Electromagnetism
RLC at resonance
ω matches ω₀ = 1/√(LC) — Z is minimum, I is maximum; graph I(t).
RLC at resonance — interactive Electromagnetism simulation. ω matches ω₀ = 1/√(LC) — Z is minimum, I is maximum; graph I(t). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
RLC resonance
ω matches ω₀ = 1/√(LC) — Z is minimum, I is maximum; graph I(t).
At resonance ω = ω₀ = 1/√(LC), inductive and capacitive reactances cancel so impedance Z is minimum and current I is maximum. Press Play to graph I(t); read Z and phase in the Properties panel. Tuning radios and MRI coils exploits this sharp current peak.
- ω₀ = 1/√(LC)
- Z_min at resonance
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 is driven by an AC source of varying frequency. Does the circuit's total opposition to current (impedance) reach a minimum at some particular frequency?
Predictions to weigh
- Impedance reaches a maximum at some frequency.
- Impedance doesn't depend on drive frequency.
- Yes — impedance reaches a minimum (equal to just R) at the resonant frequency ω₀ = 1/√(LC).
Variable roles
What you set:
- Drive frequency ω (rad/s)
What you measure:
- Phase angle φ (rad)
- Impedance Z (Ω)
How the investigation runs
- Open the rlc-resonance preset and press Reset. R = 20 Ω, L = 1 H, C = 0.01 F are fixed (same as the linked rlc-series circuit experiment).
- Enable the impedance and phase-angle readouts.
- Set the drive angular frequency for each trial (as a multiple of ω₀ = 1/√(LC) = 10 rad/s) and record the impedance.
What the printable worksheet asks students to work out
- For one trial, compute the reactance X = ωL − 1/(ωC), then Z = √(R² + X²) and φ = atan2(X, R), using R = 20 Ω, L = 1 H, C = 0.01 F. Compare both to the table.
- At ω = ω₀ = 10 rad/s, confirm Z = R exactly and φ = 0. Explain why the inductive reactance ωL and capacitive reactance 1/(ωC) exactly cancel at resonance, leaving only the resistor's opposition.
Where this shows up beyond the lab
- A radio tuner is essentially an RLC circuit whose resonant frequency you adjust (usually via a variable capacitor) to match a station's broadcast frequency, where impedance drops and current — and signal — peaks. Explain why stations at other frequencies are suppressed instead.
- The phase angle φ is negative below resonance and positive above it. Explain, using the reactance formula X = ωL − 1/(ωC), why low frequencies make the capacitor dominate (negative X) while high frequencies make the inductor dominate (positive X).
- AP Physics 2 — Unit 12: Magnetism and Electromagnetism
- AP Physics C: Electricity and Magnetism — Unit 13: Electromagnetic Induction
- IB Physics — D.4 Induction
- General High School Physics — Magnetism & electromagnetism
- NGSS High School Physics — Electric current and magnetic fields
- Welcome to Rlc Resonance
- Select the RLC circuit
- Press Play
- Minimum impedance
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.