Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 240

conductivity is greater than 10 5 S/m. Between these two
arbitrary boundaries are semiconductors and electrolytes.
Conductors, such as metals, contain many loosely bound
electrons and so the electric current can ow compara-
tively easily when an electric field (a potential difference) is
applied. The equivalent materials in the plumbing analogy
are porous and permeable formations through which water
passes freely. Insulators, also called non-conductors or
dielectrics, do not have free electrons so the flow of the
current is much more difficult, with dielectric conduction
the usual mechanism. These materials are equivalent to
rocks with minimal porosity and permeability.
Semiconductors, and electrolytes, resemble the conduct-
ors when a static electrical potential is applied, in that
conductivity involves movement of electrons. However,
they have fewer free electrons and more energy is required
to move them, so their conductivity is lower. It is also
critically dependent on even very small amounts of impur-
ities which cause imperfections in the minerals

known as the resistivity ( ) of the material and is obtained

by applying a geometric correction factor (k geom ) to the
measured resistance, as follows:

ρ

ρ ¼ Rk geom ð 5 : 2 Þ

For the case of a cylindrical specimen

r 2
L

Cross ‐ sectional area

Length

¼ π

k geom ¼ ð 5 : 3 Þ

where r is the radius of the cylinder and L its length with
both measured in metres.
The unit of electrical resistance is the ohm (

Ω ) and the

unit of resistivity is the ohm-metre ( m). It is also common

to quantify the ease with which electric current may

Ω

ow in
terms of the reciprocals of these parameters, respectively
conductance and conductivity. Their units of measurement
are, respectively, siemen (S) and siemens per metre (S/m).
Conductivity is commonly designated by the Greek letter

.
It is obvious in the plumbing analogy that increasing the
water pressure causes an increase in the flow of water
around the plumbing system; the greater the resistance to
the flow, the smaller will be the flow, and vice versa. In
terms of the equivalent electrical parameters, the current
(I) is proportional to the potential difference (V), applied
across a resistance (R) and inversely proportional to the
resistance and given by:

σ

crystal
lattice where there may be unbalanced charges and poten-
tially mobile electrons. Conductivity is also dependent
upon temperature; increasing the temperature increases
the energy of the electrons so they can move more easily
and increase the conductivity. At low temperatures semi-
conductors behave more like insulators.

'

5.2.1.4 Alternating current
When a constant potential difference is applied to a circuit,
the current flows in one direction only and is referred to as
direct current (d.c.). Continuously varying the potential in
a sinusoidal manner creates an alternating back-and-forth
flow, known as alternating current (a.c.). Analogous
plumbing and a.c. electric circuits are shown in Fig. 5.4 .
In this case the water pump creates a back-and-forth water
flow. Similarly, in a.c. circuits the varying potential pro-
duced by the generator causes the charge carriers to oscil-
late around a point in the circuit. The rate of sinusoidal
oscillation de

Voltage
Resistance or I

V
R

Current ¼ ¼ ð 5 : 4 Þ

This linear relationship between current and voltage is
known as Ohm s Law and it quantifies the intrinsic rela-

tionship between potential difference, current and resistiv-
ity. It is often presented in a rearranged form as:

'

Voltage ¼ current resistance or V ¼ IR ð 5 : 5 Þ

Stated in terms of the resistivity and geometry of the body:

ρ
k geom

V ¼ I ð 5 : 6 Þ

nes the frequency of the alternating current
(see Appendix 2 ).
The alternating current also experiences resistance to its
flow, but the situation is more complex than for the case of
a direct current. In the context of the description of con-
ductivity, resistivity and voltage given so far, it would be
expected that the variations in potential difference and
current would occur simultaneously, i.e. they would be
exactly in phase ( Fig. 5.5a ) (see Appendix 2 ) . However,
electrical phenomena known as inductance and capaci-
tance cause the variations in current to occur out-of-step

It is clear from Ohm is Law that the difference in potential

across parts of a body will be less if it has low resistivity.
For a perfect conductor (

'

zero), all points within it will
be at the same potential. In the plumbing analogy, the
perfect conductor is a void within which the water pressure
is constant throughout.

ρ ¼

5.2.1.3 Conductors, semiconductors and insulators
Materials are considered to be insulators if their
conductivity is less than 10 - 8 S/m, and conductors if their