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Electrical resistivity is defined as the resistance of a conductor of unit length and unit cross-sectional area. It is an intensive property of materials that measures their ability to oppose, or inhibit (that is, to resist) the flow of electrical current within them. In this sense, it is the inverse or opposite of conductivity, which is also an intensive property that measures the ability of a material to allow the flow of electric current.
Resistivity is represented by the Greek letter ρ (ro) and is an intensive property: it depends neither on the quantity nor on the dimensions of a material but only on its composition. For example, the conductivity of pure copper is the same regardless of whether we have a fine wire like a human hair or a bar 5 cm thick.
This is one of the characteristic electrical properties of materials and is essential to select, for example, the materials from which the components of an electronic circuit, conductors or electrical resistors, among others, must be made.
resistivity versus resistance
When talking about resistivity it is very common to also talk about resistance. Both concepts are related, but they are not the same. While resistivity measures the intrinsic resistance of a material to the flow of electrical current and is related solely to its composition and internal structure, resistance is an extensive property that measures the absolute resistance of a particular body to current flow.
The resistance of a conductor is determined by measuring the current through it given a potential difference applied to both ends of the conductor, then applying Ohm’s law.
However, resistance can also be calculated theoretically from the resistivity and from the shape and dimensions of the conductor, since resistance is proportional to the length of the conductor and inversely proportional to the cross-sectional area of the conductor:
This formula for calculating resistance also allows us to define electrical resistivity as the constant of proportionality between the resistance of a conductor and the relationship between its length and the area of its cross section .
Electrical resistivity formula
The resistivity can be determined in different ways. The simplest way is by experimentally measuring the resistance of a conductor and its physical dimensions, and then applying the following formula:
where R is the resistance, S is the cross-sectional area, and l is the length of the conductor in question.
In addition to this formula, resistivity can also be related to the internal electric field of the conductor and the current density that this electric field generates, in the same way as the conductivity of a material is determined. In this case, the formula is:
where E and J correspond to the magnitudes of the electric field and the current density along the direction of current flow.
resistivity units
Given the above formulas for the determination of resistivity, it is easy to guess what the units of this intensive property should be.
In the international system of units, the unit of resistance is the ohm (Ω) while the units of length and area are m and m 2 , respectively. In view of the above, the SI units of resistivity are:
That is, the international units of electrical resistivity are ohm.meters or Ω.m . However, when used in different types of calculations, these units are not always practical.
For example, electrical engineers often carry out complex calculations of resistances and other quantities using resistivity, as well as some other technical specifications for materials and conductors used when designing electrical circuits. In these cases, the length of a conductor is almost always expressed in the units of the international system, that is, in meters, but this is not the case for its cross-sectional area, which is generally expressed in mm 2 . This is because m 2 is too large a unit to express the cross-sectional area of a conductor just one or two millimeters thick.
To avoid having to carry out unit conversions when calculating the resistance of a conductor, resistivity is often expressed in units of Ω.mm 2 /m .
On the other hand, electrical resistivity is a property used to estimate the degree of purity of water. When very pure water samples are required, they are subjected to a deionization process that reduces their electrical conductivity to a minimum, increasing their resistivity to a maximum. The equipment that measures the resistivity of water uses a cell with electrodes with an area of 1cm 2 and with a separation of 1cm between them. Also, the resistance values measured in high purity water cases are in the order of millions of ohms. For these reasons, the electrical resistivity of pure water is expressed in units of MΩ.cm.
Some representative resistivity values of good and bad conductors
Below are some characteristic values of materials considered good conductors, as well as those that are insulators, that is, those that do not conduct electricity well and are therefore poor conductors.
Conductive materials are characterized by having a very low resistivity, which allows them to conduct electricity very well. On the other hand, an insulating material is one that has a very high resistivity.
conductive materials
| Material | Conductivity (Ω.m) |
| graphene | 1.00 x 10 -8 |
| Silver | 1.59 x 10 -8 |
| Copper | 1.71 x 10 -8 |
| Gold | 2.35 x 10 -8 |
| Aluminum | 2.82 x 10 -8 |
Insulating materials
| Material | Conductivity (Ω.m) |
| ultrapure water | 1.8 x 10 5 |
| Wood | 10 8 – 10 14 |
| Glass | 10 10 – 10 14 |
| Rubber or hard rubber | 10 13 – 10 16 |
| Amber | 5.10 14 |
| Sulfur | 10 15 |
As can be seen when comparing both tables, the difference between the resistivities of the good and bad conductors can cover about 23 orders of magnitude and even more.
References
- Britannica, T. Editors of Encyclopaedia (2018, August 22). Resistivity . Encyclopedia Britannica. Retrieved from https://www.britannica.com/science/resistivity
- Jewett, JW, & Serway, RA (2006). Physics for Science and Engineering – Volume II (6th ed.). Thomson International.
- Resistance and Resistivity | Calculisto – Summaries and Calculus Classes . (n.d.). I calculate. Available at https://www.calculisto.com/topics/circuitos-electricos/summary/348
- Electrical resistivity . (2020, August 9). AcMax. Available at https://acmax.mx/resistividad
- Resistivity, specific resistance . (2019, March 30). Unichrom electronics. Available at https://unicrom.com/resistividad-resistencia-especifica/
- Storr, W. (2021, January 14). Resistivity and Electrical Conductivity . Basic Electronics Tutorials. Available at https://www.electronics-tutorials.ws/resistor/resistivity.html
