Student understanding of open switches and open circuits:
What do we (not) know?
Dion Timmermann
Hamburg University of Technology, Hamburg, Germany
dion.timmermann@tuhh.de
Christian Kautz
Hamburg University of Technology, Hamburg, Germany
kautz@tuhh.de
Abstract: We investigate student understanding of the voltage across an open
switch. We will present and compare questions and data from literature and
identify four possible misconceptions about open switches. Across many different populations with students from different countries, we find that 54 % of
students incorrectly think that the voltage across an open switch is zero. While
this number of incorrect answers is quite consistent across all studies, not much
is known about the student misconceptions that cause it. Consequently, further
research into these misconceptions is required to help teachers design suitable
instruction.
Introduction
One of the most prominent aspects in electrical engineering education is the analysis of circuits. Many of the circuits presented to students contain (open) switches or open circuits, for
a variety of reasons: On the one hand, many actual devices contain switches and an open
circuit can e. g. be found at every socket which has no plug connected to it. On the other hand,
open circuits are a requirement for more advanced topics, as e. g. Thévenin’s and Norton’s
theorems. Additionally, in instructional settings, switches allow us to increase the variation of
an exercise by “switching on or off” certain parts of a circuit.
Although switches and open circuits are very relevant for instruction, there is not much known
about student understanding of these elements. Many instructors see that their students have
trouble determining open circuit voltages, and the fact that students “assume the voltage
across an open circuit is zero” is even listed as one of the “Ten Common Mistakes in Circuit
Analysis”, gathered by Santiago (2013). But apart from these informal observations, little
research on student understanding of the voltage across open switches and open circuits has
been published in literature.
The purpose of this paper is to gather and analyze the published data about student understanding of the voltage across open circuits and open switches. We will give an overview of
studies that provide data on this problem. After that, we will compare the observations about
the frequency of incorrect answers on the open circuit voltage and summarize different misconceptions that were proposed to explain these incorrect answers.
Theoretical Framework
Our research is based on the assumption that students have or develop alternative ideas
about key concepts in the subject matter (McDermott, 1993). One goal of instruction is then
to help students overcome these alternative ideas though a process of conceptual change
(Redish, 2003). In order to build effective learning environments, instructors need to be aware
of frequent misconceptions (McDermott, 1993).
This leads us to use empirical methods for gathering student statements in verbal or shortanswer form that allow us to make inferences about their understanding (Pride et al., 1998).
We use questions about technical scenarios to probe students’ understanding about the top-
1
ics in question. This study contains some data gathered by our group, as well as data reported by other studies that are based on the same or a similar theoretical framework.
Literature Review
This section will give an overview of all studies we were able to find on this topic. We searched
the archives of the American Journal of Physics, the IEEE Transactions on Education and the
European Journal on Engineering Education, as well as Google Scholar with the search terms
“open circuit” or “open switch” in combination with “student understanding” or “conceptual understanding”. For all papers we found, we also analyzed the references for cited studies on
the same subject. The quantitative data presented and possible misconceptions reported in
these studies will be categorized and compared in the following two sections.
In 1982, von Rhöneck reported on secondary school (grade 9) students’ understanding of
voltage, particularly their predictions about the voltage at open switches. This is possibly the
first published report on this problem. After instruction, 22 out of 26 students believed that the
voltage across an open switch was zero. Later, Rhöneck (2008) added to this, commenting
that “the voltage concept is one of the most abstract concepts introduced in a secondary
school physics course. Usually students do not develop an independent voltage concept, but
interrelate it to the concept of electric current. That means voltage is seen as a property of the
electric current.”
About the same time as von Rhöneck’s first study, Cohen et al. (1983) reported on a test
to gauge high school students’ and teachers’ conceptual understanding of simple electric
circuits. The students had completed instruction on DC circuits that was on a level equivalent
to first-year college in the U.S. One of 14 questions in the test by Cohen et al. contained a
circuit with a light bulb connected in series with a resistor. Participants were asked how the
potential difference across the bulb’s socket changed, when the bulb was removed from its
socket. This is basically the same as asking about the voltage across a switch that is opened.
While they provided quantitative data on that question, Cohen et al. mostly discussed why
their participants selected one distractor that is connected to the misconception of batteries
being sources of constant current.
In 1997, Engelhardt published DIRECT, a concept inventory about resistive DC circuits. During the validation of the test’s versions 1.0 and 1.1, answers from 1827 high school and university students from mostly the U.S. were gathered. This was possibly the first data published
about university students’ understanding of the voltage across open switches. However, the
data do not show large differences between high school and university students. Engelhardt
explained the large amount of incorrect answers as students confusing voltage and current.
One form of this is similar to von Rhöneck’s interpretation. Many students saw voltage as a
property of current and reasoned that without current, there would be no voltage.
In 2005, Periago and Bohigas published a study amongst Italian university students. One
of the nine open-ended questions in their study was based on the question by Cohen et al.
(1983) that was described above. The distribution of answers in their study varied quite strongly
from those reported by Cohen et al. Contrary to the studies mentioned above, they suggested a different explanation. In their opinion, students incorrectly apply Ohm’s Law at open
switches.
Recently, Hussain et al. (2012) started to investigate alternative conceptions of students about
open and short circuits. While this seems to be the only study that primarily deals with students’ understanding of open circuits, with 47 second semester university students from
Malaysia their study has the lowest number of participants. Their study consisted of a pre and
a post test with a intervention in between. Unfortunately, we were not able to find a publication
with detailed information about the intervention. In their tests, they asked 12 conceptual questions, including one about the voltage across an open switch. After the tests, group interviews
were done to gain insight into the students’ reasoning. Hussain et al. (2012) conclude that
students “relied heavily on Ohm’s Law, where they assumed current as the prime concept”.
2
Figure 1: Question number 10 from Hussain et al. (2012)
In 2014, we published results on university students’ understanding of the concepts of voltage
and potential (Timmermann and Kautz, 2014). For the evaluation of instructional materials
developed by our group, we used a quiz and results from an exam. While the exam contained
a question that was based on a bulb being removed from its socket, the quiz asked students
to rank several voltages in a circuit, including ones across an open switch. We reported on the
frequency of correct and incorrect answers for both tasks.
A recent publication from our group (Timmermann et al., 2015) presented instructional material that was designed to help students gain a conceptual understanding of potential in electric
circuits. This material confronted students with their misconceptions about the voltage across
an open switch. A quiz question similar to that from our 2014 publication was used to evaluate
the material. We found that the material had some success, but the learning gain was still not
as high as we had hoped for. We proposed that the misconception about open circuit voltage
might be particularly hard to overcome.
Quantitative Data
Several of the studies presented above used similar or identical questions. In the following,
these will be grouped and compared.
Of all the studies listed in the previous section, Hussain et al. (2012) asks most directly about
the voltage across an open switch. Their question, which is reproduced in Figure 1, is a twotier question that not only asks students to make a prediction about the voltage across the
open switch, but also to indicate their reasoning. Their question was used twice, once before and once after an intervention. We were not able to find any specific information about
the intervention. The percentages of student answers were reported for 4 of the 12 possible
combinations of answers and reasons. These were selected by 83 % of the 47 participants in
the pre test and 87 % in the post test. It is unclear if the remaining students did not select any
answer or if they did select an answer and the numbers were just not reported. Of the 47 students in their study, the correct answer and reason were selected by 0 % (4 %) before (after)
the intervention. The answer that the voltage across the open switch is zero was selected by
79 % (68 %) of the students.
While these low numbers of correct answers surely are dramatic, the phrasing of the question
might have had a large influence on the results: The correct solution was answer b (12 V) and
reason d (“others”). However, while reason d was one of the multiple choice reasons, it asked
students to additionally write down their own reasoning. We believe this causes this option to
appear less likely to be correct.
Data that is more easily interpretable was provided by Engelhardt with Question 28 of the
DIRECT concept inventory (see Figure 2). The circuit in her question is very similar to that
3
from Hussain et al. In version 1.0 of the test, only the four answering options 0 V, 3 V, 6 V, and
12 V were given. In version 1.1, the fifth option, “none of the above” was added. However,
Engelhardt remarks that better options might have been 4 V or 8 V, which would be fitting to
the idea of the open switch and the bulbs having the same resistance.
Table 1 shows the results gathered during the validation of the inventory for two versions of
the test, with data separated for university and high school students. As can be seen, the correct answer (12 V) is selected by no more than 27 % of the students. About half of the students
select 0 V, i. e. assume there is no voltage across the open switch. The distribution of answers
is very similar for all four groups of participants, although a comparison between the results of
test versions 1.0 and 1.1 is problematic because of the fifth answering option being added.
The studies carried out by Cohen et al. (1983), Periago and Bohigas (2005), and Timmermann and Kautz (2014) used questions that were similar to each other. These are reproduced
in Figures 3, 4, and 5, respectively. In each study, students were asked about the voltage
across one bulb’s socket when that bulb was removed. While some of the answering options
were different, all studies listed the percentages of students that stated the voltage across the
socket would increase, would stay the same, or would decrease to 0.
Table 2 shows these data with some modifications to improve comparability. Cohen et al. (Figure 3) had the answering option “the bulb M will light more strongly”, which tests for the misconception of batteries being sources of constant current. Since the selection of this choice
gives no indication about ones understanding of the voltage across the open switch, we modified all percentages to not include participants that selected this answer. Periago and Bohigas
(2005) asked an open ended question. In Table 2, only students with answers that were could
be assigned to one of the three options mentioned above were used to calculate the percentages. Timmermann and Kautz (2014) gave students the option to state that the voltage would
decrease, but not to 0. As students that selected this answer clearly decided against the other
three options, they were not removed from the dataset.
Looking at the data in Table 2, one can see that the percentages are relatively similar. The
percentage of correct answers (the voltage across the socket increases) in always equal to or
Figure 2: Question 28 from the DIRECT v1.0 concept inventory (Engelhardt, 1997 and
2004)
Table 1: Results for question 28 of the DIRECT concept inventory shown in Figure 2
Answer
Test Version
1.0
Student Level
High school
University
1.1 High school
University
a!
Electronic mail: engelhar@phys.ksu.edu
1
N
0V
3V
454
681
251
441
45 %
63 %
45 %
44 %
6%
0%
5%
2%
D. Hestenes, M. Wells, and G. Swackhamer, ‘‘Force concept inventory,’’
Phys. Teach. 30 "3!, 141–158 "1992!.
2
R. J. Beichner, ‘‘Testing student interpretation of kinematics graphs,’’ Am.
J. Phys. 62 "8!, 750–762 "1994!.
3
P. V. Engelhardt, ‘‘Examining students’ understanding of electrical circuits
through multiple-choice testing and interviews,’’ unpublished doctoral dissertation, North Carolina State University "1997!. The interested reader
can read a more in-depth literature review in Chap. 2.
6V
12 V
none of the above
26 % 20 %
14 % 22 %
15 % 20 %
14 %
17 % Schmidt
27 %and Klaunig,
7%
"Vertrieb
Kiel, Germany, 1984!, pp. 139–151; L. C.
McDermott and P. S. Shaffer, ‘‘Research as a guide for curriculum development: An example from introductory electricity. Part I: Investigation of
student understanding,’’ Am. J. Phys. 60 "11!, 994 –10034"1992!.
9
See McDermott and Shaffer, Ref. 7.
10
R. Gott, ‘‘The place of electricity in the assessment of performance in
science,’’ in Aspects of Understanding Electricity, Proceedings of an International Workshop, edited by R. Duit, W. Jung, and C. von Rhöneck
"Vertrieb Schmidt & Klaunig, Kiel, Germany, 1984!, pp. 49– 61.
The voltage source E in the figure has no internal resistance. Both bulbs M and N are lit. N is removed from its
socket.
Consequently:
a. The bulb M will light more strongly.
b. The potential difference between D and E will become zero.
c. The potential difference between D and E will not
change.
d. The potential difference between D and E will increase.
Figure 3: Question 3 from Cohen et al. (1983)
Q9. We have a circuit made up of a battery, two light
bulbs M and N, and two resistors. If we disconnect light
bulb N and put nothing in its place, explain:
a) How will the potential difference vary between points
D and E?
b) How will the brightness of bulb M change?
(Comment on the variations regarding the first situation,
when bulb N was still connected).
Figure 4: Question 9 from Periago and Bohigas (2005)
The battery in the circuit at right can be treated as
an ideal voltage source. The long line indicates the
positive terminal. The five bulbs are identical. All
occurring voltages are within operating range of the
bulbs.
Does the absolute value of the voltage between
Y and Z, |VYZ |, (a) increase, (b) stay the same, (c)
decrease to 0, or (d) decrease, but not to 0, when
bulb D is removed from its socket.
I
X
I2
I1
I3
C
A
Y
B
E
D
Z
Figure 5: Exam Task 5 from Timmermann and Kautz (2014)
Table 2: Comparison of the answers reported to the questions in Figures 3, 4, and 5.
The percentages are modified to improve comparability.
potential difference between D and E / |VY Z |
Source
Teachers from Cohen et al. (1983)
Students from Cohen et al. (1983)
Periago and Bohigas (2005)
Timmermann and Kautz (2014)
N
increases
stays the same
decreases to 0
17
109
94
483
5%
13 %
4%
12 %
59 %
27 %
43 %
16 %
36 %
60 %
53 %
62 %
5
The circuit at right contains two identical batteries,
which can be treated as ideal voltage sources. The
short line indicates the negative clamp of the battery, the long line the positive clamp. The symbol
at node D indicates, that the potential there is zero.
Bulbs 1 and 2 are also identical, switch S is open
at first. Rank the voltages VAB , VAC and VAD . If two
voltages are equal to each other or one voltage is
equal to zero, state this explicitly.
(b) Circuit used in 2014
quiz and 2015 pre test
(a) Question used in quiz and both tests
(c) Circuit used in
2015 post test
Figure 6: Ranking questions from Timmermann and Kautz (2014) and Timmermann
et al. (2015). The same question was used with two different circuits.
below 13 %, and the percentage of participants answering that the voltage decreases to 0 is
between 36 % and 62 %. Considering only responses by students, this percentage is between
53 % and 62 %. This is only slightly higher than the percentages for 0 V across an open switch
reported by Engelhardt (1997).
In addition to the exam task shown in Figure 5, our 2014 publication also contained the quiz
question which is reproduced in Figure 6. Our 2015 publication used that same question
as a pre test and and as a post test. The pre test circuit was discussed in class during an
intervention to improve students’ understanding of voltage and thus could not be reused for
the post test. Instead, the post test used a circuit that was almost electrically identical but
looked very different. Table 3 lists the percentages of students that made certain incorrect
statements in their rankings. While they were administered during lecture time, the quizzes
were anonymous and students did not receive any credit for their participation. As not all
students handed in complete rankings, the percentages for incorrect statements are relative to
the number of students that ranked all the quantities in that statement.
The students in the 2014 publication made more incorrect statements than those in the 2015
publication. Unfortunately, we did not ask students to rank VBC explicitly in 2014. In the post
test, after students had instruction about the electric potential at the example of an open
switch, the percentages of incorrect statements is lower, although still higher that what we
had hoped for.
Possible Misconceptions
In the literature mentioned above, four misconceptions that could explain the incorrect answers are proposed. These will be discussed in the following.
Engelhardt (1997) describes three forms of what she calls “current/voltage confusion”. According to her, students can assume “(1) that the potential difference is a property of the current
and since there is no current, there can be no voltage, (2) more simply when there is one,
Table 3: Percentage of students that made specific statements in the ranking tasks. All
statements are incorrect. N gives the number of students that wrote an answer in the
respective ranking.
Incorrect Statement
Source
Type
Timmermann and Kautz (2014)
Timmermann et al. (2015)
Timmermann et al. (2015)
Quiz
Pre test
Post test
N
310
139
97
VBC = 0
VAB = VAC
VAC = 0
49 % of 91
31 % of 87
69 % of 287
50 % of 80
40 % of 83
51 % of 288
44 % of 89
31 % of 87
6
there is the other. They always come together, or (3) current causes the voltage so you must
have current to have voltage” (Engelhardt, 1997). Misconception (1) was also proposed by
Rhöneck (1982). An example for it would be the following statement made by a student in an
interview conducted by our group (described in Timmermann and Kautz, 2013). He stated
that “voltage is actually kind of the speed and current the number of electrons.”1 In this mental
model, there cannot be voltage without current, as there would be nothing that could have the
property of speed.
Periago and Bohigas (2005) suggested another misconception, which we will label as (4).
They conclude (4) “that the application of Ohm’s Law has not been learned meaningfully”.
Thus, students assume that Ohm’s Law can be applied to open switches, not recognizing
the infinite resistance of the open switch. In the quiz in Timmermann and Kautz (2014), one
student reasoned: “There is no current through A→B and B→C. Thus, from V = R · I follows
VAB = VAC = 0 V. There is current through A→D, thus (I 6= 0) ⇒ V 6= 0.”2 This interpretation
was also supported by Hussain et al. (2012).
Unfortunately, all four misconceptions are difficult to distinguish. In the quiz and tests, whose
results are presented in Table 3, 312 students gave a reasoning for their ranking of voltages.
Of those, 54 % made an argument along the lines of “because there is no current there also is
no voltage”. This statement could be a result of each of the misconceptions presented above.
While this could be considered a problem of language being too vague or ambiguous, we
believe the problem could be even more fundamental. To us, it seems several of these statements are logically identical, making it impossible to find an operational difference between
the statements.
Summary and Conclusions
In this paper, we compared data from several different studies. All studies report a relatively
small number of correct answers for the voltage across an open switch. Amongst the incorrect
answers, the idea that there is no voltage across an open switch (VOpen Circuit = 0 V) seems to
be the most prominent one. While the correct answers in the studies differ quite a lot in their
complexity, all studies include the VOpen Circuit = 0 V answer. Table 4 lists the frequency of this
answer for all university and high school students from the studies above. Not included are
students that had an intervention on this particular problem. The fact that 54 % of the students
who have had regular instruction in electrical engineering believe that there is no voltage drop
1
Original German transcript: Spannung ist ja eigentlich sozusagen die Geschwindigkeit und Strom die Anzahl
der Elektronen.
2
Original German transcript: Durch A→B und B→C fließt kein Strom, nach U =R·I gilt also UAB =UAC =0 V.
Durch A→D fließt Strom (I6=0)⇒U 6=0.
Table 4: Frequency of the misconception that the voltage across an open switch is zero
for all students that have not had instruction focusing on this misconception.
Study
Hussain et al. (2012)
Engelhardt (1997), test version 1.0, High school students
Engelhardt (1997), version 1.0, University students
Engelhardt (1997), version 1.1, High school students
Engelhardt (1997), version 1.1, University students
Cohen et al. (1983), students
Periago and Bohigas (2005), University students
Timmermann and Kautz (2014)
Timmermann et al. (2015)
All studies
N
VOpen Circuit = 0 V
47
454
681
251
441
109
94
483
91
66 %
45 %
63 %
45 %
44 %
60 %
53 %
62 %
49 %
2651
54 %
7
across an open switch is alarming. It is not unlikely that these students would answer the
same for open circuits in general.
Clearly, this is a mistake that experts do not do. In Timmermann et al. (2015) we tried to help
students gain a better understanding of voltage by introducing them to the concept of potential and confronting them with their inconsistent answers about the voltage across an open
switch. After the intervention, still 31 % of the students stated that the voltage across an open
switch would be zero. One of the problems during the design of the intervention was that the
students’ misconceptions about open circuit voltage are not fully understood.
Therefore, further investigation into the misconceptions about the voltage across open switches
and circuits is required. Until now, we failed to create well written questions to measure the
frequency of these misconceptions, as all misconceptions are often reduced to the “no current, therefore no voltage” reasoning. Consequently, we would recommend a series of interviews to gain a better insight into these four misconceptions and then – if possible – design
written questions to determine their frequency.
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Copyright © 2015 Dion Timmermann, Christian Kautz: The authors assign to the REES organisers and educational non-profit
institutions a non-exclusive licence to use this document for personal use and in courses of instruction provided that the article
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