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CODE 101133
SEMESTER 1° Semester


Electric Circuit Analysis (Resistive-only DC, Transient, Steady State AC and Three-phase analyses).


Contents will also take into consideration STCW Section A-III/6 Mandatory minimum requirements for certification of electro-technical officers.



The course gives the essential elements for understanding of analysis and exploitation of the electromagnetic phenomena. In the first part of the course the instruments for static and quasi-static analysis by circuit methods are introduced. In the second part of the course the principal application aspects of exploitation of power electromagnetic phenomena are introduced: electrical motors, power electronics and power electrical systems.


The aim of this course is to provide the Students the basic knowledge necessary to study and solve simple Circuital Models, with particular attention to power aspects.

The basic methods for Linear, Time Independent and Lumped Parameter Circuit Analysis will be adressed, and the techniques for their application to the problems will be proposed. The analysis will be made within time-domain (Resistive-Only DC, Transient Analysis), and within frequency domain (Steady State AC).

At the end of the course, Student shall have correctly understood the basic concepts of Electric Circuit Analysis, shall be able to correctly classify the different types of Circuit problems, and to correctly formulate the solution, arriving, when and where possible, to determine their analytical solution.


The course does not require particular prerequisites. In the same time, Students should know the basis of algebric computation with real and complex numbers and the meaning of linear differential equation of firsrt and second order with constant coefficients.


Theory lectures and related exercises.  All the lectures will be organized in frontal mode. Bytheway, the organization could change with respect to "nCOVID-19" healthy emergency, so that there it could happen that all the lectures will be provided (also) in remote way via Microsoft TEAMS platform. 

Working students and students with certified SLD (Specific Learning Disorders), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination arrangements so to take into account individual learning patterns, while respecting the teaching objectives.


The Circuit Model: basic concepts and lows

Current and Voltage. Potential Difference. The Electric Circuit: Model inherent Hypotheses and Limits. Circuit components: Terminals and Connectors, Bipoles and Multipoles, Limit Surface. Lumped Parameter Circuits. Reference directions for Voltage and Current. Kirchhoff’s Voltage and Current Laws. Linearly independent relations among Kirchhoff’s Laws, and elementary selection techniques.

Component’s Equations expressed on voltage-current plane. Elementary bipoles: Resistor, Open Circuit, Short Circuit, Voltage and Current Ideal Generators. Representation of Components on voltage-current plane.

Instantaneous Electric Power. Power of a Bipole. Power Conventions for Generators and Loads. Power dissipated by a Resistor. Joule effect. Tellegen’s Theorem. Conservation of Power. Graphs, oriented Graphs, and their application to Circuit Analysis.

Resistive-only Circuits.

Definitions and inherent Hypotheses. Resistor: Linear, Time-Independent Resistor, its constitutive equation (Ohm’s Law). Definition of Resistance and Conductance. Concept of equivalent network, formulae of equivalent network of Resistors in series and in parallel, Voltage Divider and Current Shunt. Network reduction techniques. The star-delta transform. Theorems for resistive networks: Thevenin’s, Norton’s and determination of equivalent networks. Maximum power transfer theorem. Real generators, Millmann’s Theorem. Superposition Theorem and its application. Description of general techniques for Circuit Analysis (Nodal and Loop Analysis).

Capacitors and inductors

Ideal capacitor and inductor, elementary properties. Characteristic equations, stored energy, initial conditions, state variables. Formulae of equivalent network of Capacitors and Inductors in series and in parallel. Real components. 

Dynamic Circuit Equations, and their solution.

The solution of Linear Ordinary Differential Equations with constant coefficients. General and Particular Integral, initial conditions, characteristic polynomials. Solution of simple first-order R-C or L-R Circuits. Behaviour of inductors and capacitors during sudden variations of state variables. Circuit of second order with Inductors and Capacitors. Roots of characteristic polynomial, and their relationship with output waveforms. Natural response and forced response. Example of solution of simple dynamic circuits. 

Equations of circuits in Steady State Alternate Current (SSAC), and their solution.

Representation of sinusoidal waveforms through the use of complex numbers: the phasors. Definition of impedance and admittance for all types of linear components. Extension of already defined network theorems to the networks in SSAC. Voltage drop across a line. Power factor correction. Example of solution of simple linear circuits of applicative significance.

Power in SSAC: instantaneous power, active power, reactive power, complex power. Tellegen’s Theorem for SSAC networks. Balance of active and reactive power.

Resonance and anti-resonance conditions. 

Techniques for the practical solution of SSAC networks: power balance method, methods based on impedance computations, equivalence theorems in SSAC (Thevenin’s, Norton’s, Millmann’s Theorem, Superposition Theorem and their applications)

Example of solution of simple linear circuits.

Three-phase circuits.

Definitions and reasons leading to introduce three-phase circuits. Three-phase circuits with balanced (3 conductors) or unbalanced (4 conductors) load. Phase and line voltages. Symmetric/unsymmetrical systems. Balanced/unbalanced loads. Positive, negative sequences. Phase and line currents. Power in three-phase circuits. Solution of simple circuits.

Examples of solution of three-phase circuits, both balanced and unbalanced.


Besides the books in Bibliography, available in Department Library, on AulaWeb are available copies slides and notes.

Reference (for OPTIONAL study deepening on specific subjects)

  • M. Repetto, S. Leva: “Elettrotecnica – Elementi di Teoria ed Esercizi”, 2^ edn, Città Studi Edizioni, Torino, 2018
  • L. Verolino: “Elementi di Reti Elettriche”, 1^ edn, EdiSES, Napoli, 2019
  • C. K. Alexander, M.N.O. Sadiku: “Circuiti elettrici” III edn., McGraw Hill Italia, 2008.
  • C. K. Alexander, M.N.O. Sadiku: “Foudamentals of Electric Circuits" Circuiti elettrici” V ed. McGraw Hill,  2013
  • G. Rizzoni: “Elettrotecnica – Principi e applicazioni”, II edn., McGraw Hill Libri Italia, 2008


Exam Board



ANDREA BONFIGLIO (President Substitute)


Class schedule

The timetable for this course is available here: Portale EasyAcademy



Attention: due to the nCOVID-19 health emergency, the methods described below may be subject to significant changes.

The final test consists of a written and an oral part, where students will be required to solve circuits in steady state, in dynamic evolution or in sinusoidal regime (single-phase or three-phase) and the presentation of theoretical concepts addressed during the course.

The written exam is sucesfully passed if the student has obtained a score greater than or equal to 16 (where 30 is the maximum score). To participate in the written test, students must register at least five days before the date of the exam on the website

The oral exam will take place in the same session of the written part (during the afternoon or in the following days, according to the number of partecipants). Special cases where students are not able to take the oral part in the same sesson for justified reasons will be examined  individually by the Commission.

The final score is a weighted average of the results obtained in the two parts. If the oral exam is insufficient, the Commission reserves the right to cancel the written exam as well. A score equal to or greater than 27/30 in the written test does not affect the possibility of obtaining a final grade of 30/30 after the oral test.

There will be two partial tests (typically the first between late October and early November, the second in December). Students who will obtain an average score greater than 16/30, could decide to go directy to the oral part, in one of the fixed calendar date. The overall score with which the oral exam will be accessed is the average of those obtained in the two partial tests.


The methodology for evaluating  the learning outcomes acquired by the student is based  on the continuous interaction in the classroom during the course, in the practical part consisting of solving simple electric circuits, and collect all these information in the oral part of the exam.


Details for preparing the exam and the importance of each topic will be given during the theoretical lessons and during the exercises.

The written exam will verify the basic knowledge, especially the practical one for resolving circuits, whether in steady state, dynamic and sinusoidal (single-phase and three-phase). The student must be able to answer the questions posed in the problems, adequately motivating them, presenting a clear and ordered paper in which each quantity used must be defined. The numerical result and the proposed solution procedure will also be evaluated.

The oral exam will mainly focus on the topics covered during the theoretical lectures and will aim to assess not only whether
the student has reached an adequate level of knowledge, but if he has acquired the ability to critically analyze any electrical circuits that will be asked during the exam. The theorems and proofs explained during the theoretical lessons and/or during the exercises will be requested during the oral exam. Accuracy, clarity, personal re-elaboration and the use of correct terminology with which the required concepts will be presented will also be evaluated.

Exam schedule

Data Ora Luogo Degree type Note
10/01/2023 09:30 GENOVA Scritto + Orale
07/02/2023 09:30 GENOVA Scritto + Orale
30/05/2023 09:30 GENOVA Scritto + Orale
14/06/2023 09:30 GENOVA Scritto + Orale
04/07/2023 09:30 GENOVA Scritto + Orale
05/09/2023 09:30 GENOVA Scritto + Orale


Mathematical analysis and Physics kowledge are essntial basis for this teaching course. In particular Students must have learned the main concepts, the scientific method and the critical approach typical of these teaching subjects.