Exploring Resonance in LC Circuits: A Practical Guide

In this guide, we will explore the principles of resonance through practical experiments with LC circuits. You will learn how to set up your own experiments to observe resonance, measure key parameters, and understand the underlying physics.
By Jamie

Understanding LC Circuits

An LC circuit consists of an inductor (L) and a capacitor (C) connected together. These circuits are fundamental in understanding resonance, which occurs when the inductive and capacitive reactances are equal, resulting in maximum oscillation in the circuit.

Key Concepts

  • Inductance (L): The property of an inductor that opposes changes in current.
  • Capacitance (C): The ability of a capacitor to store charge.

  • Resonant Frequency (f₀): The frequency at which the circuit naturally oscillates, given by the formula:

    \[f₀ = \frac{1}{2\pi\sqrt{LC}}\]

Experiment 1: Measuring the Resonant Frequency

Materials Needed:

  • Inductor (L)
  • Capacitor (C)
  • Function generator
  • Oscilloscope
  • Connecting wires

Procedure:

  1. Set Up the Circuit: Connect the inductor and capacitor in series with the function generator and the oscilloscope.
  2. Choose Values: Select a specific inductor (e.g., 100 mH) and capacitor (e.g., 10 µF).

  3. Calculate the Theoretical Resonant Frequency:

    • Use the formula to calculate the resonant frequency:

      \[f₀ = \frac{1}{2\pi\sqrt{(100 \times 10^{-3}) \times (10 \times 10^{-6})}} ≈ 159.15 \text{ Hz}\]

  4. Generate a Signal: Set the function generator to output a sine wave starting at a low frequency (e.g., 10 Hz) and gradually increase it to around 300 Hz.
  5. Observe Oscilloscope Readings: Monitor the output on the oscilloscope. Look for the frequency at which the amplitude of the oscillation peaks, indicating resonance.
  6. Record Data: Note the observed resonant frequency and compare it with your theoretical calculation.

Expected Results:

  • You should observe a peak in voltage amplitude at the calculated resonant frequency of approximately 159.15 Hz.

Experiment 2: Damping in LC Circuits

Materials Needed:

  • Same materials as Experiment 1
  • Variable resistor (potentiometer)

Procedure:

  1. Set Up the Circuit: Use the same configuration as in Experiment 1, but include a variable resistor in series to introduce damping.
  2. Adjust Resistance: Start with the resistance set to a low value, then gradually increase it.
  3. Measure Amplitude: As you adjust the resistance, monitor how the peak amplitude of voltage changes on the oscilloscope.
  4. Record Observations: Note how the damping affects the height of the peaks and the sharpness of the resonance.
  5. Analyze Results: Discuss how increased resistance leads to decreased amplitude and broader resonance curves, illustrating the damping effect.

Expected Results:

  • As resistance increases, the peak amplitude decreases, demonstrating the effect of damping on resonance in the circuit.

Conclusion

Conducting resonance experiments with LC circuits provides insight into fundamental concepts in physics, such as oscillation, resonance frequency, and damping. By following the outlined procedures, you can effectively observe and measure these phenomena, enhancing your understanding of electromagnetic principles.