Research in Engineering Education Symposium 2011 - rees2009

Universidad Politécnica de Madrid (UPM) Página 45 de 957
Student understanding of modeling aspects
In order to probe student understanding of the model aspects of DC circuit analysis, we
administered two ungraded quiz questions at the beginning of a lecture period well into
the final third of the semester. By that time, coverage of DC circuits had been completed
and the course had moved on to other topics (AC circuits in TUHH-ME, static electric and
magnetic fields in TUHH-EE). A variant of one question was also given as part of a final
exam to a different cohort of students in one of the courses (TUHH-ME).
Question on mathematical representation
In one of the questions given to about 300 students in TUHH-ME, the students were shown
the circuit diagram in Figure 1. They were then given the following three tasks: (a) to state
a mathematical relationship between the electric potentials at points Q and T, (b) to state
a mathematical relationship between the currents I1 and I2, and between I1 and I3, and (c) to
decide whether it is possible to insert an additional voltage source UC between points X
and Y (with its arrow pointing down), and to state what values can be chosen for UC.
We expected students to recognize that for the potentials at points Q and T, the most
simple relationship that could be inferred from the diagram (and the only one in terms of
the given quantities) involves the voltage source UB. By the definition of a voltage source
(and considering the sign convention used in the course), the correct answer for part (a)
would be √T – √Q = UB. Similarly, for part (b) one may infer from the definition of a current
source and Kirchhoff’s current law (KCL) that I1 – I2 = IA and I1 + I3 = IA. In part (c), students
needed to recognize that the presence of UB in the circuit diagram mathematically
corresponds to the statement in part (a) above; that a duplication of that statement has no
effect on the solvability of the corresponding system of equations; and that therefore an
additional source may be added between X and Y as long as it satisfies the condition that
UC = – UB. A more physical argument would be that two ideal batteries (i.e., ideal voltage
sources) can be connected in parallel without any resulting change to the circuit.
Figure 1: Circuit diagram in quiz question on mathematical representation
Of the 188 students who gave a non-blank answer to task (a) of this question, about 30%
specified a relationship between the potentials at points Q and T involving UB that was
correct apart from possibly a sign error. Most of the remaining answers asserted that one
Proceedings of Research in Engineering Education Symposium 2011
Madrid, 4 th - 7 th October 2011