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Series resonance
Intermediate
Impedance is minimum when X_L = X_C.
ω₀ = 1/√(LC)When X_L = X_C the impedance is minimum (= R) and the current maximum at ω₀ = 1/√(LC). Used to tune radios.
L = 1 mH, C = 100 pF: f₀ ≈ 503 kHz.
Voltages across L and C can exceed the supply.
In more detail
Series resonance occurs when inductive and capacitive reactances are equal, so they cancel. The impedance is then minimal, equal to R, and the current is at its maximum for the given voltage.
Real-world uses
- Radio receivers tune to stations by adjusting resonance.
- Series resonance is used in filters and oscillators.
- Radio tuners rely on series resonance, where the impedance is low and a large current flows at the chosen frequency.
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Frequently asked questions
What is the resonant frequency?
f0 = 1/(2π sqrt(LC)).
What current flows at resonance?
The maximum current, limited only by the resistance.
What is special about resonance?
At resonance, the inductive and capacitive reactances cancel, so the current is limited only by the resistance.
Related topics in AC Circuits & EM Waves
Capacitor in AC · LCR series circuit · Phase angle · Quality factor in LCR · Bandwidth · Power factor