RLC Impedance vs. Drive Frequency: Finding Resonance
1 · Predict
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?
- Yes — impedance reaches a minimum (equal to just R) at the resonant frequency ω₀ = 1/√(LC).
- Impedance reaches a maximum at some frequency.
- Impedance doesn't depend on drive frequency.
2 · Set Up
- 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.
3 · Collect Data
| Drive frequency ω (rad/s) | Phase angle φ (rad) | Impedance Z (Ω) |
|---|---|---|
| 5 | ||
| 10 | ||
| 15 |
Plot impedance Z (y-axis) against drive frequency ω (x-axis) for your three trials. Where's the minimum?
4 · Analyze
- 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.
5 · Extend
- 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).