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 animation can be started using the start button, causing the phasors to rotate and the sine waves to 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: The resistor R converts electrical energy into heat, the inductor L stores energy in its magnetic field, and the capacitor C stores energy in its electric field. The inductor and capacitor periodically exchange energy, while the resistor dampens this oscillation.
At the resonant frequency ( f_0 = frac{1}{2pisqrt{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