Since Ruth Chabay and I have successfully taught the microscopic model of
DC and RC circuits (followed by the standard macro model) for many years in
the university-level calculus-based intro course, I should describe why we
do that. The most important reason is to treat electrostatics and circuits
as one subject rather than two. Traditionally circuits are taught as though
circuit behavior has nothing to do with electrostatics. This is a sin
against the drive for unification.
A closely related reason is to keep alive the central concepts of charge
and field, which tend to fade away when circuits are studied, because only
currents and potential appear, and charge and field disappear from view.
Circuits seen from a micro viewpoint broaden and deepen the important
concept of polarization. In electrostatics, currents flow briefly during a
transient that establishes the final equilibrium state, in which the
polarization charges add a contribution to the net field in such a way as
to reduce the net field to zero in the interior of a conductor. In DC
circuits there is a transient phase in which polarization charges appear on
the surfaces of the circuit elements which add a contribution to the net
field in the wires in such a way as to lead to a distribution of field in
the wires that is consistent with the steady-state conditions
(characterized by the Kirchhoff loop and node rules).
We emphasize that the Kirchhoff node rule is not something special to
circuits: it's just charge conservation in the steady state, and that the
Kirchhoff loop rule is not something special to circuits, it's just the
electrostatic law that round-trip potential difference is zero.
There are some additional issues that sometimes arise that have answers in
the micro view but not in the macro view, such as "When the electrons come
to a Y in the circuit, how do they know which branch to take?"
The micro description of circiuts offers an accessible example of a fedback
system, which can be interesting.
The standard treatment in terms of special-case Kirchhoff rules provides no
sense of mechanism, no sense of how the steady state comes into being. It
can be and often is taught in a way that is rather heavily rote in nature,
with little or no physics in it. I once heard a talk at an AAPT meeting by
a group who were teaching intro physics that only required calculus
concurrently, not as a prerequisite. They decided to delay kinematics until
the students had encountered derivatives. What to do while waiting? I
quickly made the guess that, since it had to be something with little or no
physics content, it had to be either geometrical optics or DC circuits. It
turned out that they had chosen DC circuits.
We've had engineering students tell us, "I'm taking EE circuits this
semester at the same time I'm taking your physics course, and they
complement each other,. In my circuits course I'm calculating voltages and
currents, and in your course I'm learning why there are these voltages and
currents."
We were particularly delighted by the student who told us proudly, "My
boyfriend is a senior in EE and taking a circuits course, and I'm
explaining to him how circuits actually work."