Capacitive Reactance (X_C)
Enter C and frequency (or solve for either) with a series resistance to get reactance, impedance, phase, current and reactive power.
Step-by-step
- Enter valid values to begin.
Ideal capacitor in series with a resistor R, sinusoidal steady state, RMS voltage. ESR, leakage, lead inductance and self-resonance are not included; above the self-resonant frequency the part is inductive and these results do not apply. Real capacitor values drift with tolerance, temperature, age and DC bias. The corner frequency fc = 1/(2πRC) is for the RC pair formed with the series resistance (0 Ω gives no corner).
Capacitive Reactance: How a Capacitor Resists AC
Core Engineering Principles
A capacitor passes current only while its voltage is changing, so its opposition to AC depends on how fast the voltage swings. We call that opposition reactance, XC = 1/(2πfC), and it falls as either frequency or capacitance rises. At DC the frequency is zero and XC is infinite, which is why a series capacitor blocks bias while letting signal through. Coupling capacitors use that; bypass capacitors shunt noise to ground. Keep XC well below the circuit impedance at the lowest frequency of interest.
Reactance is not resistance. Current leads voltage by 90°, so an ideal capacitor dissipates nothing and the energy swaps back and forth as reactive power Q = I²XC. That matters in the field. A capacitor-dropper supply lets a small film capacitor drop mains voltage without a heat sink, and motor-run and power-factor-correction capacitors supply leading var to cancel lagging motor current. A real part adds ESR, an inductance that makes it self-resonant (SRF), and drift in value. Above the SRF it behaves like an inductor, so a 100 nF part can be a poor bypass at 100 MHz.
|Z| = √(R² + XC²) • φ = −atan(XC / R) • I = V / |Z|
Q = I² × XC • fc = 1 / (2π R C)
NEC & Standard References
IEC 60050-131 is the International Electrotechnical Vocabulary entry that defines reactance, impedance and related circuit terms. IEC 60252-1 covers AC motor capacitors, including motor-run types, and sets tolerance and endurance requirements. IEC 60384-14 covers fixed capacitors for electromagnetic interference suppression and mains connection, the X and Y classes, and is the document to read before putting a dropper capacitor across the line. IEEE Std 18 covers shunt power capacitors used for power-factor correction. This is a calculation, not a compliance test; confirm against the adopted edition and the datasheet.1. XC = 1 / (2π × 60 × 10×10−6) = 265.26 Ω.
2. |Z| = √(10² + 265.26²) = 265.45 Ω.
3. Phase = −atan(265.26 / 10) = −87.84°, so current leads.
4. I = 230 / 265.45 = 0.8665 A.
5. Q = 0.8665² × 265.26 = 199.1 var leading.
6. Corner frequency of the RC pair fc = 1 / (2π × 10 × 10×10−6) = 1591.5 Hz.
- Ripple current heats the part. I²×ESR heating at high ripple current shortens electrolytic life; check the ripple rating.
- Derate the voltage. Pick a rating well above peak, not RMS, and allow for mains surges; for a 230 V line that means a peak near 325 V plus margin.
- Dropper supplies are not isolated. The whole circuit sits at mains potential, so use a rated X2 capacitor, a bleed resistor and an enclosure nobody can touch.
- Capacitance drifts. Tolerance, temperature, ageing and DC bias on ceramics all move C, and XC moves inversely, so dropper current moves with it.
- Watch the SRF. Above self-resonance the part turns inductive and the formula no longer applies.