# FUNDAMENTALS OF ELECTRICAL ENGINEERING + INTRODUCTION TO ELECTRONICS (UNIT 1)

## Learning outcomes of the course unit

The course will give students ability to:

* comprehend the symbolic description of electrical circuits;

* analyze the behavior of electrical networks in stationay, sinusoidal and transient conditions;

* find the mathematical relationships of an electric circuit for both analysis and design;

* know the limitations in electric energy transport;

* apply modeling of measuring instruments and loads to their area of interest.

1) Knowledge and understanding.

This module aims at providing students with basic knowledge and understanding of:

- electric systems behavior in steady state, quasi steady state and dynamic conditions;

- electromechanical system behavior

- electric circuit analysis

- energetic behavior of electric systems

- magnetic circuit behavior under linear assumption

2) Applying knowledge and understanding

Students will be able to:

- analyzing and designing electric circuits

- compensate the reactive power in electric power plants

- make use of analog or digital voltmeter, ampere meter and wattmeter.

## Prerequisites

There are no compulsory prerequisites. Nevertheless, the course will need contents from:

* complex numbers algebra;

* trigonometry;

* linear system solution;

* differential equation solution;

* Maxwell's equations.

The students are expected to be familiar with the notions of mathematics and physics taught in the 1st and 2nd year of the Laurea in Mechanical Engineering

(Analisi matematica 1, Analisi matematica 2, Fisica generale 1, Fisica generale 2).

## Course contents summary

The course aims to provide the students with the general criteria to analyze and predict the behavior of electrical circuits used in industrial applications.

The course aims to provide the students with the general criteria to analyze the behavior electrical circuits used for industrial applications. Therefore, the contents proposed during the course include the following topics:

a) Electric Systems in steady state conditions.

b) Electric Systems in quasi steady state conditions.

c) Electric systems dynamic behavior.

d) Magnetic circuits.

## Course contents

> Introduction to Electrical Circuits (2 hours)

* Electrical and Electronic Engineering

* Models, methods and representations

* Pros and cons for Mechanics and Informatics

* Logistics of the course

> DC networks - Introduction (2 hours)

* Fundamental quantities

- Charge and charge density

- Electric field, electric potential, voltage

- Current and current density

- Conductivity and resistivity

* Ohm's laws

- First Ohm's Law

- Second Ohm's Law

* Components modeling

- Generators

- Resistors

- Capacitors

- Inductors

- Conventions (load, generator)

> DC networks - Methods 1 (2 hours)

* From Maxwell to Kirchhoff

- Loops and nodes

- KVL and KCL

- Hints to the derivation from Maxwell's equations

* Analysis methods

- Nodal analysis

* Exercises

> DC networks - Methods 2 (2 hours)

* Analysis methods

- Loop analysis

* Exercises

> DC networks - Methods 3 (2 hours)

* Exercises

> Reti in continua - Methods 4 (2 hours)

* Exercises

> DC networks - Theorems 1 (2 hours)

* Network theorems

- Linearity

- Superposition principle

* Exercises

> DC networks - Theorems 2 (2 hours)

* Network theorems

- Thevenin's theorem

- Norton's theorem

* Exercises

> DC networks - Applications 1 (2 hours)

* Applications

- Resistors in parallel and in series

- Voltage and current dividers

* Exercises

> DC networks - Applications 2 (2 hours)

* Applications

- Millman's theorem

- Instruments

* Exercises

> AC networks - Phasors (2 hours)

* Phasors

* Impedance and admittance

* Exercises

> AC networks - Resonance (2 hours)

* Resonance and antiresonance

* Exercises

> AC networks - Power 1 (2 hours)

* Potenza

* Exercises

> AC networks - Power 2 (2 hours)

* Impedance matching

* Power factor correction

* Exercises

> AC networks - Poliphase systems (2 hours)

* Poliphase systems

* Power in three-phase systems

* Exercises

> Transients 1 (2 hours)

* First-order transients

* Autonomous and forced responses

* Exercises

> Transients 2 (2 hours)

* Second-order transients

* Autonomous and forced responses

* Exercises

> Electrical machines 1 (2 hours)

* Definition of magnetic quantities

- Magnetic field

- Flux density

- Magneto-motive force

- Flux and linked flux

- Inductance and reluctance

* Hopkinson's law

* Exercises

> Electrical machines 2 (2 hours)

* Magnetically-coupled circuits

* Transformers

* Exercises

> Electrical machines 3 (2 hours)

* Transformers

* Hints about motors and generators

> Practice on exercises (8 hours)

a) Electric circuits in steady state conditions.

Basic of electric linear circuit theory.

Analysis of DC electric circuits

From Maxwell field theory to lumped parameters circuits. Fields, charge and current.

Kirchhoff’s current and voltage laws.

Parallel and series connections for linear circuits. Wye-Delta transformation.

Node and loop analysis.

Network theorems. Thevenin’s and Norton’s theorem. Maximum power transfer theorem.

b) Electric circuits in quasi steady state conditions.

Second order circuits. Series and parallel RLC circuits. Analysis of AC electric circuits

Phasor representatives of sinusoidal signals. Steady-state circuit analysis using phasors. Sinuosoidal steady-state power calculations. Analysis of Three-Phase circuits.

Economical aspects of electric power transmission. Frequency Response of linear circuits.

c) Electric circuits dynamic behavior.

Transient analysis of electric circuits Inductors, Capacitors and duality. First order RL and RC circuits.

d) Magnetic circuits

Magnetic circuit definition and magnetic materials behavior.

The analysis of the magnetic circuit.

Electric transformers (three phases transformers are included).

## Recommended readings

* C.K. Alexander, M.N.O. Sadiku, C. Gerardi, P. Gubian, "Circuiti elettrici", McGraw-Hill libri Italia, 2008

* G. Rizzoni, F. Vacca, S. Vergura, M. Travagnin, "Elettrotecnica. Principi e applicazioni", McGraw-Hill Education, 2018

* G. Fabricatore, "Elettrotecnica e applicazioni. Reti, macchine, misure, impianti", Liguori, 1994

Additional material is loaded on the Elly website.

The student can study the topics discussed during the course reading the following textbooks:

• G. Rizzoni “Elettrotecnica principi e applicazioni” McGraw-Hill

• G. Fabricatore, “Elettrotecnica ed applicazioni”, Ed. Liguori.

The notes of the lectures and exercises will be available to students and shared on the Elly web site.

## Teaching methods

The course consists of 48 lecture hours. 70% of those are delivered as frontal classes, targeting the fundamentals of the subject. Remaining 30% hours are used as group solution of exercises, targeting applied problems in electric engineering.

The module 1 of the course counts 6 CFUs (one CFU, University Credits equals one ECTS credit and represents the workload of a student during educational activities aimed at passing the exams), which corresponds to 42 hours of lectures. The educational activities include lectures and exercises. During lectures, the course topics are proposed from the theoretical and design point of view in order to promote a deep understanding of the issues and to bring out by the students any previous knowledge on the subjects in question.

The slides and notes used to support the lessons will be uploaded to the Elly platform. Notes, slides, spreadsheets, tables, and all shared material are part of the educational material. For non-attending students, it is important to stay up-to-date on the course through the Elly platform, the only communication tool used for direct teacher / student contact. On this platform, the topics discussed in the lesson will be pointed out and registered, providing the students with an index of the contents for the final exam.

## Assessment methods and criteria

The contents of the first module of the course are verified with a written text, focusing on the topics presented in the classroom. The test is made up of both exercises about circuit solution and questions about theoretical elements explained during the course. The final mark is obtained as weighted average of the single scores obtained in each module.

Exams could be taken online on the Teams platform, in case other solutions are not possible. In that case, a threshold test (with multiple answers format) will be prepended to the written test.

Oral exam. There is a single exam for the two modules making up the integrated course.

Students who have not passed one or more exams of mathematics and physics taught in the 1st and 2nd year of the Laurea in Mechanical Engineering (Analisi matematica 1, Analisi matematica 2, Fisica generale 1, Fisica generale 2), before the oral examination, will have to demonstrate their problem-solving skills related to these courses.

As far as Applicazioni Industriali Elettriche students will have to demonstrate knowledge of the techniques for the time analysis and synthesis of electric systems including energy behavior.

It is considered important the capability to solve simple quantitative exercises by hand calculation.

The final vote is calculated by assigning a mark in the range 0-30 for each question and then performing the weighted average of the individual evaluations, with final ceiling to the next unit; the test is exceeded if it reaches a score of at least 18 points. “30 cum laude” is given to students who achieve the highest score on each item and use precise vocabulary.

## Other informations

In the eventuality of restrictions for in-presence classes, they will be given in remote, asynchronously. Recorded videos will be available on Elly via links. There will be the possibility to have shared discussions on Teams (live) and remote office hours.

DSA and BES students should directly contact the teacher, to identify proper tools in support to the exam.