Series RLC Electromagnetic Oscillator — 3D Lab Simulation
Energy exchange between inductor magnetic field and capacitor electric field
Theoretical Foundation & Historical Context
The RLC circuit is the foundation of radio communications, tuned filters, and signal processing, demonstrating resonant Thomson frequency and Joule dissipation.
Law: Kirchhoff's Voltage Law & Thomson Resonant Formula | Scientist: William Thomson (Lord Kelvin) | Year: 1853
Key Learning Objectives & Competencies
- ✓ Model the series RLC second-order ODE: L(d²q/dt²) + R(dq/dt) + (1/C)q = V(t).
- ✓ Calculate the resonant angular frequency ω₀ = 1/√(LC) and Quality factor Q = (1/R)√(L/C).
- ✓ Demonstrate the electro-mechanical duality between RLC circuits and mass-spring-damper systems.
Mathematical Formulations & Differential Equations
L \frac{d^2q}{dt^2} + R \frac{dq}{dt} + \frac{q}{C} = 0
Differential equation of capacitor charge
Physical Parameters & Units of Measurement
| Symbol | Physical Quantity | SI Unit | Default |
|---|---|---|---|
| R | Resistance (R) | Ohm | 1 |
| L | Inductance (L) | H | 1 |
| C | Capacitance (C) | F | 1 |
Real-World & Industrial Engineering Applications
Radio frequency tuner circuits in AM/FM receivers and software-defined radios (SDR).
Inductive wireless power transfer pads for smartphones and electric vehicle charging.
Harmonic suppression filters in industrial power electronics grids and audio equalizers.
3-Step Controlled Experimental Protocol
- Step 1: Baseline Setup — Initialize the simulation in standard conditions and observe undisturbed system dynamics.
- Step 2: Parameter Variation — Gradually modulate physical parameters using the control panel sliders.
- Step 3: Verification & Phase Space Analysis — Compare phase space trajectories and conservation metrics against analytical ODE solutions.
Frequently Asked Questions (FAQ)
What occurs in a series RLC circuit when it hits electrical resonance?
At resonance (ω = 1/√(LC)), inductive reactance equals capacitive reactance (X_L = X_C). The imaginary impedances cancel out completely, reducing total impedance to pure resistance Z = R and maximizing circuit current.
How does the mechanical mass-spring system correspond mathematically to the electrical RLC circuit?
Inductance L corresponds to mechanical mass m (inertia), resistance R corresponds to friction damping γ, and inverse capacitance 1/C corresponds to spring stiffness k. Charge q corresponds to displacement x.
What does the Quality Factor Q represent in an RF tuning circuit?
Q measures the sharpness of the frequency response curve. A high Q means very narrow bandwidth and high selectivity, allowing a radio receiver to filter out adjacent channel interference.
Related Simulations & Experiments
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