We have investigated students' qualitative understanding of dc circuits containing resistors and a capacitor. We found that a year after traditional lecture instruction as part of an introductory physics course, most students were unable to predict the behavior of a series circuit consisting of a battery, a bulb, and a capacitor. Among the difficulties identified we found that almost half of the students implicitly abandoned the idea that a complete circuit is necessary for a bulb to light when a capacitor is introduced into the circuit. We have developed curriculum that enables students to construct a phenomenological model in which they liken the behavior of a capacitor to that of a wire, a switch, and a battery; this allows them to qualitatively describe circuits with batteries, bulbs, and capacitors. We have also developed curriculum on the determination of RC times. Post-test results show a significant increase in understanding of capacitive circuits.

1.
R.
Cohen
,
B.
Eylon
, and
U.
Ganiel
, “
Potential difference and current in simple electric circuits: A study of students concepts
,”
Am. J. Phys.
51
(
5
),
407
412
(
1983
).
2.
See examples from
R.
Duit
,
W.
Jung
, and
C.
von Rhöneck
, “
Aspects of Understanding Electricity
,” in
Proceedings of an International Workshop
, Ludwigsburg, IPN, Kiel,
1984
.
3.
D.
Psillos
,
P.
Koumaras
, and
A.
Tiberghien
, “
Voltage presented as a primary concept in an introductory teaching sequence on DC circuits
,”
Int. J. Sci. Educ.
10
(
1
),
29
43
(
1988
).
4.
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
).
Also see the companion article,
L. C.
McDermott
and
P. S.
Shaffer
, “
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
).
5.
P.
Mulhall
,
B.
McKittrick
, and
R.
Gunstone
, “
A perspective on the resolution of confusions in the teaching of electricity
,”
Res. Sci. Educ.
31
,
575
587
(
2001
).
6.
A. S.
Rosenthal
and
C.
Henderson
, “
Teaching about circuits at the introductory level: An emphasis on potential difference
,”
Am. J. Phys.
74
(
4
)
324
328
(
2006
).
7.
R.
Duit
,
Students' and Teachers’ Conceptions and Science Education
(
IPN
,
Kiel, Germany
,
2009
). Available online at <http://www.ipn.uni-kiel.de/aktuell/stcse/stcse.html>.
8.
R. G.
Newburgh
, “
Capacitors, Water Bottles, and Kirchhoff's Loop Rule
,”
Phys. Teach.
31
,
16
17
(
1993
).
9.
B. A.
Thacker
,
U.
Ganiel
, and
D.
Boys
, “
Macroscopic phenomena and microscopic processes: Student understanding of transients in direct current electric circuits
,”
Am. J. Phys.
67
(
7
)
S25
S31
(
1999
).
10.
S. J.
Osmond
, “
A simple analogy useful in the teaching of capacitors at A-level
,”
Phys. Educ.
19
,
132
134
(
1984
).
11.
M. S.
Steinberg
and
C. L.
Wainwright
, “
Using models to teach electricity—The CASTLE Project
,”
Phys. Teach.
31
,
353
357
(
1993
).
For a critique of this model, see the paired article:
E. P.
Mosca
and
M. L.
de Jong
, “
Implications of Using the CASTLE Model
,”
Phys. Teach.
31
,
357
359
(
1993
).
12.
L. C.
McDermott
and the Physics Education Group,
Physics by Inquiry
(
Wiley
,
New York
,
1996
), pp.
383
517
.
13.
D. P.
Smith
and
P.
van Kampen
, “
Teaching electric circuits with multiple batteries: A qualitative approach
,”
Phys. Rev. ST Phys. Educ. Res.
7
,
020115
1
020115
10
(
2011
).
14.
P. V.
Engelhardt
and
R. J.
Beichner
, “
Students’ understanding of direct current resistive electrical circuits
,”
Am. J. Phys.
72(
1
),
98
115
(
2004
).
15.
D. M.
Shipstone
, “
Electricity in Simple Circuits
,” in
Children’s Ideas in Science
, edited by
R.
Driver
,
E.
Guesne
, and
A.
Tiberghien
(
Open U.P.
,
Milton Keynes
,
1985
) pp.
291
316
.
16.
H.
Schwedes
, “
Teaching with Analogies
,” in
Proceedings of the second PhD Summerschool on European Research in Science Education
, edited by
D.
Psillos
(
Art of Text S.A.
,
Thessaloniki
,
1995
). See also H. Schwedes and W. G. Dudeck, “Teaching Electricity by Help of Water,” in Research in Science Education in Europe, edited by G. Welford, J. Osborne, and P. Scott (The Falmers Press, London, 1996).
17.
The pilot version of the curriculum on capacitors in single loops was developed by Mike Gearen (Punahou High School, Honolulu, Hawaii) and Andrew Crouse, then a graduate student in the Physics Education Group at the University of Washington.
18.
For various reasons only 39 out of a total of 51 students completed the pretest.
19.
Typically, the pretest and post-test questions were answered by 30–50 students, which is not a large enough sample size to allow for a robust quantitative analysis. Nevertheless, we think it is meaningful to indicate the prevalence of certain answers in percentages rounded to the nearest 5%; however, one must bear in mind that the error bars are larger than suggested by this practice. The small number allowed us to examine all answers independently and compare our analyses.
20.
For a discussion of students making a false analogy between RC and LR circuits, see
R. G.
Newburgh
, “
Conceptual difficulties with rates of change, or Zeno redux
,”
Phys. Educ.
37
,
147
149
(
2002
).
21.
This has been noted previously; see, e.g.,
R.
Ehrlich
,
Turning the World Inside Out and 174 Other Simple Physics Demonstrations
(
Princeton U.P.
,
Princeton, NJ
,
1990
), pp.
150
151
.
22.
Alternatively, at this stage students can think of the capacitor as a battery with varying voltage, but few spontaneously do so.
23.
For an in-depth discussion of students’ difficulties with the concept of a complete circuit, see
M. R.
Stetzer
,
P.
van Kampen
,
P. S.
Shaffer
, and
L. C.
McDermott
, “
New insights into student understanding of complete circuits and the conservation of current
,”
Am. J. Phys.
81
(
2
),
134
143
(
2013
).
24.
As an aside, an understanding of this circuit would be very useful preparation for the teaching of, say, a monostable multivibrator circuit, where bulb B could be replaced with a simple integrated circuit. See, for example,
P.
Horowitz
and
W.
Hill
,
The Art of Electronics
(
Cambridge U.P.
,
1989
), p.
517
ff
.
25.
For a full discussion of hysteresis effects in flashlight bulbs, see
D. A.
Clauss
,
R. M.
Ralich
, and
R. D.
Ramsier
, “
Hysteresis in a light bulb: Connecting electricity and thermodynamics with simple experiments and simulations
,”
Eur. J. Phys.
22
(
5
),
385
395
(
2001
).
26.
R. C.
Tolman
and
T. D.
Stewart
, “
The electromotive force produced by the acceleration of metals
,”
Phys. Rev.
8
,
97
117
(
1916
);
R. C.
Tolman
and
T. D.
Stewart
, “
The mass of the electric carrier in copper, silver, and aluminium
,”
Phys. Rev.
9
,
164
167
(
1917
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.