Lab Report

Title: Analyzing the Impact of Resistance on Damping in an RLC Circuit

Instructions:

1. Circuit Simulation:

   • Write a Python program to simulate the response of an RLC circuit for underdamped, critically damped, and overdamped conditions using a square wave input. Ensure you calculate and plot the results for different resistor values.

2. Data Collection:

   • Using the Arduino setup, collect data on the voltage and current response of the RLC circuit for at least three resistance values: underdamped, critically damped, and overdamped cases.

3. Data Analysis:

   • Plot the recorded data and compare it with your simulated results. Identify key differences and similarities in the behavior of the circuit for different damping conditions.

4. Report Writing:

   • Write a report summarizing your findings, including the simulated vs. experimental results, and discuss how damping affects the frequency response and oscillation patterns.

Submission Requirements:

• Python code for simulation.

• Graphs for experimental and simulated results.

• A written report (maximum 2 pages) explaining your findings and the physical implications of damping in RLC circuits.

Other task:

Write a report summarizing why the experiment failed (e.g., cant see Under damping) 

Problem Set:

 Problem 1: RLC Circuit Response

Consider an RLC series circuit with the following components:

• L=50 mH

• C=0.1 μF

• R values: 10 Ω (underdamped), 20 Ω (critically damped), and 100 Ω (overdamped).

Tasks:

• Write the equation for the voltage across the capacitor for each damping condition.

• For each resistor value, determine the natural frequency f0​ and the quality factor Q.

• Plot the time-domain response for each case using Python.

Problem 2: Damping and Frequency Response

 Given an RLC circuit, simulate the frequency response for the following resistor values: 10 Ω, 50 Ω, and 100 Ω.

• Plot the Bode plot (magnitude vs. frequency).

• Identify the resonant frequency and bandwidth for each case.

• How does the bandwidth change with increasing resistance? Explain the physical significance.

Problem 3: Energy Dissipation in RLC Circuit

Using the RLC circuit in the experiment, calculate the energy dissipated in the resistor over time for each damping condition:

• Calculate the power dissipated in the resistor as a function of time.

• For each damping case, plot the energy dissipated vs. time.

• Discuss how damping affects the efficiency of energy transfer in the circuit.

Problem 4: Arduino Data Analysis

Collect data using the Arduino setup for different damping conditions and perform the following analysis:

• Calculate the damping factor α\alphaα for each case.

• Compare the experimentally obtained α with the theoretical values from your simulations.

• What factors could cause deviations between the theoretical and experimental results?

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format