Electrical Conduction - Ohm's
Law
The Beginning:
Stephen Gray,
a British chemist, is generall credited with discovering that
electricity can flow (1729). He found that corks stuck in the
ends of glass
tubes become electrified when the tubes are rubbed. He also
transmitted
electricity approximately 150 metres through a hemp thread supported by
silk cords and, in another demonstration, sent electricity even farther
through metal wire. Gray concluded that electricity flowed
everywhere. (reference)
The Great Enabling Technology
- Alessandro Volta's "Column Battery" (~1800)
 |
The "electromotive
force" is scalable!
|
Quantification of Electrical
Conductivity - Ohm's Law
|
In 1827 what is now known as Ohm's
law appeared in Die
galvanische Kette, mathematisch bearbeitet.
Between 1825-27, Georg Simon Ohm (1789-1854), professor of mathematics
at the Jesuit College of Cologne, had been studying electrical
conduction
following as a model Fourier's study of heat conduction.
Ohm's
Law states that the strength of an unvarying electric current is
directly
proportional to the electromotive force, and inversely proportional to
the resistance of the circuit concerned. Need it be said, the
unit of resistance
is named after him. (Reference
1 and Reference
2)
|
In a series of experiments in
1825 Ohm demonstrated that there
are
no "perfect" electrical conductors.
Every conductor he tested offered some level of "resistance."
Ohm's law of states that if temperature remains constant,
the current flowing through a conductors is proportional to the
potential
difference (voltage) across it. In modern words, current equals
voltage divided
by resistance. In most equations and
diagrams, "I" represents the current, "V" the
voltage, and "R" the resistance.
Current = Voltage/Resistance
The diagram below shows
exactly how
Ohm's Law works with a common battery. The yellow symbol represents a
current measuring device - say, a light
bulb. The tan wire shows where the
resistence
occurs.
Formally, electrical resistance
is the property of any object or substance to resist or oppose the flow
of
an electrical current. The unit of resistance is the
ohm symbolized by the Greek letter omega and the value of the electric
resistance is commonly abbreviated as
R. For certain electrical calculations the
reciprocal
of resistance is used, 1/R, which is termed the conductance, G.
The unit of
conductance is the mho, or ohm spelled backward, and the symbol is an
inverted
omega.
In principle, it is relatively
simple
to measure the resistance of a strand of wire by connecting a battery
to a wire
of known voltage and then measuring the current flowing through the
wire.
The problem with using
resistance
as a measure is that it depends not only on the material from which
the wire is made, but also the geometry of the wire. If we were to
increase
the length of wire, for example, the measured resistance would
increase.
Also, if we were to decrease the diameter of the wire, the measured
resistance
would increase. We want to define a property that describes a
material's
ability to transmit electrical current that is independent of the
geometrical
factors.
The
geometrically-independent
quantity
that is used is called resistivity and is usually indicated by the
Greek
symbol rho. In the case of a wire,
resistivity
is defined as the resistance in the wire, times the cross-sectional
area
of the wire, divided by the length of the wire. The units
associated
with resistivity are thus,
ohm - m
(ohm
- meters). The diagram below shows this equation as it would work with
a common wire, represented by the tan cylinder.
High
values of resistivity
imply
that the material making up the wire is very resistant to the flow of
electricity.
Low values of resistivity imply that the material making up the wire
transmits
electricial current very easily.
The Resistivity of
Several
Natural Elements and Compounds
|
| Substance |
Resistivity (rho)
(ohm - meters)
|
Substance |
Resistivity (rho)
(ohm - meters) |
Silver
|
1.59 x 10-8
|
Sea Water |
0.2 |
Copper
|
1.68 x 10-8 |
Ground Water |
0.5 - 300 |
Gold
|
2.21 x 10-8 |
Germanium
|
0.46
|
| Aluminum |
2.65 x 10-8
|
Silicon |
640 |
| Brass |
3.5 x 10-8 |
Sphalerite |
1.5 - 1 x 107 |
Sodium
|
4.8 x 10-8 |
Igneous Rock - Diabase |
20 - 5 x 107 |
| Tungsten |
5.6 x 10-8 |
Wood |
1010 |
Iron
|
9.71 x 10-8 |
Calcite |
2 x 1012 |
| Platinum |
10.6 x 10-8
|
Rock Salt |
30 - 1 x 1013 |
| Lead |
20.8 x 10-8 |
Mica |
1013
- 1014 |
| Constantan |
49 x 10-8
|
Glass |
1010
- 10 14 |
Stainless Steel
|
72.0 x 10-8 |
Aluminum Oxide
|
1011
|
| Mercury
|
98 x 10-8 |
Silicon Dioxide
|
1016 |
|
Nichrome
(Ni,Fe,Cr alloy) |
100 x 10-8
|
Rubber |
1013 - 10 16 |
|
|
Quartz |
4 x 1010
- 2 x 1014 |
| Carbon (graphite) |
3-60 x 10-5
|
Quartz (fused) |
7.5 x 1017
|
|
|
Carbon (diamond)
|
>1015 |
