LC Circuit: Unknown Inductance
Ideal series LC with known C and hidden L. Time the period at several capacitances and recover L from a fit of T² versus C.
Goal
Determine L from T = 2π√(LC). A plot of T² versus C has slope 4π²L, so L = slope / 4π².
Equipment
- Series LC bench
- Known C box
- Period meter
Experiment
Theory
Undamped LC: ω₀ = 1/√(LC), T = 2π√(LC), T² = 4π² L C. The bench hides L, ω₀, f₀ and live T. You set C. The on-screen oscillation is cosmetic and must not be timed.
Procedure
- You only change capacitance C. L is hidden.
- Record. A period meter logs T of one cycle with small timing noise. There is no live T, f₀ or L.
- The notebook computes T². Repeat for at least 6 capacitances from about 1 μF to 10 μF.
- Fit T² versus C (in F); L = slope / 4π². Compare with the reference.
Conclusion
The fitted L agrees with the hidden inductance. Main uncertainties: period-meter noise and neglecting coil resistance.