Resonant frequency

Definition

Resonant frequency is the natural frequency at which an AC circuit's impedance is minimized, and current is maximized. It occurs when the inductive reactance equals the capacitive reactance, leading to a purely resistive impedance.

5 Must Know Facts For Your Next Test

1. At resonant frequency, the impedance of an LC circuit is purely resistive.
2. The formula for resonant frequency in an LC circuit is $f_0 = \frac{1}{2\pi\sqrt{LC}}$, where L is inductance and C is capacitance.
3. Resonance leads to maximum current flow in an AC circuit.
4. In RLC circuits, at resonance, the voltage across L and C can be much higher than the source voltage.
5. Quality factor (Q-factor) determines the sharpness of resonance; higher Q indicates a narrower and sharper peak.

Review Questions

• What happens to the impedance of an AC circuit at its resonant frequency?
• How do you calculate the resonant frequency of an LC circuit?
• What effect does resonance have on current in an AC circuit?

Related terms

Inductive Reactance:

The opposition to current flow in a circuit due to inductors, given by $X_L = 2\pi f L$.

Capacitive Reactance:

The opposition to current flow in a circuit due to capacitors, given by $X_C = \frac{1}{2\pi f C}$.

Quality Factor (Q-Factor): A dimensionless parameter that describes how underdamped an oscillator or resonator is, defined as $Q = \frac{f_0}{BW}$ where $BW$ is bandwidth.