Circuits

Series RLC

R, L and C in series — the capacitor settles to the source

Series RLC — interactive Circuits simulation. R, L and C in series — the capacitor settles to the source Free browser-based virtual physics lab with live SI measurements and a guided tutorial.

Series RLC transient

R, L, and C in series produce a damped transient toward steady state.

Energy swaps between the capacitor and inductor while the resistor dissipates energy.

• ω₀ = 1/√(LC)
• Damping from R

Investigation brief

Plan the question before you open the lab

The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.

Driving question

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?

Predictions to weigh

• A bigger resistance makes oscillation more likely.
• Resistance doesn't affect whether the circuit oscillates, only how fast it settles.
• A bigger resistance suppresses oscillation — more resistance means more energy dissipated per cycle, damping any ringing.

Variable roles

What you set:

• Resistance R (Ω)

What you measure:

• Resonant frequency f₀ (Hz)
• Damping ratio ζ

How the investigation runs

1. Open the rlc-series preset and press Reset. L = 1 H, C = 0.01 F are fixed; the battery supplies 10 V.
2. Enable the capacitor-voltage and inductor-current readouts.
3. Set the resistor's value for each trial and compute the damping ratio ζ = R / (2√(L/C)).

Governing equation

RLC Resonant Frequency — f₀ = 1 / (2π·√(L·C))

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.

What the printable worksheet asks students to work out

• 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).

Where this shows up beyond the lab

• 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.

• AP Physics 2 — Unit 11: Electric Circuits
• AP Physics C: Electricity and Magnetism — Unit 11: Electric Circuits
• IB Physics — B.5 Current and circuits
• General High School Physics — Electricity & DC circuits
• NGSS High School Physics — Electric current and magnetic fields

1. Welcome to Rlc Series
2. Press Play
3. Select the capacitor
4. Watch the transient
5. Open the Properties panel
6. You did it!

Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.

Open Interactive Lab →

Download lab sheet →

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