The research reported in this paper represents an in-depth examination of the finding from an earlier investigation that university students often do not develop a functional understanding of the concept of a complete circuit. Participants in this study included undergraduates in introductory and upper-division physics courses as well as graduate teaching assistants. Although the concept of a complete circuit is covered in the standard undergraduate curriculum, students in all three groups had difficulty in applying this concept to single-loop, resistive circuits. Students frequently did not apply the conservation of current when analyzing circuits containing more than one battery. Certain basic conceptual difficulties spanned all of the populations and even persisted after instruction in upper-division courses that involved analog electronics.

1.
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
1003
(
1992
);
L. C.
McDermott
and
P. S.
Shaffer
,
printer's erratum
to Part I,
61
(
11
),
81
(
1993
).
2.
L. C.
McDermott
,
P. S.
Shaffer
, and
C. P.
Constantinou
, “
Preparing teachers to teach physics and physical science by inquiry
,”
Phys. Educ.
35
(
6
),
411
416
(
2000
);
and
P. V.
Engelhardt
and
R. J.
Beichner
, “
Students' understanding of direct current resistive electrical circuits
,”
Am. J. Phys.
72
,
98
115
(
2004
).
3.
Related work on transients in dc circuits is reported in
B. A.
Thacker
,
U.
Ganiel
, and
D.
Boys
, “
Macroscopic phenomena and microscopic processes: Student understanding of transients in direct current electric circuits
,”
Phys. Educ. Res., Am. J. Phys. Suppl.
67
(
7
),
S25
S31
(
1999
).
4.
Related work was recently reported by Smith and van Kampen. See
D. P.
Smith
and
P.
van Kampen
, “
Teaching electric circuits with multiple batteries: A qualitative approach
,”
Phys. Rev. ST Phys. Educ. Res.
7
,
020115
(
2011
);
and
D. P.
Smith
and
P.
van Kampen
, “
A qualitative approach to teaching capacitive circuits
,”
Am. J. Phys.
(submitted).
5.
P. V.
Engelhardt
,
K. E.
Gray
, and
N. S.
Rebello
, “
How many students does it take before we see the light?
,”
Phys. Teach.
42
(
4
),
216
221
(
2004
).
6.
See, for example,
N. H.
Fredette
and
J. J.
Clement
, “
Student misconceptions of an electric circuit: What do they mean?
,”
J. College Sci. Teach.
10
,
280
285
(
1981
);
D. M.
Shipstone
,
C. v.
Rhöneck
,
W.
Jung
,
C.
Kärrqvist
,
J.
Dupin
,
S.
Johsua
, and
P.
Licht
, “
A study of students' understanding of electricity in five European countries
,”
Int. J. Sci. Educ.
10
,
303
316
(
1988
);
R.
Cohen
,
B.
Eylon
, and
U.
Ganiel
, “
Potential difference and current in simple electric circuits: A study of students' concepts
,”
Am. J. Phys.
51
,
407
412
(
1983
);
R.
Cohen
,
B.
Eylon
,
U.
Ganiel
, and
Research on Physics Education
, in Proceedings of the First International Workshop, La Londe Les Maures, France, organized by
G.
Delacôte
,
A.
Tiberghien
, and
J.
Schwartz
(Éditions du CNRS, Paris, 1983).
7.
L. C.
McDermott
and the Physics Education Group at the University of Washington,
Physics by Inquiry
(
Wiley
,
NY
,
1996
). This is a self-contained, laboratory-based curriculum intended for use in courses and workshops for preservice and inservice K-12 teachers.
8.
L. C.
McDermott
,
P. S.
Shaffer
, and the Physics Education Group at the University of Washington,
Tutorials in Introductory Physics
, First Edition (
Prentice-Hall
,
Upper Saddle River, NJ
,
2002
); Instructor's Guide (2003). (A Preliminary Edition was published in 1998 and a Second Edition will be available in 2013.) This is a supplementary curriculum designed for use in small-group sessions accompanying a standard introductory course taught by lecture, laboratory, and textbook.
9.
P. S.
Shaffer
and
L. C.
McDermott
, “
Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of instructional strategies
,”
Am. J. Phys.
60
(
11
),
1003
1013
(
1992
).
10.
For an overview of the role of research in the development of tutorials, see
L. C.
McDermott
, Oersted Medal Lecture 2001: “
Physics education research—the key to student learning
,”
Am. J. Phys.
69
(
11
),
1127
1137
(
2001
).
11.
T. R.
Brown
,
T. F.
Slater
, and
J. P.
Adams
, “
Gender differences with batteries and bulbs
,”
Phys. Teach.
36
(
9
),
526
527
(
1998
);
and
T. F.
Slater
,
J. P.
Adams
, and
T. R.
Brown
, “
Undergraduate success—and failure—in completing a simple circuit: Locating a short in students' basic physics knowledge
,”
J. Coll. Sci. Teach.
30
(
2
),
96
99
(
2000
).
12.
This question is very similar to that used by Engelhardt et al in Ref. 5.
13.

Although not explicitly stated in Ref. 5, this question was likely administered prior to university-level circuits instruction since E&M is typically covered in the second-semester of the course. It is also important to note that the question in Ref. 5 was not paired with the battery, bulb, and wire question; it is possible that this may have contributed to observed differences in student performance.

14.

On multiple-choice versions of the single- and double-wire questions, up to 30% of students who identified the internal structure of the light bulb correctly selected at least one incorrect external circuit (e.g., a short or open circuit) or indicated that it was not possible to light the bulb.

15.

If a student who drew a short circuit also sketched or described an unclear internal structure of the bulb, it was not possible to claim that the internal and external connections were consistent. These responses were therefore categorized as inconsistent shorts.

16.

A functional understanding connotes the ability to interpret a concept properly, to distinguish it from related concepts, and to do the reasoning required to apply the concept correctly to objects and events in the real world.

17.

In the introductory calculus-based course, instruction takes place in lecture, laboratory, and tutorial. There are two published tutorials on electric circuits in the First Edition of Ref. 8. Throughout this investigation, the first of the two tutorials was omitted since a laboratory session adapted from the first tutorial was in routine use as part of a sequence of 3–4 laboratory sessions on electric circuits. During this same period, a new tutorial on multiple-battery, multiple-loop dc circuits was also introduced and revised. The new tutorial will appear in the Second Edition of Ref. 8.

18.
A.
Benseghir
and
J.-L.
Closset
, “
The electrostatics-electrokinetics transition: historical and educational difficulties
,”
Int. J. Sci. Educ.
18
(
2
),
179
191
(
1996
).
19.
L.
Viennot
, “
From electrostatics to electrodynamics: historical and present difficulties
,” in
Reasoning in physics: The part of common sense
, Trans. Amelie Moisy (
Kluwer Academic Publishers
,
Norwell, MA
,
2001
), pp.
173
189
.
20.

This estimate is in good agreement with results from a multiple-choice version of ISBQ also administered on a final examination (N = 100). Approximately 90% of the students identified the correct internal structure of the bulb.

21.

The term operational definition was first introduced to many physicists by Percy W. Bridgman (1927) in The Logic of Modern Physics. There is more than one interpretation of this term. In this paper and in the curricula developed by the Physics Education Group, an operational definition is a series of steps that, if followed by different individuals, would lead unambiguously to the same result (e.g., a specific number or event). Thus, an operational definition of a complete circuit specifies the conditions under which a (real or imagined) bulb will light.

22.

Multiple-battery questions were designed during the development of a new tutorial on multiple-battery, multiple-loop dc circuits. See Ref. 17.

23.

Related work is reported in the articles listed in Ref. 4.

24.

This student incorrectly interpreted the longer line of the battery symbol as a representation of the negative terminal.

25.
The text for the course is
P.
Horowitz
and
W.
Hill
,
The Art of Electronics, Second Edition
(
Cambridge U.P.
,
NY
,
1991
).
26.

Such differences arise from a variety of factors. For example, only a small percentage of students enrolled in the introductory course pursue degrees in physics (and therefore take analog electronics). On the other hand, not all of the students enrolled in analog electronics took introductory physics at UW; in addition, for those students who did take introductory physics at UW, there is at least one quarter in which the tutorial on multiple-battery circuits was not used (after it was developed).

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