What Are Resonance and the LC Circuit?
Resonance is the special condition in a circuit containing a coil (L) and a capacitor (C) where their reactances cancel each other at a certain frequency. At that frequency the circuit behaves in a very special way.
What Is Resonance?
A coil's reactance rises with frequency, a capacitor's falls. At the frequency where they're equal, the circuit resonates; energy oscillates between L and C.
Resonant Frequency
The frequency at which resonance occurs depends on the coil and capacitor values:
f = 1 / (2π√(L × C))
As L or C grows, the resonant frequency drops.
LC Oscillation (Tank Circuit)
If an L and a C are connected in parallel, energy oscillates back and forth between them; this is called a tank circuit. Ideally, this oscillation sustains at the resonant frequency.
Where Is It Used?
Station tuning in radio and TV, band-pass filters, oscillators and wireless power transfer all rely on resonance.
Common Mistakes
- Mixing up units: L must be in henries, C in farads; mH/µF values must be converted before using the formula.
- Ignoring losses: in a real circuit, resistance damps the oscillation; there's no ideal infinite oscillation.
- Confusing series and parallel resonance: at series resonance impedance is minimum, at parallel it's maximum.
Frequently Asked Questions
Why is resonance used in radio?+
What does the resonant frequency depend on?+
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