Function generator
RMS voltage
- Frequency
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- Waveform
- Sine
Virtual engineering lab
Series RLC Resonance
Drive a series RLC network with the virtual function generator, inspect current and phase, and verify resonance against f0 = 1/(2π√LC).
Electrical Engineering / InstrumentationintermediateValidated educational model
0% complete0 / 0 requirements
Complete the procedure, collect the required measurements, pass the engineering validation, and answer every graded concept question correctly.
What you should establish
- Predict the resonant frequency of a series RLC circuit.
- Observe cancellation of inductive and capacitive reactance at resonance.
- Relate impedance magnitude to measured RMS current.
- Interpret current phase below, at, and above resonance.
- Use a deterministic frequency sweep to verify the current peak.
Work through the experiment
Collect evidence from the model
- Analytic resonanceResonance from f0 = 1/(2π√LC).Pending
- Sweep-measured resonanceFrequency of maximum current in the deterministic sweep.Pending
- Quality factorSeries-RLC Q = ω0L/R.Pending
- Impedance magnitudeSeries impedance magnitude at the selected generator frequency.Pending
- RMS currentRMS series current at the selected frequency.Pending
- Current phaseCurrent phase relative to source voltage; positive leads, negative lags.Pending
- Inductive reactanceXL = 2πfL at the selected frequency.Pending
- Capacitive reactanceXC = 1/(2πfC) at the selected frequency.Pending
Verify the result, not just the workflow
- Series-RLC resonance checkCompares the current-peak sweep frequency with the analytic f0 relationship.Pending
Only a passed engineering check satisfies guided completion. Warnings and failures remain visible even if the procedure checklist is complete.
Answer the graded multiple-choice questions
Choose one answer for each question. Each selection is graded immediately and saved locally. Guided Lab completion requires every concept question to be correct.
Concept score: 0 / 3 correct
Integrated virtual bench
Ideal instrumentsSeries RLC resonance bench
Resistance check
COM + VΩ · circuit unpowered
Confirm the modeled series resistance before applying the source.
Oscilloscope
—Frequency sweep
Adjust experiment parameters to preview the ideal response, then run the experiment for validation.
Series R–L–C network
- Analytic f₀
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- Q factor
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- Selected phase
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Measurements
Instrument readings
- Analytic resonance
- — Resonance from f0 = 1/(2π√LC).
- Sweep-measured resonance
- — Frequency of maximum current in the deterministic sweep.
- Quality factor
- — Series-RLC Q = ω0L/R.
- Impedance magnitude
- — Series impedance magnitude at the selected generator frequency.
- RMS current
- — RMS series current at the selected frequency.
- Current phase
- — Current phase relative to source voltage; positive leads, negative lags.
- Inductive reactance
- — XL = 2πfL at the selected frequency.
- Capacitive reactance
- — XC = 1/(2πfC) at the selected frequency.
Result visualization
Resonance and operating-point check
Compare the analytic resonant frequency with the frequency-sweep current peak, then inspect the selected-frequency current and phase.
- Analytic resonance
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- Sweep peak
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- Selected RMS current
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- Selected current phase
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Independent check: at series resonance XL = XC, |Z| reaches R, and source voltage and current are in phase.
Theory
Equations and model
Series impedance
The resistor contributes real impedance while the inductor and capacitor contribute opposing reactances.
Z = R + j(ωL − 1/ωC)|Z| = √(R² + (XL − XC)²)Irms = Vrms/|Z|Resonance
At series resonance XL = XC, so reactive terms cancel. The ideal series impedance is then minimum and equal to R, producing maximum current.
f0 = 1/(2π√LC)XL = XC at f0Q = ω0L/RPhase interpretation
Below resonance the circuit is net capacitive and current leads source voltage. Above resonance it is net inductive and current lags. At resonance the current and source voltage are in phase.
Validation
Independent checks
Series-RLC resonance checkNot run
Compares the current-peak sweep frequency with the analytic f0 relationship.
- Expected
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- Simulated
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- Error
- —
- Tolerance
- 0.01%
Run the experiment to perform this check.
Engineering interpretation
Run the experiment to generate an engineering interpretation.
Assumptions and limitations
Assumptions
- Ideal sinusoidal steady state.
- R, L, and C are linear and frequency independent.
- Inductor/capacitor losses and parasitics are omitted.
- The DMM and oscilloscope do not load the network.
Limitations
- The frequency sweep uses an ideal lumped-element model and does not include self-resonance or component ESR/ESL.
- Phase 1.7 provides the shared tolerance/noise/calibration/quantization model, but this RLC fundamentals sweep remains ideal for analytic resonance validation. Generator output impedance, probe loading, bandwidth, ESR/ESL, and self-resonance remain future extensions.
Local experiment export
Phase 1.9Save your measurements and setup
Exports are generated in your browser. No account or server upload is required.
- Settings JSON
- Current parameter values for reproducibility and later project handoff.
- Measurements CSV
- Completed instrument readings with labels, units, and descriptions.
- Plot PNG
- The current canvas-based scope, transient, sweep, or statistics visualization when available.
- Summary
- Markdown report with objectives, setup, measurements, validation, interpretation, assumptions, and graded guided concept-check results.
Ready to export the current local experiment state.
What this experiment should establish
- Predict the resonant frequency of a series RLC circuit.
- Observe cancellation of inductive and capacitive reactance at resonance.
- Relate impedance magnitude to measured RMS current.
- Interpret current phase below, at, and above resonance.
- Use a deterministic frequency sweep to verify the current peak.
Questions to answer from the experiment
- Why does the ideal series current reach its maximum value at resonance?
- Why does current lead below resonance and lag above resonance?
- How does increasing series resistance affect Q and the sharpness of the resonance peak?