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The Physics of Electricity
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CHAPTER 1
The Physics of Electricity
1.1
BASIC QUANTITIES
1.1.1
Introduction
This chapter describes the quantities that are essential to our understanding of elec-
tricity: charge, voltage, current, resistance, and electric and magnetic elds. Most
students of science and engineering nd it very hard to gain an intuitive appreciation
of these quantities, since they are not part of the way we normally see and make
sense of the world around us. Electrical phenomena have a certain mystique that
derives from the difculty of associating them with our direct experience, but also
from the knowledge that they embody a potent, fundamental force of nature.
Electric charge is one of the basic dimensions of physical measurement, along
with mass, distance, time and temperature. All other units in physics can be
expressed as some combination of these ve terms. Unlike the other four,
however, charge is more remote from our sensory perception. While we can
easily visualize the size of an object, imagine its weight, or anticipate the duration
of a process, it is difcult to conceive of charge as a tangible phenomenon.
To be sure, electrical processes are vital to our bodies, from cell metabolism to
nervous impulses, but we do not usually conceptualize these in terms of electrical
quantities or forces. Our most direct and obvious experience of electricity is to
receive an electric shock. Here the presence of charge sends such a strong wave
of nervous impulses through our body that it produces a distinct and unique sen-
sation. Other rsthand encounters with electricity include hair that deantly
stands on end, a zap from a door knob, and static cling in the laundry. Yet these
experiences hardly translate into the context of electric power, where we can
witness the effects of electricity, such as a glowing light bulb or a rotating motor,
while the essential happenings take place silently and concealed within pieces of
metal. For the most part, then, electricity remains an abstraction to us, and we
rely on numerical and geometric representationsaided by liberal analogies from
other areas of the physical worldto form concepts and develop an intuition
about it.
1
Electric Power Systems: A Conceptual Introduction, by Alexandra von Meier
Copyright # 2006 John Wiley & Sons, Inc. 1.1.2
Charge
It was a major scientic accomplishment to integrate an understanding of electricity
with fundamental concepts about the microscopic nature of matter. Observations of
static electricity like those mentioned earlier were elegantly explained by Benjamin
Franklin in the late 1700s as follows: There exist in nature two types of a property
called charge, arbitrarily labeled positive and negative. Opposite charges attract
each other, while like charges repel. When certain materials rub together, one type of
charge can be transferred by friction and charge up objects that subsequently repel
objects of the same kind (hair), or attract objects of a different kind (polyester and
cotton, for instance).
Through a host of ingenious experiments,
1
scientists arrived at a model of the
atom as being composed of smaller individual particles with opposite charges,
held together by their electrical attraction. Specically, the nucleus of an atom,
which constitutes the vast majority of its mass, contains protons with a positive
charge, and is enshrouded by electrons with a negative charge. The nucleus also con-
tains neutrons, which resemble protons, except they have no charge. The electric
attraction between protons and electrons just balances the electrons natural ten-
dency to escape, which results from both their rapid movement, or kinetic energy,
and their mutual electric repulsion. (The repulsion among protons in the nucleus
is overcome by another type of force called the strong nuclear interaction, which
only acts over very short distances.)
This model explains both why most materials exhibit no obvious electrical prop-
erties, and how they can become charged under certain circumstances: The oppo-
site charges carried by electrons and protons are equivalent in magnitude, and when
electrons and protons are present in equal numbers (as they are in a normal atom),
these charges cancel each other in terms of their effect on their environment. Thus,
from the outside, the entire atom appears as if it had no charge whatsoever; it is
electrically neutral.
Yet individual electrons can sometimes escape from their atoms and travel else-
where. Friction, for instance, can cause electrons to be transferred from one material
into another. As a result, the material with excess electrons becomes negatively
charged, and the material with a decit of electrons becomes positively charged
(since the positive charge of its protons is no longer compensated). The ability of
electrons to travel also explains the phenomenon of electric current, as we will
see shortly.
Some atoms or groups of atoms (molecules) naturally occur with a net charge
because they contain an imbalanced number of protons and electrons; they are
called ions. The propensity of an atom or molecule to become an ionnamely, to
release electrons or accept additional onesresults from peculiarities in the geo-
metric pattern by which electrons occupy the space around the nuclei. Even electri-
cally neutral molecules can have a local appearance of charge that results from
1
Almost any introductory physics text will provide examples. For an explanation of the basic concepts of
electricity, I recommend Paul Hewitt, Conceptual Physics, Tenth Edition (Menlo Park, CA: Addison
Wesley, 2006).
2
THE PHYSICS OF ELECTRICITY imbalances in the spatial distribution of electronsthat is, electrons favoring one
side over the other side of the molecule. These electrical phenomena within mol-
ecules determine most of the physical and chemical properties of all the substances
we know.
2
While on the microscopic level, one deals with fundamental units of charge
(that of a single electron or proton), the practical unit of charge in the context of
electric power is the coulomb (C). One coulomb corresponds to the charge of
6.25
10
18
protons. Stated the other way around, one proton has a charge
of 1.6
10
219
C. One electron has a negative charge of the same magnitude,
21.6
10
219
C. In equations, charge is conventionally denoted by the symbol
Q or q.
1.1.3
Potential or Voltage
Because like charges repel and opposite charges attract, charge has a natural ten-
dency to spread out. A local accumulation or decit of electrons causes a
certain discomfort or tension:
3
unless physically restricted, these charges will
tend to move in such a way as to relieve the local imbalance. In rigorous physical
terms, the discomfort level is expressed as a level of energy. This energy (strictly,
electrical potential energy), said to be held or possessed by a charge, is analo-
gous to the mechanical potential energy possessed by a massive object when it is
elevated above the ground: we might say that, by virtue of its height, the object
has an inherent potential to fall down. A state of lower energycloser to the
ground, or farther away from like chargesrepresents a more comfortable
state, with a smaller potential fall.
The potential energy held by an object or charge in a particular location can be
specied in two ways that are physically equivalent: rst, it is the work
4
that
would be required in order to move the object or charge to that location. For
example, it takes work to lift an object; it also takes work to bring an electron
near an accumulation of more electrons. Alternatively, the potential energy is the
work the object or charge would do in order to move from that location, through
interacting with the objects in its way. For example, a weight suspended by a
rubber band will stretch the rubber band in order to move downward with the pull
of gravity (from higher to lower gravitational potential). A charge moving toward
a more comfortable location might do work by producing heat in the wire
through which it ows.
2
For example, water owes its amazing liquidity and density at room temperature to the electrical attraction
among its neutral molecules that results from each molecule being polarized: casually speaking, the elec-
trons prefer to hang out near the oxygen atom as opposed to the hydrogen atoms of H
2
O; a chemist would
say that oxygen has a greater electronegativity than hydrogen. The resulting attraction between these
polarized ends of molecules is called a hydrogen bond, which is essential to all aspects of our physical life.
3
The term tension is actually synonymous with voltage or potential, mainly in British usage.
4
In physics, work is equivalent to and measured in the same units as energy, with the implied sense of
exerting a force to push or pull something over some distance (Work ¼ Force
Distance).
1.1
BASIC QUANTITIES
3 This notion of work is crucial because, as we will see later, it represents the
physical basis of transferring and utilizing electrical energy. In order to make
this work a