EA3: Systems Dynamics
VIII. SYSTEMS DYNAMICS – Electrical Domain
Let us now delve into some simple electrical systems.
Once again, we will adopt a
systems approach here and infer a lot about the behavior of electrical systems by analogy
with their counterparts in the mechanics domain.
VIII.1 Electrical Systems Basics
VIII.1.1 Dynamic Variables:
The physical entities of interest in the electrical domain
are charge, current, and voltage.
While a complete physical understanding of these
concepts must be deferred to another course (PhysA35-2, or other courses on
electromagnetism), I will attempt to briefly highlight some of the essential concepts here.
: The building blocks of matter (elementary particles) have a property associated
with them called
, symbolically denoted by q
At one level of understanding, charge can be thought of as an analog of another
property of elementary particles -- mass.
Matter is discrete (quantized) and therefore the
mass of any measured amount of matter must be some multiple of the masses of all the
elementary particles making up that amount of matter.
When we are concerned with
things at the atomic scale, it makes sense to consider the unit of mass to be the mass of an
electron at rest: m
. The mass of a proton is 1836.15m
, and that of a neutron is
. However, when large amounts of matter are under consideration, it is simpler
to consider matter as being
and to use a better known (and larger) unit of
mass, the kilogram.
kg.) This is what we have been doing all
Analogous to mass, charges in nature are also quantized; that is, they occur only
in discrete multiples of the
, which is denoted by
mass, charges come in two types: positive or negative.
The charge of an electron is
labeled negative and the charge of a proton is labeled positive.
particles such as the neutron are neutral with no charge.
Once again, when large amounts
of charges are considered, it makes sense to ignore the fact that they come only in
discrete multiples, and to use a larger unit of charge, the Coulomb (C).
The charge of an
electron is –e; the charge of a proton is +e, where e=1.60x10
In nature, positive and
negative charges are found in great abundance, but they are almost always perfectly
This is not the primary analogy that we will use in this course.
But it is important to realize that different
analogies can be drawn between different physical entities depending on the context.
The purpose of an
analogy (or ‘similarity’ to use the standard terminology) is to leverage our understanding of one aspect of
nature to another area where we observe similar phenomena.