Geoscience Reference
In-Depth Information
5.2 ohM'S lAW And ReSIStIvIty (oR eleCtRICAl CondUCtIvIty)
Consider a cylinder, as shown in Figure 5.1, composed of uniform material, having a length, L ,
and at each of its ends, a cross-sectional area, A . An electric current, I , defined as the flow rate of
electric charge, is applied at one end of the cylinder and exits the other. The cylinder, to a greater
or lesser extent, opposes this through-flow of electric current, thereby causing a drop in electric
potential, Δ V , which occurs along the column's length from the end where I enters to the end where
I leaves. Electric potential can be described as the potential energy for a unit charge resulting from
its position within an electric field. As indicated by Equation (5.1), Δ V is proportional to I , and the
proportionality constant is the resistance, R , which is a characteristic of the cylinder's overall ability
to oppose current flow:
V I
=−
(5.1)
The minus sign in Equation (5.1) simply indicates that current flow is in a direction opposite to that
of increasing electric potential. Equation (5.1) is referred to as Ohm's law, and the resistance, R , of
the cylinder can itself be expressed:
= ρ
L
A
R
(5.2)
where again, L and A , respectively, are the length and cross-sectional area of the cylinder, and ρ is
the resistivity.
Resistivity is a property only of the material
composing the cylinder (Figure 5.1) and repre-
sents the capability of that particular material to
oppose the flow of electric current. The ρ values
for soil and rock materials are typically reported
in units of ohm-meters (Ωm). Electrical conduc-
tivity, σ, is the reciprocal of ρ (= 1/ρ), and is a
property indicative of a material's ability to con-
vey electrical current, not oppose it. Instead of
ρ, the value of σ, in units of millisiemens/meter
(mS/m), is most commonly reported in agricul-
ture. For reference, a ρ value of 1 Ωm corre-
sponds to a σ value of 1000 mS/m. Furthermore,
it should be pointed out that agricultural literature often employs EC as the symbol for electri-
cal conductivity rather than, σ, which is the symbol for electrical conductivity routinely found in
near-surface geophysics texts. The resistivity methods utilized for agricultural purposes are focused
largely on the determination of σ (EC) values for soil materials.
V
ρ
I
I
A
L
fIGURe 5.1 Flow of electric current, I , through a
cylinder composed of uniform material with resis-
tivity , ρ, which produces a difference in an electric
potential, Δ V , from one end of the cylinder to the
other.
5.3 fACtoRS InflUenCInG ReSIStIvIty (oR eleCtRICAl CondUCtIvIty)
In SoIl MAteRIAlS
This section provides a brief overview of the factors influencing soil resistivity (or electrical con-
ductivity). Additional discussion regarding this subject is given in Chapter 2 and Chapter 4. The
ability of a soil material to transfer electric current, as indicated by the resistivity (or electrical con-
ductivity) of the soil, is determined by the components that make up the soil. Soil typically consists
of solid, gas, and liquid phases (Figure 5.2). The solid phase of the soil includes both mineral and
organic matter and, excluding the larger fragments (generally rock materials), can be divided by
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