Series RLC: Damping and Resonance
1 · Predict
A series RLC circuit combines a resistor, inductor, and capacitor. The resistor's value determines whether the circuit's approach to its final state oscillates (underdamped) or not (overdamped). Does a bigger resistance make oscillation more or less likely?
- A bigger resistance suppresses oscillation — more resistance means more energy dissipated per cycle, damping any ringing.
- A bigger resistance makes oscillation more likely.
- Resistance doesn't affect whether the circuit oscillates, only how fast it settles.
2 · Set Up
- Open the rlc-series preset and press Reset. L = 1 H, C = 0.01 F are fixed; the battery supplies 10 V.
- Enable the capacitor-voltage and inductor-current readouts.
- Set the resistor's value for each trial and compute the damping ratio ζ = R / (2√(L/C)).
3 · Collect Data
| Resistance R (Ω) | Resonant frequency f₀ (Hz) | Damping ratio ζ |
|---|---|---|
| 10 | ||
| 20 | ||
| 40 |
Sketch, for each R value, whether you'd expect the capacitor voltage to overshoot and ring (ζ < 1, underdamped), settle in the fastest possible smooth approach (ζ = 1, critically damped), or approach slowly without overshoot (ζ > 1, overdamped).
4 · Analyze
- For one trial, compute f₀ = 1/(2π√(LC)) using L = 1 H, C = 0.01 F (same for every trial, since it doesn't depend on R), then ζ = R/(2√(L/C)). Compare both to the table.
- This circuit's default R = 20 Ω gives exactly ζ = 1 (critically damped) — press Play at that value and watch the capacitor voltage approach 10 V as fast as possible without overshooting. Explain what you'd expect to see instead at R = 10 Ω (ζ = 0.5, underdamped).
5 · Extend
- Critically damped systems (ζ = 1) are prized in engineering — car shock absorbers, for instance — because they return to equilibrium fastest without any overshoot or bouncing. Explain why an underdamped shock absorber (ζ < 1) would make for an uncomfortable, bouncy ride.
- The resonant frequency f₀ = 1/(2π√(LC)) depends only on L and C, not on R at all — R only controls the damping. Explain why an RLC radio tuning circuit uses L and C (not R) to select which station's frequency it responds to.
The Physics Behind This Experiment
RLC Resonant Frequency
A series RLC circuit's natural oscillation frequency is f₀ = 1/(2π√(LC)), set entirely by the inductance and capacitance. The resistance R doesn't shift this frequency — it only controls how strongly any oscillation is damped.