposition falls as either the frequency or the capacitance rises.
Calculator
- Angular frequency ω314.2 rad/s
- Current at 230 V RMS0.7226 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.
- A capacitor blocks DC (infinite reactance) and passes high frequencies, the opposite of an inductor.
- Reactance equals the resistance of a series RC filter at its corner frequency f = 1/(2πRC).
- The current through a capacitor leads its voltage by 90°.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| C Capacitance | 0.001 to 1,000 µF | 3.183 | 3,183,000 | 3,183,000 | +10% | −9.09 % |
| f Frequency | 1 to 1,000,000 Hz | 0.01592 | 15,920 | 15,920 | +10% | −9.09 % |
Sweep of Frequency
| Frequency (Hz) | Reactance (Ω) |
|---|---|
| 1 | 15,920 |
| 5.623 | 2,830 |
| 31.62 | 503.3 |
| 177.8 | 89.5 |
| 1,000 | 15.92 |
| 5,623 | 2.83 |
| 31,620 | 0.5033 |
| 177,800 | 0.0895 |
| 1,000,000 | 0.01592 |
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. Inversely proportional: doubling frequency halves the reactance.
Capacitance
Capacitor value. Inversely proportional.
Worked example with the values above
- Convert capacitance: 10 µF = 1×10−5 F. ω = 2πf = 314.2 rad/s.
- XC = 1/(ωC) = 1 / (314.2 × 1×10−5).
- XC = 318.3 Ω.
Assumptions and limits
- Ideal capacitor with no series resistance or inductance.
- Sinusoidal steady state.
- Constant capacitance (no voltage coefficient).
Common mistakes
- Forgetting the 2π.
- Mixing µF with F.
- Treating XC as a resistance that dissipates power.
Statistics and uncertainty
Electrolytic capacitors have tolerances of −20%/+80% in some cases, and capacitance changes with temperature and age. The inverse relationship means the reactance error equals the capacitance error: δX/X = δC/C when frequency is accurate.
Where it is used
- AC coupling and bypass capacitors.
- Power-factor correction.
- Filter design.
Maths you need
- AC frequency: cycles per second
- Reciprocal: reactance falls as C rises