Practical - 23 :- Finding the Resonance Frequency of Series and Parallel LC Circuits

Objective

To determine and compare the theoretical and experimental resonance frequency (fr) of a given series LC circuit and a parallel LC circuit.

🔬 Apparatus and Components

• Tools/Equipment:

  • Function Generator (Signal Generator)

  • Milliammeter (mA, e.g., 0-30 mA range)

  • Dual Trace CRO (Oscilloscope)

  • Trainees tool kit

• Materials/Components:

• Inductor (L = 40 mH)

• Capacitor (C = 0.1 µF)

• LED (Light Emitting Diode)

• Breadboard / Lug board

• Hook-up wires

• Procedure

  Part A: Series Resonance Circuit (Task 1)

1. Theoretical Calculation:

        Record this as your Theoretical fr.

        

        2. Circuit Assembly:

          

         Connect the Function Generator, Milliammeter, Inductor (L), Capacitor (C), and LED all 

         in series, as shown in the diagram (based on Fig 1).

        3. Setup:

• Set the Function Generator to output a sine wave.
• Set the output amplitude to 10 Vrms (or a voltage that gives a clear reading).
• Set the initial frequency to 1 kHz. Record the current I.

        4. Finding Resonance:

• Slowly increase the frequency from the generator.
• Watch the Milliammeter and the LED.
• The current I will increase, reach a peak, and then decrease.
• The LED will get brighter, shine brightest at the peak, and then dim.
• The frequency at which the current I is MAXIMUM is the Experimental Resonance Frequency (fr). Record this value.

        5. Data Collection:

• Vary the frequency in steps of 500 Hz (or other appropriate steps) around the            resonance frequency you found.
• Record the current I at each frequency f in the observation table.

 

Part B: Parallel Resonance Circuit (Task 2)

1. Theoretical Calculation: The theoretical $f_r$ is the same as calculated in Part A (approx. 2516 Hz).

2. Circuit Assembly:

   • Connect the Inductor (L) and Capacitor (C) in parallel to form a "tank circuit".

   • Connect the Function Generator, Milliammeter, and LED in series with this parallel combination, as shown in the diagram (based on Fig 2).

3. Setup:

• Set the Function Generator to output a sine wave.

• Set the output amplitude to 4 Vrms. Start at 1 kHz.

• Caution: Adjust the voltage to keep the current below 10-12 mA, especially at frequencies far from resonance, to avoid damaging the meter.

4. Finding Resonance:

   • Slowly increase the frequency from the generator.

   • Watch the Milliammeter and the LED.

   • The current $I$ will decrease, reach a minimum, and then increase again.

   • The LED will get dimmer, become dimmest (or go out), and then get brighter.

   • The frequency at which the current I is MINIMUM is the Experimental Resonance Frequency (fr). Record this value.

5. Data Collection:

• Vary the frequency in steps around the resonance frequency and record the current $I$ at each frequency f.

6. Observation Table

   (Create one table for Part A and one for Part B)

Sr. No.	Frequency (f) (Hz)	Current (I) (mA)
1	500
2	1000
3	1500
4	2000
5	2500
6	3000
7	3500
8	4000
...	(add more readings)

📈 Plotting

1. For Part A: Plot a graph of Current (I) vs. Frequency (f). The graph should show a peak at the resonance frequency.

2. For Part B: Plot a graph of Current (I) vs. Frequency (f). The graph should show a dip (or valley) at the resonance frequency.

Conclusion

1. Theoretical Resonance Frequency (fr): _________ Hz

2. Experimental fr (Series Circuit): _________ Hz

3. Experimental fr (Parallel Circuit): _________ Hz

Compare the theoretical and experimental values. Discuss any differences, which may be due to the internal resistance of the inductor and other component tolerances.