How it works
A coil resists changes in current more as the frequency rises, so its reactance grows with frequency. A capacitor does the opposite: it passes high frequencies easily, so its reactance falls as frequency rises. Both are measured in ohms but neither dissipates power like a resistor does.
In a series RLC circuit, X_L and X_C oppose each other. The net reactance is X_L − X_C, and the impedance is the resistance and net reactance combined at right angles. At the resonant frequency the two reactances are equal and impedance drops to just the resistance.
Worked example
A 10 mH coil and a 100 µF capacitor in series with 10 Ω of resistance on a 60 Hz supply:
- X_L = 2π f L = 2π × 60 × 10 mH = 3.77 Ω
- X_C = 1 ÷ (2π f C) = 1 ÷ (2π × 60 × 100 µF) = 26.526 Ω
- |Z| = √(R² + (X_L − X_C)²) = √(10² + (3.77 Ω − 26.526 Ω)²) = 24.856 Ω
- Resonant f₀ = 1 ÷ (2π √(L C)) = 159.155 Hz
| Input | Value |
|---|---|
| Frequency | 60 Hz |
| Inductance | 10 |
| Inductance unit | mH |
| Capacitance | 100 |
| Capacitance unit | µF |
| Series resistance | 10 Ω |
| Result | Value |
|---|---|
| Inductive reactance X_L | 3.77 Ω |
| Capacitive reactance X_C | 26.526 Ω |
| Series impedance |Z| | 24.856 Ω |
| Phase angle (positive = inductive) | -66.28 ° |
| Resonant frequency | 159.155 Hz |
Assumptions and limits
- Ideal inductor and capacitor. Real coils have winding resistance and real capacitors have equivalent series resistance and inductance.
- Series circuit with a sinusoidal supply at a single frequency.
- Resonant frequency is for the series LC pair and does not depend on the resistance.
Common questions
What is the reactance of a 1 henry inductor at 60 Hz?
X_L = 2π × 60 × 1 = 377 Ω.
What is the reactance of a 100 µF capacitor at 60 Hz?
X_C = 1 ÷ (2π × 60 × 0.0001) = 26.5 Ω.
What happens at resonance?
X_L and X_C are equal and cancel, so a series circuit has its minimum impedance (just R) and the current peaks. A parallel LC pair does the opposite and has maximum impedance.
Is reactance the same as resistance?
No. Resistance turns energy into heat. Reactance stores and returns energy each cycle and shifts the current out of phase with the voltage.
Sources
- Standard AC circuit theory: X_L = 2πfL, X_C = 1/(2πfC), series RLC impedance and resonance.
Updated 2026-09-30