Basic Principles of Electrical Resistivity

Electrical Resistivity is the one of the most commonly used methods for measuring earth resistivity at which current is injected into the ground by using galvanic metal electrodes. For almost all electrical geophysical methods, the true and the specific resistivity of the rock is of interest. Let us look through this post for brief principles on how this technique works.



basic principles

Electrical Resistivity (ρ): Is the measure of the tendency of a material to resist a flow of electric current. The inverse is electrical conductivity.

Conductivity (σ): is the relative ability of material to conduct electricity when a voltage is applied. It has units of Siemens/meter (S/m) which are equivalent to mhos/meter (Ω-1m-1).

Mathematically, σ = 1/ρ 

Conversely, the resistance offered by a material to current flow is expressed in terms of resistivity. The true resistivity of a rock unit is defined as being equal to the resistance of a unit cube of the rock.

It is well known that: The resistance (R) in ohm of a sample is directly proportional to its length (L) of the resistive material and inversely proportional to its cross sectional area (A) that is:

R α L

R α 1/A        

Then, R α L/A

R = ρL/A …………. (1)

Where ρ, the constant of proportionality, is known as Electrical (true) Resistivity, It is a characteristic of the material which is independent of its shape or size. 

But according to Ohm's law:

R = ∆V/I…. ………… (2)

Where ΔV = V2 – V1, the potential difference across the resistor and 

I = the electric current through it.

R = the resistance of the conductor

If you substitute equation (1) into equation (2) and rearranging by making ρ the subject we get:

ρ = ∆VL/IA …...……… (3)

Equation (3) may be used to determine the resistivity (ρ) of homogeneous and isotropic materials in the form of regular geometrical shapes such as cylinders, cubes.

In a semi-infinite material, the resistivity at every point must be defined using Ohm's law which states that “the electric field strength (E) at a point in a material is proportional to the current density (J) passing that point”.

E α J

E = ρJ

ρ = E/J …………...........(Ohm's law)

E - Expressed in V/m

J - Expressed in A/m2

The unit of resistivity in the mks system (meter-kilogram-second) is ohm-meter (Ωm) which is convenient for expressing the resistivity of earth materials.

Ohm-centimeter can also be used where: 1m = 100 cm

Ohm' law: For an electrical circuit, Ohm's law gives R = V/I, where V and I are the potential difference across a resistor and the current passing through it, respectively. This can be written alternatively in terms of the electric field strength (E) and current density (J) as:

ρ = E/J

But ρ = VA/IL

In practice, generally, it uses Direct current (DC) or very low frequency AC signal, at which four – terminal electrodes are used since the effect of material near the current contacts can be minimized.

If you consider the figure 1 below, the electric current is injected into the ground through current electrodes (C1 and C2) which are connected to power source such as battery and the potential difference resulted in the earth by this current is measured at the potential electrodes (P1 and P2) which are connected to a sensitive voltmeter device. It is then possible to determine an effective or apparent resistivity of the subsurface. 

Figure 1: Simple current injection into ground

Anomalous conditions or in-homogeneities within the ground, such as electrically better or poorer conducting layers are inferred from the fact that they deflect the current and distort the normal potentials.

All in all the chief challenge of the resistivity method is the practical difficulty involved in plugging electrodes over  hard rocky terrain. This made the Electromagnetic method become more utilized than resistivity in mineral exploration.

The Electrical resistivity method provides a quantitative measure of the conducting properties of the subsurface. This technique can be used to find the depths of layers in the earth having anomalously high or low conductivities and to determine the depth, approximate shape of ore bodies with anomalous resistivity.

Thanks for your time!

Follow this blog on Telegram group

Don't hesitate to check out with Online Scientist Assistance for any enquiry of your geoscience Assignment.

Do you want to carryout Electrical resistivity Surveying? If Yes, here below is the simple list of equipment and tools.

BASIC RESISTIVITY EQUIPMENTS and TOOLS

- Electrical resistivity meter

- Handheld GPS receiver

- glass-Fiber tape

Geological Hammer (The friend of Geologists)

- Digital Electrical Tester with EM display

- AC Voltage Testing with Auto Range

- Handheld Electromagnetic detector - Multifunction




Post a Comment

0 Comments