RLC circuits, consisting of resistors (R), inductors (L), and capacitors (C) connected in series, serve as fundamental components in studying electrical oscillations and resonance. This experiment aims to investigate the resonant frequency of an RLC circuit by measuring the oscillations generated upon discharging the circuit, utilizing the Red Pitaya board for precise measurements.

**Objective**

The goal is to measure the oscillation frequency of a series RLC circuit to determine its resonant frequency. The experiment will involve a setup with a 100Ω resistor, a 1mH inductor, and a 10nF capacitor, using the Red Pitaya’s oscilloscope function to capture and analyze the oscillating voltage.

**Experimental Setup**

**Materials**

- Red Pitaya board
- 100Ω resistor
- 1mH inductor
- 10nF capacitor
- Breadboard and jumper wires
- Button for initiating the charge

**Assembly Instructions**

**Circuit Construction:**Arrange the 100Ω resistor, 1mH inductor, and 10nF capacitor in series on a breadboard. Connect the series circuit to the Red Pitaya as illustrated, with probe IN1 across the resistor and IN2 across the capacitor and inductor.**Measurement Preparation:**Set up the Red Pitaya's oscilloscope to capture the voltage response upon discharging the circuit. Charge the circuit to 3.3V using the button switch provided in the setup.

**Procedure**

**Charging and Observing:**Charge the circuit by holding the button, then release to observe the oscillating voltage response. The Red Pitaya should capture a decaying oscillation waveform.**Frequency Measurement:**Utilize the Cursor function on the Oscilloscope app to measure the time interval for one complete oscillation cycle, from peak to peak.

**Calculations**

The frequency of the oscillation can then be calculated using the formula:

$f = \frac{1}{T}$where f is the frequency in hertz (Hz), and T is the time interval for one complete cycle of the oscillation in seconds.

The results of the experiment for the RLC circuit are as follows:

Measured time interval for one complete cycle of the oscillation (T) = 0.0000218 seconds

Frequency (f) = 45.8 kHz

We can confirm our measurements using the values of elements, and calculate the resonant frequency of the RLC circuit using the formula:

$f_{resonant} = \frac{1}{2 \pi \sqrt{LC}}$where L is the inductance in Henries, and C is the capacitance in farads.

The calculated resonant frequency of the RLC circuit is:

$f_{resonant} = \frac{1}{2 \pi \sqrt{(1 \times 10^{-3}) \times (10 \times 10^{-9})}} = 50.329 kHz$The measured frequency of the oscillation is close to the calculated resonant frequency, which indicates that the RLC circuit is operating as expected, and the error we got came from the tolerances of the elements.

**Conclusion**

In this experiment, we used the Red Pitaya to measure the frequency of an oscillating signal generated by an RLC circuit. We demonstrated how the oscilloscope application and frequency measurement tool in the Red Pitaya web interface can be used to measure the frequency of a signal. The Red Pitaya is a versatile and affordable instrument that can be used for a wide range of measurements, including frequency measurement.