The following animation illustrates the behavior of a series RLC circuit in an AC circuit. Impedance, phase shift, and resonance behavior are visualized in real time.
Links
Animation Description
The animation shows a series RLC circuit with four synchronized displays: circuit diagram, formulas, phasor diagram, and time-domain graph. The start button begins the animation. The phasors rotate and the sine waves move through the diagram.
The impedance of the circuit is calculated as:
\[ Z = \sqrt{R^2 + (X_L – X_C)^2} \]
With the reactances:
- \( X_L = 2\pi f L \) – inductive reactance
- \( X_C = \frac{1}{2\pi f C} \) – capacitive reactance
The phase shift φ between voltage and current is displayed as a double arrow in both the phasor diagram and the time-domain graph.
Interactive Controls
The following parameters can be adjusted using the sliders:
- U (1–24 V): AC voltage amplitude
- f (1–200 Hz): AC voltage frequency
- R (1–1000 Ω): Resistance
- C (1–100 µF): Capacitance
- L (10–1000 mH): Inductance
The checkboxes L, C, and R allow individual components to be shown or hidden to examine different circuit configurations (e.g., pure RC or RL circuit).
Physical Background
In a series RLC circuit, three effects combine: R converts energy into heat, L stores it in a magnetic field, C in an electric field. The inductor and capacitor periodically exchange energy. The resistor dampens this oscillation.
At the resonant frequency \( f_0 = \frac{1}{2\pi\sqrt{LC}} \), the reactances cancel out (\( X_L = X_C \)), the impedance reaches its minimum and equals the resistance. The current reaches its maximum and is in phase with the voltage.
Practical Applications
- Radio receivers: Tuned circuits select specific frequencies through resonance
- Filters: High-pass, low-pass, and band-pass filters in audio engineering
- Oscillators: LC oscillators for clock generation in digital circuits
- Power factor correction: Capacitors compensate for inductive loads in power grids
Overview
| Title | RLC Circuits |
| Target Audience | Teachers and Lecturers |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | MIT |