Public University of Navarre

Academic year: 2019/2020
Bachelor's degree in Industrial Engineering at the Universidad Pública de Navarra
Course code: 252302 Subject title: ELECTRIC CIRCUITS
Credits: 6 Type of subject: Mandatory Year: 2 Period: 1º S
Department: Ingeniería Eléctrica, Electrónica y de Comunicación

Partes de este texto:


Module/Subject matter

Common Industrial Education/ Electrical engineering



Electric circuits. AC/DC circuits. Single-phase three-phase circuits.


General proficiencies

  • CG3: Knowledge in basic and technological subjects, which enables the student to learn new methods and theories, and give them versatility to adapt to new situations.
  • CG4: Ability to solve problems with initiative, decision-making, creativity, critical reasoning and to communicate and transmit knowledge, skills and abilities in the field of Industrial Engineering.
  • CG10: Ability to work in a multilingual and multidisciplinary environment.


Specific proficiencies

CC4: Acquire knowledge and understand the principles of circuit theory and electrical machines.


Learning outcomes

  • R1: Learn the main elements that are part of electric circuits and in particular their mathematical models, constructive characteristics and physical behavior.
  • R2: Learn and understand the basic principles that govern the behavior of electric circuits, fundamental theorems and resolution methods.
  • R3: Understand the concepts of energy and instantaneous power, active, reactive and apparent power as well as the power factor and its correction, in electric systems and their importance in industrial electric installations.
  • R4: Understand and learn how to work with three-phase systems.
  • R5: Understand and learn how to use the main instruments for measuring the main electric variables (voltage, current, active and reactive power, power factor).
  • R6: Learn the general fundamentals of electric machines.
  • R7: Understand the principle of operation of transformers.



The Electric Circuits course uses a theoretical-practical approach, combining master classes, problem classes, activities and group work, laboratory sessions and autonomous learning by the student.

The lectures will consist on the theoretical explanation of the fundamental aspects of each topic, as well as the resolution of questions raised by the students from their autonomous learning of each topic. As part of the practical, individual and / or group activities, practical exercises and works related to the topics covered will be carried out.

To understand the subject and obtain an adequate outcome, it will be necessary for the student to carry out continuous work around the following activities:

  • Attend class regularly.
  • Carry out a reflective reading and an in-depth study of the material that is provided or indicated in each topic.
  • Solve the exercises and work proposed throughout the course.
  • Actively participate in discussions that may arise in class.
  • Asking questions that may arising during the study of the subject in the hours arranged by the teacher for this purpose.

As a teaching complement, MiAulario will be used. Through it, the calendar of the different activities of the subject will be indicated, it will be possible to access the teaching material and it will be used to send the works requested in class.

Activity summary:

Activity In classroom Out of classroom
A-1 Master classes 45  
A-2 Laboratory sessions 15  
A-3 Debates, group mentoring   5
A-4 Homework   12
A-5 Notes reading   5
A-6 Individual study   58
A-7 Exams 5  
A-8 Individual mentoring   5
Total 65 85



Relationship between formative activities and proficiencies


Proficiency Activity
CG3 CG4 CG10 CC4 A-1 Master classes
CG3 CG4 CG10 CC4 A-2 Laboratory sessions
CG3 CG4 CG10 CC4 A-3 Debates, group mentoring
CG3 CG4 CG10 CC4 A-4 Homework
CG3 CG4 CG10 CC4 A-5 Individual studyl
CG3 CG4 CG10 CC4 A-6 Estudio individual
CG3 CG4 CG10 CC4 A-7 Exams
CG3 CG4 CG10 CC4 A-8 Individual mentoring






Learning outcome Evaluation system Weight (%)
  R1,R2, R3, R4, R6, R7 Final exam. 80% (Note: mínimum 5/10 mark is needed to pass this subject. Otherwise, subject is failed and the final mark is that of the exam)
R4,R5 Laboratory sessions, homework and exam. 20% (Note: not attending the laboratory sessions results in not being able to take the final exam. Final mark will be "Absent".)



  • Introduction to electric circuits.
  • Elements of electric circuits. Association of elements.
  • Wave forms.
  • Power and energy
  • Fundamentals of applied electrometry.
  • Analysis of circuits. Fundamental theorems.
  • Circuits in alternating current in sinusoidal regime.
  • Three-phase systems.
  • Magnetically coupled circuits.
  • Transformers



The Electric Circuits course is divided into six subjects, whose specific contents are detailed below:

  • Topic 1: Resistive circuits
    • Electrical magnitudes
    • Polarity. Sign conventions.
    • Ohm and Kirchhoff laws
    • Resistors connection.
    • Voltage and current dividers.
    • Introduction to resolution methods: nodes and meshes.
  • Topic 2: Basic tools for circuit analysis
    • Introduction.
    • Superposition.
    • Thevenin and Norton.
  • Topic 3: Energy storage elements
    • Introduction.
    • Capacitor.
    • Inductor.
  • Topic 4: Sinusoidal steady state analysis
    • Introduction.
    • Wave forms.
    • The sinusoidal function and phasors. Complex numbers.
    • Circuits with sinusoidal inputs. Voltages and currents.
    • Definition of impedance and admittance.
    • Measurement and calculation of power.
    • Correction of power factor.
  • Topic 5: Three-phase systems
    • Polyphase systems.
    • Balanced and unbalanced three-phase systems.
    • Measurement and calculation of power.
    • Correction of power factor.
  • Topic 6: Magnetically coupled circuits
    • Introduction.
    • Basic principles of the inductor.
    • Coupled inductors.
    • Single phase transformer.
    • Three-phase transformer.


  • Theoretical training will be complemented with laboratory sessions in which experimental work will be carried out:
    • Session 1: Measurements in direct current (i).
    • Session 2: Measurements in direct current (ii).
    • Session 3: The oscilloscope: measurement and interpretation of electrical signals.
    • Session 4: Measurements in single-phase systems.
    • Session 5: Measurements in three-phase systems.
    • Session 6: Single-phase transformer
    • Session 7: Three-phase transformer



Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.

Basic bibliography:

[1]     Scott, Donald E. Introduction to Circuit Analysis.

[2]     Charles I. Hubert. Electric Circuits Ac/Dc: An Integrated Approach.

[3]     Jesús Fraile Mora. Circuitos eléctricos. Ed. Pearson, Madrid, 2012. ISBN: 9788483227954.

[4]     A. Gómez Exposito, et al. Fundamentos de teoría de circuitos. Thomson, Madrid. ISBN: 978-84-9732-417-5.

[5]     J. Usaola García y Mª A. Moreno López de Saá. Circuitos Eléctricos. Problemas y ejercicios resueltos. Pearson Educación, Madrid, 2002. ISBN: 9788420535357.

[6]     A. E. Fitzgerald, Jr Charles Kingsley, Stephen D. Umans; Electric machinery.

[7]     Jesús Fraile Mora, Máquinas Eléctricas; Colegio de Ingenieros de caminos, canales y puertos, tercera edición, 1995

Advanced bibliography:

[8]     A. J. Conejo. Circuitos eléctricos para la ingeniería. Mc Graw Hill/Interamericana de España, S.A, 2004. ISBN: 8448141792.

[9]     William H Hayt, et al. Engineering Circuit Analysis.

[10]     J. David Irwin. Engineering Circuit Analysis.

[11]     A. Bruce Carlson. Circuits: Engineering Concepts and Analysis of Linear Electric Circuits.

[12]   A. Joseph Edminister, Mahmood Nahvi. Electric circuits.

[13]   E. Thomas Roland, Albert J Rosa. Circuitos y señales: introducción a los circuitos lineales y de acoplamiento. Reverté Barcelona, 2000. ISBN: 84-291-3458-1.



Classroom and laboratories