Meaning and mechanism
In AC circuits, inductors and capacitors produce different sizes and phase responses depending on the frequency. The sum of resistance and this effect is impedance.
The reactance of a coil increases as the frequency increases, while the reactance of a capacitor decreases. When their magnitudes are equal, the imaginary part of the sum in a series circuit is canceled out.
Relationships and conditions
Z=R+j(ωL−1/ωC), and the resonant frequency is f₀=1/(2π√LC). In an ideal series circuit with fixed supply voltage and R, current is greatest at resonance.
This result concerns a series circuit in steady state. It does not transfer directly to parallel resonance or real circuits with parasitic elements and frequency-dependent losses.
What to observe in the simulation
At resonance inductive and capacitive reactance cancel and current is maximal.
Only steady state of ideal lumped elements is modeled. Coil losses and parasitic effects are omitted. Experiment on screen; do not reproduce this with real power supplies, outlets or high voltage.
Key relationships and symbols
Z = R + j(ωL−1/(ωC)) · f₀ = 1/(2π√LC)
| Symbol | Meaning | Unit |
|---|---|---|
| Z | Complex impedance | Ω |
| ω | Angular frequency 2πf | rad/s |
| L, C | Inductance and capacitance | H, F |
Worked example
At resonance, what is the RMS current for a 6 V RMS input and 20 Ω resistance?
0.3 A
Common misconceptions
- In a resonance circuit, neither the inductor nor the capacitor will have a voltage of 0.