LC Tank Circuit Resonance Experiment

Objective

The objective of this experiment is to construct and analyze an LC tank circuit to observe the resonance phenomenon and understand the behavior of resonant circuits.

Components Required

• 1 x Inductor (L)
• 1 x Capacitor (C)
• 1 x Signal Generator
• 1 x Oscilloscope
• 1 x Resistor (for damping, optional)
• Connecting Wires
• Breadboard (optional)

Theory

An LC tank circuit consists of an inductor (L) and a capacitor (C) connected in parallel or series, which can store energy in the magnetic field and electric field, respectively. At the resonance frequency, the circuit can oscillate at maximum amplitude. The resonant frequency \( f_0 \) can be calculated using the formula:

• \( f_0 = \frac{1}{2\pi\sqrt{LC}} \)
• Where: \( f_0 \) = resonant frequency (in hertz), \( L \) = inductance (in henries), \( C \) = capacitance (in farads).

Circuit Diagram

Experimental Setup

1. Connect the inductor and capacitor in parallel or series according to the circuit diagram.

2. Connect the signal generator to the circuit to provide an AC input signal.

3. Use the oscilloscope to measure the voltage across the LC circuit.

Procedure

1. Set up the LC tank circuit according to the circuit diagram.
2. Turn on the signal generator and set it to produce a sine wave.
3. Gradually vary the frequency of the signal generator and observe the output voltage on the oscilloscope.
4. Identify the frequency at which the output voltage reaches its maximum value; this is the resonant frequency.
5. Optionally, add a resistor in parallel with the circuit to observe the effect of damping on the resonance peak.

Results and Observations

Document the resonant frequency observed and the behavior of the circuit at frequencies below and above resonance. Note the changes in amplitude and the effects of damping if a resistor is added.

Conclusion

This experiment demonstrates the resonance phenomenon in an LC tank circuit, highlighting how the inductance and capacitance values determine the resonant frequency. Understanding resonance is crucial in applications such as radio transmitters and receivers.