AC circuit opposition
What is capacitive reactance?
Capacitive reactance is the opposition a capacitor presents to alternating current as it repeatedly charges and discharges.
It depends on both AC frequency and capacitance and is measured in ohms.
Main AC formula
Capacitive reactance formula
Capacitive reactanceXc = 1 ÷ (2πfC)
- Xc is capacitive reactance in ohms.
- f is frequency in hertz.
- C is capacitance in farads.
Worked example
Calculate capacitive reactance
Suppose a capacitor has a capacitance of 100 μF in a50 Hz AC circuit.
- Convert 100 μF to 0.0001 F.
- Use Xc = 1/(2πfC).
- Substitute f = 50 Hz and C = 0.0001 F.
- Xc = 1/(2 × π × 50 × 0.0001).
- The capacitive reactance is about 31.83 Ω.
Frequency relationship
How frequency affects reactance
Capacitive reactance decreases as frequency increases. A capacitor therefore opposes low-frequency current more strongly than high-frequency current.
Capacitance relationship
How capacitance affects reactance
Larger capacitance produces lower reactance at the same frequency. Smaller capacitors provide greater opposition to alternating current.
AC versus DC
Capacitors in DC circuits
At steady-state direct current, frequency is effectively zero, so ideal capacitive reactance approaches infinity.
A charged ideal capacitor therefore behaves like an open circuit under steady DC conditions.
SI unit guidance
Capacitive reactance units
- Reactance: ohms (Ω).
- Frequency: hertz (Hz).
- Capacitance: farads (F).
- Angular frequency: radians per second.
- 1 microfarad = 1 × 10⁻⁶ F.
- 1 nanofarad = 1 × 10⁻⁹ F.
- 1 picofarad = 1 × 10⁻¹² F.
Practical applications
Where capacitive reactance matters
- AC filters and crossover circuits.
- Signal coupling and decoupling.
- Power-factor correction.
- Timing and oscillator circuits.
- RLC circuit analysis.
- Radio-frequency networks.
Model limitations
Assumptions and limitations
- The capacitor is treated as ideal.
- Equivalent series resistance is ignored.
- Leakage current is not included.
- Parasitic inductance is ignored.
- Capacitance is assumed constant.
- All values must use compatible SI units.
Common questions
Capacitive reactance calculator FAQ
What formula does the capacitive reactance calculator use?
It uses Xc = 1/(2πfC), where Xc is capacitive reactance, f is frequency, and C is capacitance.
What is the unit of capacitive reactance?
Capacitive reactance is measured in ohms, written Ω.
How does frequency affect capacitive reactance?
Capacitive reactance decreases as frequency increases. Doubling frequency halves reactance when capacitance remains constant.
How do I calculate capacitance from reactance?
Divide one by two pi times frequency times reactance using C = 1/(2πfXc).
Is capacitive reactance the same as resistance?
No. Resistance dissipates electrical energy, while ideal capacitive reactance opposes alternating current through electric-field storage.