potential and the analysis of the complete circuit. According to the theory in
electrostatics, there could be no volume charge gradient inside the conductor, and
Kirchhoff solved the problem by putting a charge gradient on the surface (Whittaker
1987). Furthermore, Kirchhoff experimentally demonstrated that Volta’s “electrical
voltage” and Poisson’s potential function were numerically identical in a conductor
and therefore could be reduced to a single concept. Since advances in Kirchhoff’s
electrical theory, electrostatics and electrokinetics have converged into a single
electrical theory (Heilbron 1979). Taking Coulomb’s law into account, the theory
explained that direct current is due to the flow of electrons under the influence of
electrical forces and under the influence of a potential difference across the poles of a
battery. Later, with works on the field model of Faraday and, Maxwell (1865), the
electrical theory of current circuits received a new impulse. In this interpretation, the
electrical currents in cables, resistors, etc., are driven by electric fields. The electric
field has its source only in the surface charge distributions on the cable (Jefimenko
1966; Härtel 1993).
The epistemological analysis identifies three key problems: (a) relations between
electrostatics and current; (b) relations between macroscopic phenomena and microscopic level models; (c) relations between operative definitions of charge, potential,
and electric capacity and their meaning in electrostatics and current.
We consider explanations at macroscopic level those that are focused on the
physical quantities, such as resistance, current, and potential difference from the
overall perspective of the circuit. Quantities such as conventional current and those
defined at the level of operational definitions (for example, Ohms’ law or the formula
that relates potential and field). Instead, we consider explanations at the microscopic
level those that are focused at the local level in terms of electrons, electron current, or
charge density (Griffith 2014). After covering electrostatics, students are often
confronted with a new situation (e.g., electrokinetic phenomena) that not only
leads to new phenomena (charges of movement in a wire) but also challenges their
view that an electric field is required for a current to flow in a wire. However,
literature show that students do not use to seeing circuits as being driven by an
electric field that acts on electrons at the microscopic level (whether or not this
results in a conventional current at the macroscopic level) (Hirvonen 2007).
Taking into account the epistemological key problems and students learning
difficulties, we defined the learning objectives for the TLS on “Fundamental of
DC circuits”. Reasoning in qualitative and quantitative terms about the phenomena
that occur in electrical circuits involves to develop robust models of the microscopic
processes underlying them, which lead to the observed phenomena and their macroscopic explanations (Leniz et al. 2017). Consequently, first of all, it is a question of
learning a microscopic model of electrical current in a simple DC circuit with the
following characteristics:
LO.1: Recognize that the magnitudes of electric field and electric potential defined in
electrostatics are the same as those used in electrodynamics. Knowing how to
apply these magnitudes in both contexts.
168
J. Guisasola et al.
electrostatics, there could be no volume charge gradient inside the conductor, and
Kirchhoff solved the problem by putting a charge gradient on the surface (Whittaker
1987). Furthermore, Kirchhoff experimentally demonstrated that Volta’s “electrical
voltage” and Poisson’s potential function were numerically identical in a conductor
and therefore could be reduced to a single concept. Since advances in Kirchhoff’s
electrical theory, electrostatics and electrokinetics have converged into a single
electrical theory (Heilbron 1979). Taking Coulomb’s law into account, the theory
explained that direct current is due to the flow of electrons under the influence of
electrical forces and under the influence of a potential difference across the poles of a
battery. Later, with works on the field model of Faraday and, Maxwell (1865), the
electrical theory of current circuits received a new impulse. In this interpretation, the
electrical currents in cables, resistors, etc., are driven by electric fields. The electric
field has its source only in the surface charge distributions on the cable (Jefimenko
1966; Härtel 1993).
The epistemological analysis identifies three key problems: (a) relations between
electrostatics and current; (b) relations between macroscopic phenomena and microscopic level models; (c) relations between operative definitions of charge, potential,
and electric capacity and their meaning in electrostatics and current.
We consider explanations at macroscopic level those that are focused on the
physical quantities, such as resistance, current, and potential difference from the
overall perspective of the circuit. Quantities such as conventional current and those
defined at the level of operational definitions (for example, Ohms’ law or the formula
that relates potential and field). Instead, we consider explanations at the microscopic
level those that are focused at the local level in terms of electrons, electron current, or
charge density (Griffith 2014). After covering electrostatics, students are often
confronted with a new situation (e.g., electrokinetic phenomena) that not only
leads to new phenomena (charges of movement in a wire) but also challenges their
view that an electric field is required for a current to flow in a wire. However,
literature show that students do not use to seeing circuits as being driven by an
electric field that acts on electrons at the microscopic level (whether or not this
results in a conventional current at the macroscopic level) (Hirvonen 2007).
Taking into account the epistemological key problems and students learning
difficulties, we defined the learning objectives for the TLS on “Fundamental of
DC circuits”. Reasoning in qualitative and quantitative terms about the phenomena
that occur in electrical circuits involves to develop robust models of the microscopic
processes underlying them, which lead to the observed phenomena and their macroscopic explanations (Leniz et al. 2017). Consequently, first of all, it is a question of
learning a microscopic model of electrical current in a simple DC circuit with the
following characteristics:
LO.1: Recognize that the magnitudes of electric field and electric potential defined in
electrostatics are the same as those used in electrodynamics. Knowing how to
apply these magnitudes in both contexts.
168
J. Guisasola et al.