# LRC Circuit Calculation

## Summary

This is a homework assignment in a course in electronics for sophomore-level physics students on the topic of AC circuits. It includes 3 questions to calculate the reactance, total impedance, and voltage across each component. Students are first asked to compute the calculations by hand. Students then fill in a template for a MATLAB Live Script and create a Simulink model to verify their results. In the process, students learn to create and use functions and scripts in MATLAB, vary parameters in their functions, and build circuit models in Simulink.

## Learning Goals

In this homework assignment, students (a) practice AC circuit calculations, (b) create functions and use them in Live Scripts in MATLAB, and (c) create Simulink models of AC circuits.

(a) Practice AC circuit calculations

Students practice calculating reactance of capacitors and inductors, impedance and phase of resistors, capacitors, and/or inductors in series and parallel, and output voltages, current, and phase in AC filter circuits.

(b) Create functions and use them in Live Scripts in MATLAB

Students convert a typical homework problems into a computational problems by filling in the programming template for the reactance calculations. Students learn to use the MATLAB functions and scripts by checking calculations of reactance, impedance, phase, and output voltage for AC series and parallel circuits.

(c) create Simulink models of AC circuits

Students build series and parallel AC circuits in Simulink and correctly represent the voltage sources, resistors, capacitors, and inductors. Students compare output voltage peak values to output voltage calculations.

## Context for Use

The course is a sophomore-level electronics course for physics majors at a liberal arts college with approximately 3000 students. Students have completed MATLAB Onramp and one other MATLAB assignment before this assignment. Students are given a week for the homework assignment. Students are new to MATLAB and are led through the script portion of the Live Script as well as the first few functions by the instructor during class. They replace the question marks with variables or values to complete the remaining functions. Students should receive instruction and have some practice during class before the problem set is assigned.

## Description and Teaching Materials

Student handout AC circuits (Acrobat (PDF) 119kB Oct3 17)
ACseriesLiveScripttemplate (MATLAB Live Script 4kB Oct3 17)
ACparallelLiveScripttemplate (MATLAB Live Script 3kB Oct3 17)
ACcircuitsSeriesLiveScript (MATLAB Live Script 28kB Oct3 17)

ACcircuitsSeriesLiveScript (MATLAB Live Script 15kB Oct3 17)

## Teaching Notes and Tips

The templates and model are for students new to MATLAB and Simulink. Students fill in the MATLAB Live Script template and determine the variables or values to replace the questions marks. In class, the instructor may work a similar problem at the board or have students work through the problem as group work. It is recommended that during class, the instructor lead the students through the process of filling in the Live Script template and demonstrate how to change the values in the Live Script to modify the calculations for different problems.

The Simulink model is an example of the first homework problem. Students must enter the correct values in the GUI window that pops up when each component is double-clicked. Students run the simulation by pressing the green arrow and then double-clicking on the scope. Students should be capable of completing models for the remaining problems if given the model for the first problem or a similar problem.

## Assessment

For each homework problem, students are assessed equally on the calculations, Matlab Live Script, and Simulink model.

1. Calculations (4 pts)
• reactance of the capacitors and inductors
• impedance of the resistor and inductor/capacitor
• output voltage
2. Matlab Live Script (4 pts)
• completion of functions
• correct parameters to the functions in the Live Script
• comparison of Live Script results to calculations