RLC Resonance: Unknown Inductance

A series RLC with known R and C and hidden L. Sweep frequency to the current peak at several capacitances, then recover L from a fit of 1/f₀² versus C.

School· 24 min·Related simulator: Electricity & MagnetismRLC Series (AC)

Goal

Find the hidden L from f₀ = 1/(2π√(LC)). A plot of 1/f₀² versus C is a straight line with slope 4π² L.

Equipment

Series RLC (unknown L)
Function generator
Known capacitor box
AC ammeter

Experiment

Series R–L–C driven by an AC source. L is not labelled on the bench.

Known resistance R = 50 Ω and source amplitude V = 10 V. Inductance is hidden. You set C and the drive frequency f; read the current on the ammeter.

Capacitance CC = 4.7 µF

Frequency ff = 260 Hz

Ammeter I = 199.56 mA

Record at least 6 capacitances (about 2–10 µF). For each C, sweep f until the ammeter is highest, then record. Frequency is not auto-parked at the peak.

Measurements

№	C F	f₀ (peak) Hz	1/f² s²
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

RLC Resonance: Unknown Inductance

Generated: 24 Aug 2026, 22:30

Goal

Find the hidden L from f₀ = 1/(2π√(LC)). A plot of 1/f₀² versus C is a straight line with slope 4π² L.

Measurement table

#	C (F)	f₀ (peak) (Hz)	1/f² (s²)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted L agrees with the hidden inductance within tolerance. Main uncertainties: parking slightly off the current peak and the series-RLC idealization (no coil resistance).

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Series RLC impedance is minimum at ω₀ = 1/√(LC), so the current peaks there. Then 1/f₀² = 4π² L C. The bench shows an ammeter and lets you set f and C; it never prints f₀, Q, or L.

Procedure

R and the source amplitude are fixed and known. L is hidden. You change C and the drive frequency f.
For each C, sweep f until the ammeter is highest — that is your f₀. Then record.
The notebook stores C, f and 1/f².
Repeat for at least 6 capacitances spread from about 2 µF to 10 µF.
Fit 1/f² versus C (in farads); L = slope / (4π²). Compare with the reference.

Conclusion

The fitted L agrees with the hidden inductance within tolerance. Main uncertainties: parking slightly off the current peak and the series-RLC idealization (no coil resistance).