part i electric circuits - engineering education research

Part I

Electric Circuits

13

Chapter 2

Study 1: Engineering StudentsDifficulties in Solving ElectricCircuits

2.1 Theoretical Background

Most studies of education and learning in relation to electric circuits are done withstudents studying in primary or secondary school. Few studies deal with learningand understanding of electric circuits at the university level. Although courses forengineering students deals with topics typically not covered in school these studiesare relevant for the university level. As will be shown below university students haveproblems with the same topics and concepts in electric circuits as younger studentshas.

Maichle (1981), and Rhoneck (1983) analyze the conceptions of the students interms of conceptual maps and try to make the connections explicit that the studentsestablish among diverse concepts such as current, voltage, energy and resistance. Thestudies of Driver (1985) and Shipstone et al. (1988) about students conceptions ofelectrical circuits, carried out in several European countries, points at similar ideasfor different communities: diminishing intensity along a circuit, distribution of voltagein the branch, influence of the form of presentation of the circuit, etc. It is possibleto see similarities in the frequency of appearance of the different conceptions on basicelectricity in every country (Sweden, France, The Netherlands, Baden-Wurttenberg,Hesse in Germany, England).

In other studies about reasoning in electrical circuits Duit (1984), Caillot (1983)and Joshua (1984), it was shown that the students tend to use topological strategies(diagrams) more than to reasoning with the concepts taught about current.

According to the research of Osborne (1980) and Shipstone and Gunstone (1984)the students use the following models to explain the movement of the electricity insimple circuits:

1. Only a conductor is necessary to take the current to a bulb.

2. There are two types of current, the positive one and negative that flow fromopposite poles of the battery.

15

16 2. Study 1

3. The current flows trough the whole circuit but it is partially consumed in thebulb, for that, there is less current for the rest of the circuit.

The laws of Ohm and Joule that establish the quantitative relations in a circuit,it represents for the students two types of difficulties, from the first type proportionalcalculation and from the second type the used magnitudes. On the other hand, themajority of the results obtained with children and students can be interpreted in termsof linear causality. This form of reasoning can have different forms depending on thesituation.

According to studies of Hierrezuelo and Montero (1991); Driver et al. (1985, 1994)students have problems with:

• Difficulties to distinguish between, and to use, terms like: potential difference,voltage, current, energy, power, etc.

• The current is thought of as a material fluid.

• They do not see the necessity to for a circuit to be closed for there to be anelectrical current.

• They tend to make local analysis and think that voltages and currents are onlyaffected there the change is made not else were in the circuit.

• They tend to use sequential reasoning and for example think that the currentbecome weakened or exhausted as it pass trough a circuit or think there be onlycharges after the circuit element changed.

• Tend to interpret the voltage as a property of the current, instead of consideringthe current to be a consequence of the difference in potential between two pointsof a conductor.

• The students have difficulties to interpret the graphical representations of thecircuits. They are not able of associating the real circuits with their graphicalrepresentations, though it is a question of simple assemblies.

Another area of difficulties in the quantitative understanding of electrical circuits isthe nature of the implied concepts. To understand the physical theory on the electricalcircuits it is not enough to understand the relations of proportionality between thedifferent magnitudes is necessary besides to integrate the meaning of the differentmagnitudes inside these relations.

In the understanding of a problem of circuit he will construct a net of the bulb ofnodes, the battery, the voltage, the current, etc. Together with the specific relationsbetween these nodes.

In the research of Fredette and Lochhead (1980) come to the conclusion that themajority of the students who come to the University do not have a clear idea of whata circuit is.

2.2 Method and Sample 17

The Conceptions of the Students on Current, Voltage and Resistance Themeaning current in the daily language about electricity and electrical applications differfrom the formal language of electricity in physics. For example, the physical terms suchas electricity, the current, the voltage and resistance are also used in the daily language,but their meaning is different.

The misunderstandings in lessons of physics, is therefore, probably because theteacher is not conscious of these differences between his way of speaking and the wayin which the students speak about electrical phenomena.

Linear Causal Effect Between Batteries and Bulbs Tiberghien and Delacote(1976) analyzed how the children handle batteries and bulbs and what explanationsthey give in relation with their actions. The results of this study are that the childrenuse very general explanations of the functionality of a simple electric circuit. In general,they establish a causal connection between the battery and the bulb and make clearthat there is an agent who moves between the battery and the bulb.

They are seeing to the electrical current or the electricity as an agent. The elec-tricity or current are stored in the battery and can “rest” in conductors. The agent isconsumed in the bulb. There is no idea of conservation of electricity in these children.The linear causal effect between the battery and bulb does not hence imply a closedcircuit.

The Local Reasoning Local reasoning describes the fact that the students concen-trate their attention in a point in the circuit and do not consider what happens inanother parts of the circuit. An example of local reasoning is that many students lookat the battery as a source of constant current and not as a source of constant voltage.The battery as a source of constant current delivers the current, independent from thecircuit that is connected to the battery.

The Voltage in Closed Circuits One of the most difficult concepts in the basicelectricity is the concept of voltage or differential potential. Before the voltage wasrelated to “the force of a battery” or “the intensity or the force of the current”. Laterthe students use the concept of voltage as having the same properties that the conceptcurrent.

The Sequential Reasoning Establishes that the students analyze a circuit in con-ditions of “before” and “after” when the current “goes through” a specific place. Achange in “the beginning” of the circuit influences the element later, where the change“in the end” does not influence elements placed before. The information of change istransmitted by the electrical current.

Also the students in the level of university they use the sequential reasoning inother situations Closset (1983).

2.2 Method and Sample

The particular aim of this research was to find information about difficulties of engineer-ing students to understand concepts of electricity and solve electric circuits problems.

18 2. Study 1

And as technique to collect data were applied two questionnaires with close and openquestions about:

• Basic concepts of electricity.

• Solve electric circuits problems.

• Topics involved in the analysis of electric circuits.

The strategy of analysis used was quantitative and qualitative, making categoriza-tions, comparing information by tables.

2.3 Results from Questionnaire 1

A first questionnaire was applied (see Appedix A.1) to a group of 22 engineering stu-dents from the Escola Politecnica Superior d’Enginyeria de Vilanova i la Geltru. Uni-versitat Politecnica de Catalunya, Catalonia in the room where they take lectures.They were given information about the meaning of the test and they were kindlyavailable to answer it and they received instructions on how to answer it.

The questionnaire was divided in two parts. The first part was objective, evaluatingthe knowledge of the students. The second part was more subjective asking about thepersonal opinions of the students concerning electric circuits.

2.3 Questionnaire 1 19

2.3.1 Part 1: Understanding of Concepts of Electricity

Question 9

9: In the lab work if the measure of a resistance is infinite, it means:

Table 2.1: Answers from students to question 9

Experiences from the teaching electric circuits and in previous research mentionedbefore shows that students present confusion between the concept of open circuit andshort circuit. With this question we want to know the answer from students (consider-ing they have done this experience in the lab) relating the measure of the resistor withthe concept in question.

The expected answer was “Open Circuit”. The table show that most of the studentschoose the correct answer. About one third of the students choose “Short Circuit”.Nobody choose the rest of the options presented.

20 2. Study 1

Question 10

10: If the voltage in the end of a resistor is constant, the current in the resistoris ... to the resistance in its ohm’s value


In an electric circuit of direct current and alternating current, the resistance is theproperty that is acting as the opposition to the flow of current. When applying analternating voltage to a resistor, an alternating current is flowing through the resistor.The magnitude of the current in any instant is directly proportional to the magnitudeof the voltage in this instant and inverse proportional to the resistor value.

According to Ohm’s law the students should answer: Inverse proportional.


Questions 11 and 12

11: The total value (ohm) “R” of some resistors connected in “series” is ...Than any else resistor consider it individually.

12: In a circuit connected in series the current ... In all the points.


22 2. Study 1


For question 11 the answer expected is: HIGER. The “potency” is the speed thatcharge works. When many charges are connected in series in a circuit, all of themconsumes some potency. The total potency consumed in the circuit is the sum ofthe potency consumed in each charge. The flow of the current depends of the totalresistance of the circuit and for a circuit connected in series the total resistance is thesum of resistances of individual charges. For question 12 the expected answer is: ISTHE SAME.

According with the statistic result all students answer the question expected, justone student in question 12 answered the opposite one.

Both questions 11 and 12 concern the students’ understanding of connection seriesin electric circuits. According the researche of McDermott (1993):

“A failure to think holistically in dealing with compound systems is onekind of reasoning difficulty that may be hard to disentangle from conceptualconfusion. For example, in predicting bulb brightness, students often con-sidered only the order of a bulb in an array. Many claimed that the firstbulb in a series network was the brightest. This error is consistent with themisconception that current is ’used up’ and also with improper use of localsequential reasoning”

Closset (1983) concluded that the models used by the students depend on theparticular situation and how the question is written. On the other hand, the majorityof the results obtained with children and students can be interpreted in terms of linearcausality. This form of reasoning can have different forms depending on what situation.Another area of difficulties in the quantitative comprehension of electrical circuits isthe nature of the concepts implied. The current flowing in a circuit depends on thevoltage source and the total resistance in the circuit. When many charges are used inseries, the total resistance of the circuit is the sum of the individual resistances.


Question 16

16: The current exist only in a closed circuit? (True/False)


The circuit has to be closed or complete for current to flow. If the conductor isopened in any point, then in the negative part, the electrons are accumulated, whilein the positive side the electrons are attracted. The movement of electrons is stoppedand it implies the flow of current too. For this reason the answer expected is TRUE.And just one student answered FALSE.

“An example of a common difficulty that research has shown to be es-pecially persistent is the apparently intuitive belief that current is ‘used up’in a circuit.” McDermott (1993)

If a negative charge is applied to the end of a conductor, this charge repels freeelectrons to the other end of the conductor. The current flows only for an instant, untilenough electrons has accumulated in the other end of the conductor to produce an equalnegative charge, so that it will not allow more electrons. This is static electricity butto have electric current, the free electrons have to be in movement. When a source ofenergy is used, to apply opposite charges to the two ends of the conductor, the negativecharge repels the electrons in the entire conductor. In the positive side of the energysource electrons are consumed and move from the conductor to the energy source. Foreach electron that leaves the conductor, at the positive side of the the energy source,a new is supplied at the negative side of the energy source. This is a complete circuitor closed.

24 2. Study 1

Questions 14 and 15

14: The tension between the ends of every branch of a net in parallel is notequal (True/False)

15: Resistances of 22Ω, 33Ω and 44Ω are connected in parallel. Their totalresistance will be less than 22Ω (True/False)



A parallel circuit is a circuit that has one or more points where the current isdivided and follows different trajectories. When elements are connected in parallel,every element has a different potential. Instead of having the differential potential of thesource in every charge, as in a circuit in series, it has the total differential potential of


the source in itself (because all charges connected in parallel are also connected directlyto the terminals of the source of energy). For this reason the sentence of the question14 is FALSE. The question 15 has the intention to show a sequence of quantitativesummarize of the resistors. In the way that it is presented the question is easy tosuppose that the total value of the resistors in the circuit should be major than the eachone, as in the case of resistors connected in series; but, according with the proprietiesof the electric circuit for any number of resistors in parallel, the reciprocal of theequivalent resistance equals the sum of the reciprocals of their individual resistances,so it means that the equivalent resistance is always less than any individual resistance.A circuit connected in parallel has different electric behavior than connected in serie.In consequence the correct answer for this question is TRUE, and it is possible to probeit with this mathematical model:

1122

+ 133

+ 144

=1

0.106060 . . .= 9.428571 . . . (2.1)

9.43Ω < 22Ω (2.2)

However, as we can observe in the quantitative result that most students answeredwrong. But comparing this result with the result from question 14 we found inconsis-tence and also for questions 11 and 12 about circuits connected in series, we observea difference: although all students answered right in question 11 and just one studentanswered wrong in question 12, the inconsistence.

“In treating the parallel branches as independent, the students were notrecognizing the difference between parallel branches connected across a bat-tery and parallel branches connected elsewhere. Instead of using qualitativereasoning to check that their predictions were consistent with what theyknew about current and potential difference, the students relied on a rulethat they had incorrectly memorized.” McDermott (1993)

2.3.2 Part 2: Perspectives on the Subject Electric Circuits

The following questions were applied with the intention to know, from the students’point of view, about the group of concepts and elements involved in the analysis ofcircuits as a subject and to be more close the side of the students not just as object ofstudy.

26 2. Study 1

Question 1

1: What is your opinion about the subject Electric Circuits? Explain why.

• Iteresting

• Boring

• Incomprihensible

• Not important

• Important

• Easy

• Complicated

• Necessary


Students’ comments on their answers The students were asked to motivate whythey choose a particular option; the following are the students comments and motiva-tion for their answers.

Interesting

• Because it gives tools to analyze electric circuits

• Because it makes more easy to get data of circuits

Important


• Because it is the base to understand other subjects

Easy

• Because it make more easy analysis of electric circuits

Complicated and Boring

• Because it became just a requirement

Necessary

• Because it is the base of technique knowledge for electronic career.

• To continue my career.

• To simplify calculus

• To understand electric circuits

• To make more easy the analysis of electric circuits

Question 5

5: Is it necessary to be skillful in mathematics to understand the analysis ofelectric circuits? Explain why.

• Yes • No

Students’ comments on their answers The students were asked to motivate whythey choose a particular option; the following are the students comments and motiva-tion for their answers.

Yes

• Because is more easy to understand mathematical operations

• It helps, because principally are mathematic calculus

• Is necessary to have it because appearing mathematical operations and toolslike the Laplace transform inverse that are more complicated than thesystem of equations.

• To make more easy the calculus

No

• The mathematical calculus are easy

• If you know interpret the unknown quantities the mathematical operationsused are basic.

28 2. Study 1

• All the concepts have been studied previously.

• Although is fundamental to have any skillful to understand

• I think is more useful to be skillful to solve electric circuits than in mathe-matics

• Although, I think, is it necessary to have clear different aspects of mathe-matics, for example: the Laplace transform.

Although the question don’t specify the sentence: “skillful in mathematics”, thestudents related it with to “make easy to understand...” and to “do calculus...” and itis interesting to observe that the topic of the Laplace transform appear in both options(yes/no) as complicated topic.

Question 8

8: Which do you identify with when solving electric circuits?

A I understand the problem and sometimes Iget the right answer without mathematicalmethods or theorems

B I don’t understand the physical phenomenaC Sometimes I fail, but only in mathematical

errorsD There are many mathematical methods, and

I don’t know which one to useE Without understanding much of the physical

phenomena I get the right result by applyingmathematical methods

F Other



“Those who learn successfully from lectures, textbooks and problem-solving do so because they constantly question their own comprehension,confront their difficulties and persist in trying to resolve them. Most stu-dents taking introductory physics do not bring this degree of intellectualindependence to their study of the subject.” McDermott (1993)

Questions 3 and 4

The intention of question 3 was to know which topic the students considered as themost difficult to learn when they studied the subject Electric Circuits.The purpose of question 4 was to know which topic the students considered as themost relevant to the students when they solve electric circuits. Important topic in thesense that the student remember this topic as something that, to the student, seemedimportant to the course. This is not necessarily the topic that they understood thebest.

3: In the subject of Electric Circuit, do you consider any topic difficult tounderstand? And why?

4: In the subject of Electric circuit, which topic do you remember more? Andwhy?

30 2. Study 1

Table 2.10 is a Table of Contigency , where it is possible to observe the intersectionbetween the topic of Laplace inverse (vertical) and Laplace transform (horizontal) andcorrespond to the answers about the topic (of electric circuits) that students considermore difficult to understand (Question 3) and the topic (of electric circuits) that theyremember more, that is, they had to work more on it (Question 4).

Table 2.10 also shows that over all the topics related with electric circuits, the topicof Laplace transform (that it is a mathematical tool solve electric circuits problems)was mentioned many times from the students as a difficult topic.


Table 2.10: Table of contigency for questions 3 and 4

32 2. Study 1

2.4 Results from Questionnaire 2

A second questionnaire was applied (Appendix A.2) to the same group of engineeringstudents fron the Escuela Universitaria Politecnica de Vilanova i la Geltru in the roomwhere they take lectures.

An interesting point observed was that after the test some students made questionsto know about their mistake and they expressed some important points that wereconsiderate.

The strategy that we used in the second questionnaire was to change the conditionsfor a problem that the students are used to solve. In our study the students were askedto solve a problem considered as a basic exercise they solve during classes, with theexception that it was to be solved using direct current instead of alternating current.This created a conceptual conflict that the students had to resolve. The motivationfor doing this was to see how the students interpret the physical phenomena and whatkind of mathematical models they use related to this phenomena.

2.4.1 Test Problem

1: Find the value of the current trough the coil and justify your answer


The solution we expected The most common solution givenby the students

10 = 4 [I(s) + ix] + (s + 6)I(s)10 = 4 [I(s) + ix] + 4

six

34 2. Study 1

Figure 2.1: The power source is direct current

Figure 2.2: The capacitor functions as an inifinite resistance

2.4.2 Expected Solution to the Problem

We expected the following answer:

2.4.3 The Given Solution to the Problem

The most common answer from the students was as following:

Figure 2.3: The coil functions as a conductor


Figure 2.4: The current through the inductor is the same as the total current in the circuit

Figure 2.5: The power source was considered by the students as alternating current

Figure 2.6: The students applied theorems to analyze the circuit and simplify it

Figure 2.7: The students obtained a reduced circuit, and from it they got a system ofequations to solve

36 2. Study 1

Figure 2.8: The students ends up with the following equations

10 = 4 [I(s) + ix] + (s + 6)I(s) (2.3)

10 = 4 [I(s) + ix] +4

six (2.4)

When they applied the Laplace transform formulas they re-alized that they needed more information to find the solution

Only one student in the group asked how to solve the problem using direct current.While other students tried to solve it by applying the Laplace models.

Reviewing their answers, raised the question of how the students interpret thisprocess that they expressed in the circuit.

This is the question that is pushing for more research.After the questionnaire some students where interested in to know the right solution

and they manifested particular (but important) comments about some aspect that theyconsider important to analyze electric circuits:


Student Comments

Student Comment TranslationS1 Antes de llegar a la asignatura de

Analisis de Circuitos I, en primero sepodrıa explicar mas la Transformada deLaplace.

Before coming to the subject of Analysisof Circuits I, in first courses, the Laplacetransform might be explain more

S1 Para mejorar la comprension de la asi-natura estarıa bien realizar tareas ex-tra, como ejercicios puntuales hechos encasa.

To improve the comprehension of thesubject; it would be nice to realize ex-tra tasks, as punctual exercises done athome

S2 En las clases de Teorıa de Circuitos/Analisis de Circuitos I, falta explicacionde corriente continua y corriente alterna(diferencias) y poner ejemplos de lo queestamos haciendo y que sucedan en lavida real o cotidiana.

In lectures of Circuits Theory /Analysisof Circuits I, lacking explanation aboutwhat is direct current and alternatingcurrent (also differences) and to see ex-amples of what we are doing and thathappen in real life/daily

S3 Me parece totalmente correcta la asig-natura y el temario es suficiente...sin em-bargo, tambien tengo que decir que laasignatura es un poco aburrida.

The subject seems to me totally correctand the agenda is sufficient ... although,I have to say that the subject is a littlebit boring too

S4 En la asignatura de Analisis de Circuitoscreo que es necesario que se le de masimportancia. al funcionamiento en sı delcircuito (que hace ese circuito) en vezde buscar tensiones o corrientes en pun-tos que a simple vista parecen poco sig-nificativos. Otra cosa que veo impor-tante es que las practicas en el labora-torio tendrıan que ser mas abundantes.

In the subject of Analysis of CircuitsI believe that it is necessary to givemore importance to the functioning cir-cuit (what does this circuit do?) in-stead of looking for tensions or currentsin points that seem to be slightly signifi-cant. Another thing that I consider im-portant is that the practices in the labo-ratory would have to be more abundant

S5 En mi opinion creo que deberıan ex-plicar menos matematicas y teoremas,solo de forma presencial e intentar ac-ercar mas el fenomeno en sı al alumno(el fenomeno fısico) ya que creo que esmuy importante tener una idea ampliay clara de lo que es la electricidad ensu forma mas basica para poder enten-der mejor las ecuaciones matematicas ysus distintos comportamientos de los ele-mentos electronicos; ¿porque se disenanası y no de otra forma? Y eso esta en elcomportamiento y la naturaleza mismade la electricidad. Si se comprende mejordesde el principio el fenomeno creo quedespues es mas facil asaltar la teorıamatematica y tecnica. Eso es lo queyo hecho mas en falta en la carrera.Por otro entiendo que es un fenomenocomplejo y difıcil de explicar ya quees como mas “invisible” e intuitivo queotros fenomenos fısicos.

In my opinion I believe that they shouldexplain fewer mathematics and theo-rems, just as presence form and theyshould try to close the phenomenon overmore in itself to the student (the physi-cal phenomenon) since I believe that it isvery important to have a wide and clearidea of what is the electricity in it ba-sic form to be able to understand betterthe mathematical equations and it differ-ent behaviors of electronic elements; whythey are designed on this way and not ofanother form? And it is in the behaviorand the nature itself of the electricity. Ifthe phenomenon is understood from thebeginning, then I believe that it is easierto assault the mathematical and techni-cal theory. This is what I don’t find inmy studies. For other one I understandthat it is a complex phenomenon and dif-ficult to explain because it is like ”invis-ibly” and intuitively that other physicalphenomena

38 2. Study 1

(continued)Student Comment TranslationS6 Creo que el actual plan de estudios esta

muy mal organizado, en las asignat-uras mas especializadas de la carrera(electronica basica, circuitos digitales,teorıa de circuitos,...) se dispone de ape-nas dos horas a la semana de teorıa; dirıaque es poco tiempo para coger una buenabase, porque viniendo del bachillerato labase tecnologica es practicamente nula,la unica base es matematica. Yo, loscambios los plantearıa no a nivel deanalisis de circuitos, sino a nivel muchomas amplio.

I believe that the current study plan isbadly organized, in the more specializedsubjects of the career (as basic electron-ics, digital circuits, theory of circuits,etc.) have only two hours per week oftheory; I would say that it is little timeto get a good base, because coming fromhigh school the technological backgroundis practically void, the only base is math-ematics. I would propose changes notonly to the level of analysis of circuits,but also to a much more wide level

S7 Yo sugiero aplicar en las horas de labo-ratorio mas comprobaciones practicas delo que se explica en teorıa y no hacer tan-tos calculos que de todas formas ya es loque hacemos en clase de teorıa.

I suggest to apply in the hours of labmore practical checking than is explainedtheoretically and not to do so many cal-culations that of all forms already it iswhat we do in class of theory

S8 Pienso que deberıa relacionar mas laasignatura con casos practicos reales.

I think that it should relate more the sub-ject to practical real cases

2.5 Conclusions 39

(continued)Student Comment TranslationS9 Creo que es de las asignaturas mas

provechosas que hemos hecho (Analisisde Circuitos I), pero creo que si pro-fundizan mas en los condensadores y lasbobinas serıa mejor.

I believe that the subject Circuit AnalysisI is one of the most profitable subjectsthat we have studied, but I believe that ifthey penetrate deeper into the topics ofcondensers and coils it would be better

Table 2.11: Comments made by some students after Questionnaire 2

2.5 Conclusions

According with results we consider the next conclusions:

• It is important to note that the engineering level education needs a special fieldof study. One of the reasons for this is that the concepts managed in this level arecomplex, comparing with the concepts in lower level education. The engineeringstudents need to be able to combine and apply new and previous knowledge tosolve real situations.

• It is important to observe that while almost all students gives the right answerin the first questionnaire about topics implicated in electric circuit, they showeddifficulty to solve the electric circuit problem in the second questionnaire. Thetopics covered in both tests are the same but the way the questions are asked isdifferent. While the first questionnaire asks direct questions where the studentshave to choose the right answer, the second is an application of more advancedconcepts, that imply a higher level of knowledge, where it is necessary to know,not only all the concepts involved, but also their behaviour.

“Predicting the effect of a change in a circuit requires a more so-phisticated level of holistic reasoning.” (McDermott, 1993)

We do not intend to affirm the statement above, only with the results fromthis “classic” test because it was formulated like an exam, and could thereforehave influenced the answers from the students. However, we do not discard thepossibility that the solving electric circuits implies handling threshold concepts.

• In both questionnaires we observed some topics that for the students are not easyto manage when they solve electric circuits. A constant topic that appears is theLaplace transform and we consider to put more attention in this topic for thenext study to know is it local or general difficulty.

“Students specialising in electrical engineering or engineering orengineering physics typically need to study not only AC-circuits butmethods for handling more complex circuits and are usually request tolearn to apply various transform methods (phasor, Fourier, Laplace)

40 2. Study 1

and Fourier-series in circuit analysis.” (Bernhard and Carstensen,2002)

Most students say that it is easy to apply the mathematical theorems or methodswithout understanding the physical phenomena and get correct answer. It implies thatstudents are able to develop “their system” to solve problems with specific conditions.By just applying the right mathematical method is possible to get right answer. But,when the conditions for the problem are changed “their system” will not work andsome of them do not know how to handle the situation. This is worrying in engineeringeducation because the students lose the principal aim (that is learn) and just becomesmachines, very skilful at using computers and calculators, producing good answers butwithout understanding the meaning of that calculus.

It is important to notice the difference between to analyze and to calculate.

Chapter 3

Study 2: Engineering StudentsUnderstanding Basic Concepts ofElectricity

3.1 Introduction

To be able to analyze electrical circuits it is necessary to have knowledge of the laws,theorems and fundamentals of the theory of electric circuits, trying to become skilledin the use of the concepts and technologies of differential calculation and diverse vari-ables. It is also necessary to have an interest in having a good “mathematical base”,such as algebra, complex numbers, differential equations and the Laplace transform.Further, it is necessary to study the concepts of static and dynamic models of the basicsemiconductor devices, as well as to study and to characterize basic circuits and sub-circuits functionality. The integrated-analogical circuits used in the subjects of basicelectronics allows the student to have a wider vision of the electronic applications.

The analysis of electric circuits among engineering students are of special interest tostudy, because engineering students are required to combine both previous knowledgeand develop new knowledge in the process of analyzing electric circuits. Few researcheshas been made on understanding of electric circuits in higher level education:

“Research on students learning and understanding electric circuit theoryis still in its infancy. Student’s conceptions in circuit theory and electric-ity are not as well investigated as those in mechanics.” Bernhard andCarstensen (2002)

3.2 Method and sample

This study is a survey of the answers from 109 engineering students from three dif-ferent contexts. 66 students from Escual Superior de Ingenierıa Mecanica y Electricadel Instituto Politecnico Nacional, Mexico, 25 students from Linkopings Universitet,Sweden and 18 students from Escola Universitaria Politecnica de Vilanova i la Geltru,UPC, Catalonia.

The method used to collect data was a questionnaire (see Appendix A) to elec-tric engineering students with open questions about the use of mathematical models,

41

42 3. Study 2

physical concepts and procedures.

The data analysis strategy for each stage was quantitative and qualitative analysis:Categorizing, comparing and summarizing information. Presenting and explainingresults and their interrelation and conclusions.

Sweden Mexico Catalonia

Figure 3.2: Students from three different contexts

Engineering students learn to solve electric circuits in different ways according withthe plan of studies of every country. And our approach is not to compare curriculum orprograms or knowledge to establish a score to say which one is better. We are interestedto know if the result gotten in Study 1 is just local situation and also to know howthe students interpret the mathematical models that they use to solve electric circuitsproblems

3.3 Results

Results from the survey show the different arguments from engineering students ex-plaining the meaning of complex concepts and formulas used to solve the electric cir-cuits.

The questionnaire had to be adapted not only with the language for each country,but also with the different technical words used.

The first part consisted in to answer true or false to each statement concerning elec-trical behaviour made in the question. Some of the statements had the same meaning,but expressed in different ways.

The second part consisted in to explain an already solved problem.

3.3.1 Concepts of voltage and current

The Tables 3.1, 3.2 and 3.3 show the results of the answers for each question in Ques-tionnaire 3 in Appendix A.

3.3 Results 43

Table 3.1: All answers to question 8 in Questionnaire 3 (Appendix A) from students inMexico

44 3. Study 2

Table 3.2: All answers to question 3 in Questionnaire 3 (Appendix A) from students inSweden

3.3 Results 45

Table 3.3: All answers to question 3 in Questionnaire 3 (Appendix A) from students inCatalonia

46 3. Study 2

Dependence between Potential Difference and Current

Figures 3.3, 3.4 and 3.5 show the analysis to the answers of the questions (a), (p),(b) and (q), that express the relation of dependence between potential difference andcurrent, but in different ways. We can see that the three countries are consistent intheir answers to questions (a) and (p), but at the same time all of them are inconsistentin their answers to questions (b) and (q).

Figure 3.3: Relation between answers to questions (a), (p), (b) and (q) from mexicanstudents

Figure 3.4: Relation between answers to questions (a), (p), (b) and (q) from swedish students

Figure 3.5: Relation between answers to questions (a), (p), (b) and (q) from catalonianstudents

The following tables show the relations between different answers from the students,where the results were the same from the three countries.

3.3 Results 47

(m): Current is an electric flow(n): Voltage is an electric flow

Mexico

m \ n Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 21 43 0 0 64False 1 0 0 0 1

True & False 0 0 0 0 0No Answer 0 0 0 1 1

22 43 0 1 66

Sweden

m \ n Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 0 17 0 0 17False 4 2 0 0 6


4 19 0 2 25

Catalonia

m \ n Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 2 13 0 1 16False 0 0 0 0 0


2 13 0 3 18

Relation between questions (m)and (n), where the following wasthe highest frequency in eachcountry

1. Mexico

(m): True and (n): False

2. Sweden


3. Catalonia


Table 3.4: Relations between questions (m) and (n)

48 3. Study 2

(i): You can feel Voltage by touching a wire(j): You can feel Current by touching a wire

Mexico

i \ j Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 12 9 0 0 21False 40 3 0 0 43


52 12 0 2 66

Sweden

i \ j Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 1 9 0 0 10False 12 2 0 0 14


13 11 0 1 25

Catalonia

i \ j Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 1 1 0 0 2False 8 5 1 0 14


10 6 1 1 18

Relation between questions (i)and (j), where the following wasthe highest frequency in eachcountry

1. Mexico

(i): False and (j): True

2. Sweden


3. Catalonia


Table 3.5: Relations between questions (i) and (j)

3.3 Results 49

(b): Potential Difference is necessary to get a Current(g): The Voltage is the cause of electric Current

Mexico

b \ g Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 28 17 0 1 46False 3 5 0 1 9


34 27 0 5 66

Sweden

b \ g Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 12 1 0 2 15False 4 4 0 1 9


16 5 0 4 25

Catalonia

b \ g Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 7 5 0 1 13False 1 4 0 0 5


8 9 0 1 18

Relation between questions (b)and (g), where the following wasthe highest frequency in eachcountry

1. Mexico

(b): True and (g): True

2. Sweden


3. Catalonia


Table 3.6: Relations between questions (b) and (g)

50 3. Study 2

(b): Potential Difference is necessary to get a Current(q): Current can occur without Voltage

Mexico

b \ q Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 9 37 0 0 46False 6 3 0 0 9


18 45 0 3 66

Sweden

b \ q Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 2 12 0 1 15False 2 7 0 0 9


4 20 0 1 25

Catalonia

b \ q Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 1 11 0 1 13False 2 3 0 0 5


3 14 0 1 18

Relation between questions (b)and (q), where the following wasthe highest frequency in eachcountry

1. Mexico

(b): True and (q): False

2. Sweden


3. Catalonia


Table 3.7: Relations between questions (b) and (q)

3.3 Results 51

(c): A Voltage impulse will cause a Current(d): The Voltage is the force driving Current

Mexico

c \ d Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 19 15 0 2 36False 14 7 0 0 21


33 25 0 8 66

Sweden

c \ d Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 15 2 0 1 18False 4 3 0 0 7


19 5 0 1 25

Catalonia

c \ d Tru

e

Fals

e

Tru

e&

Fals

e

No

Answ

er

True 3 2 0 1 6False 2 6 0 1 9


5 8 0 5 18

Relation between questions (c)and (d), where the following wasthe highest frequency in eachcountry

1. Mexico

(c): True and (d): True

2. Sweden


3. Catalonia


and also

(c): No Answer and (d): NoAnswer

Table 3.8: Relations between questions (c) and (d)

52 3. Study 2

3.3.2 Concepts of coil and capacitor

The task for the students was to give an explanation, or interpretation, to the electricphenomena that occured in the circuit in Figure 3.6

Figure 3.6: Circuit from the questionnaire

The circuit in Figure 3.6 has two solutions; first condition and second condition. Tothe first case; when the circuit has been connected to the source of 12V for a long time,the following phenomena occurs:

1. The coil acts as a ”short circuit” (like a conductor)

2. The capacitor as a ”open circuit”

Figure 3.7: The circuit in the first case

In this case only the resistor acts, and the original circuit is reduced to the circuit inFigure 3.8

Figure 3.8: The reduced circuit

The intention to ask the students what happends in the circuit, with the elements likethe coil and the capacitor, is to know how they interpret the electric phenomena andto compare the answers from the different countries.

3.3 Results 53

Examples of answers from the students

In this part of the questionnaire we explained to the students the aim of it and wetry that they do not take it as an ordinary test were their knowledge is evaluated,the problem is solved and they just have to explain the meaning of the mathematicalmodel. This kind of activity is not common for the students in neither Mexican norCatalan context. This is because in the examinations they use to solve and give theresult, but usually they do not give an explanation or interpretation of their solution.

Figure 3.9: Part of the questionnaire answered by a swedish student

54 3. Study 2

Figure 3.10: Part of the questionnaire answered by a mexican student

Answers from the engineering students, explaining the meaning of the values in thecircuit.

Table 3.9 shows the answers from the students that coincide with the expectedanswer. And we can appreciate that in three countries although the answer of “Ohmlaw” is superficial, it was found in the three countries.

3.3 Results 55

Answers from Students

Mexico Sweden Catalonia

Inductor is like short circuit.Capacitor is like open circuit.Resistor keeps equal

3 7 4

Ohm law 2 2 1Table 3.9: Expected Answers; The same arguments found in all the three different contexts

In Table 3.10 shows the misunderstandings of concepts in students when they ex-plain certain parts of the problem.



The coil opens and the capacitorcloses

x

The inductor is like a short circuitand it doesn’t flow current. Thecapacitor is like open circuit anddoesn’t flow current

x

It doesn’t exist variation x

Something but I don’t know x

I don’t interpret x x

In coil what ever? And a currentwhich blocked in the resistance

x

The capacitor is broken and this im-ply coil is broken and current goesthrows by resistor

x

Table 3.10: Misunderstandings

56 3. Study 2

We can apreciate in Table 3.10 not incidence of answers in the the different countries.



By the capacitor. x

By drop voltage and differential po-tential.

x

Total current pass trough in theshort circuit and the voltage in ca-pacitor is the same than voltagesource.

x

V (0) is in parallel to voltage source.I(0) applying Ohm law in a closedcircuit.

x

All current pass trough the induc-tor, for this reason it doesn’t ex-ist voltage, in the capacitor doesn’tnot pass current, in consequence itdoesn’t exist current and voltage ei-ther.

x

The values you got when youstarted the measure.

x

Capacitor doesn’t carry any currentat low frequency and may there forbe removed from the circuit whichbecomes open at the point.

x

All the current goes trough the re-sistor

x

Direct current x

In C arises a potential (V ) x

I(0) is the intensity that coil let go x

V in parallel is the same in all thenetworks

x

The inductor is charged and let flowcurrent by conductor

x

Table 3.11: Explanations of the meaning of values in the electric circuit

3.4 Conclusions 57

Table 3.12 shows other clasification of the students answers that are diverse and donot have incidence.



When the current flows in coilthrough the time; the coil presentsa impedance and we find a voltage.

x

By “integral- differential” equation x

Ldidt is the voltage who pass by the

coilx

I have forgotten x

Everything that comes “in” mostcomes “out”

x

As Kirchoff’s law said x

The sum of entire “in” potentials isequal to the sum of “out” potentials

x

Table 3.12: Explanations of the mathematical meaning of values in the electric circuit

3.4 Conclusions

We can see that there are inconcistencies in the majority of the answers to the ques-tions that relate to either potential difference being the cause of current or currentbeing the cause of potential difference. It can be originated from the way the questionswere written (in every country the expressions used sometimes change), from misun-derstandings, or because there is not a concencus among the teacher regarding thisaspect.

In the results from the analysis in Appendix B.

1. The students from Catalonia showed five times as the most frequent answertwo combinations of answers, this did not occur among the students from eitherMexico or Sweden.

2. We observed that some of the answers from the Catalonian and Swedish studentsagree, while for the same questions, the Mexican students answer the completeopposite.

58 3. Study 2

3. In four combinations of answers the students from the three countries agreedcompletely:

(a) That current is an electric flow, and voltage is not an electric flow.

(b) That you cannot feel voltage touching a wire, but you can feel current touch-ing a wire.

(c) That potential difference is necessary to get a current, and that the voltageis causing electric current.

(d) Potential difference is necessary to get a current, but current does not occurwithout a voltage.

The students almost agreed (only a small difference in the answes from the stu-dents in Catalonia) that voltage impulse cause a current. And that the potentialdifference is the force driving the current.

According to the results from the students in Table 3.10 we found that the studentsare able to manage the concepts without understanding the meaning of them. We canrelate these results with the difficulties that Meyer and Land suggest exists

the learners may be left in a state of liminality (Latin ‘limen’ – a thesh-old). Liminality refer to an individual or a group – a suspended state inwhich understanding approximates to a kind of mimicry. The transitionis problematic. troubling and often humbling, and students often mimicthe new status without understanding the meaning of what they are doing.Baillie (2005)

part i electric circuits - engineering education research

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