RLC circuit

Definition

An RLC circuit is an electrical circuit consisting of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. It is commonly used to study oscillatory behavior and resonance in AC circuits.

5 Must Know Facts For Your Next Test

1. The impedance of an RLC series circuit is given by $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$, where $\omega$ is the angular frequency.
2. At resonance, the inductive reactance and capacitive reactance cancel each other out, making the impedance equal to the resistance ($Z = R$).
3. The resonant frequency $f_0$ of an RLC series circuit can be calculated using $f_0 = \frac{1}{2\pi\sqrt{LC}}$.
4. In an RLC series circuit at resonance, the voltage across the inductor and capacitor can be much higher than the supply voltage, a phenomenon known as voltage magnification.
5. The quality factor (Q) of an RLC circuit is defined as $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$, which measures how underdamped the oscillator is.

Review Questions

• What happens to the impedance of an RLC series circuit at its resonant frequency?
• How do you calculate the resonant frequency of an RLC series circuit?
• What does a high quality factor indicate about an RLC circuit's damping?

Related terms

Resonance: A condition in which the inductive reactance equals the capacitive reactance, resulting in maximum energy transfer and minimum impedance.

Inductive Reactance: The opposition to current flow by an inductor, proportional to both inductance ($L$) and angular frequency ($\omega$), given by $X_L = \omega L$.

Capacitive Reactance: The opposition to current flow by a capacitor, inversely proportional to both capacitance ($C$) and angular frequency ($\omega$), given by $X_C = \frac{1}{\omega C}$.