Resistivity implies the measure of the resistance offered by an element for a given dimension at a particular temperature. Based on the resistivity, properties and characteristics of the element can be found out which are very important while designing a particular circuit, or applications. Even, based on its values, the element is categorized as conductor, insulator, or semiconductor. It need not be confined to only electrical property like the flow of electrons but it can also be defined for heat, pressure, etc. However, in this article, we would be discussing electrical resistivity.
Wha is Resistivity?
Definition: Electrical resistivity can be defined as a measure of the resistance offered to flow of charges i.e. current at a particular temperature and for a given dimension. Mathematically the resistivity formula can be expressed as
Where ‘R’ is the resistance, ‘A’ is the cross-sectional area, and ‘L’ is the length of the conductor. As can be clearly seen, this is directly proportional to the resistance of the material, cross-sectional area, and inversely proportional to the length of the conductor. The length and cross-sectional area of the conductor as shown in the following figure.
The SI unit of resistivity is given as Ohm-meter. (Ω m). As mentioned before, along with the length and cross-sectional area, it also depends on temperature. Before going into this, let us see the resistivity of various materials at a particular temperature include the following.
- The material at 200 C
- Silver 9.8
- Copper 10.37
- Gold 14.7
- Tungsten 33.2
- Steel 95.8
As it can be seen that, silver has the least resistivity, followed by copper and Gold, which means if it offers the least resistance to flow of charges, or it offers the least resistance to current. That’s why silver is considered as one of the best conductors. But due to high cost and abundance, it cannot be used for general purposes. Next in the list, copper is used mostly for all applications as carrier mediums for current. Copper is mostly used for windings in electrical and electronic applications.
Classifications for Conductors, Semiconductors & Insulators
As resistivity is the measure of opposition offered to the flow of charges, based its elements are classified as conductors, semiconductors, and insulators. They are classified as
These are the elements that offer the least resistivity so the range is ρ = 10-2 to 10-8 Ωm. The resistance offered to the flow of charges is least. They offer good conductance properties. These are used for all electrical and electronic applications where ever interconnecting two terminals are required. Examples for conductors are copper, aluminum, silver, etc.
These are the elements that offer the highest resistivity and its range is ρ = 1011 to 1019 Ωm. The resistance offered to the flow of charges is high. They offer good insulating properties. They are used where the ever insulating medium is required between two conducting bodies. Examples for insulators are rubber, mica, paper, glass, porcelain, etc.
These are the elements that offer resistivity between the range of conductors and insulators. The range is ρ = 10-5 to 10+6 Ωm. The resistance offered to the flow of charges is moderate. Due to moderate properties, they are highly used in the field of the semiconductor industry. They are mostly used in the fabrication of semiconductor devices like diodes, transistors, etc. Examples for semiconductor elements are silicon, germanium, gallium arsenide, etc.
Based on this, the elements are classified as conductors insulators and semi-conductors. Apart from this, one more parameter for the classification of materials is the energy band. Similar to the range of energy band has also a different range for respective elements.
Resistivity and Temperature
As we have seen how it varies for the conductor to an insulator, similarly the dependence of resistivity on temperature for these elements varies differently. Let’s see them one by one.
Temperature dependence on resistivity so the material varies with temperature. The mathematical expression between resistivity and coefficient of temperature is given by
ρt=ρ0 (1+α(T-T_0 ))
Where ‘ρt’ is the resistivity at ‘t’ degree centigrade, ‘ρ0’ is the resistivity at standard temperature, α is the temperature coefficient of resistivity, T is the temperature, T0 is the reference temperature. As is can be seen, it directly depends on temperature. However, dependence on temperature varies from element to element. Let’s see how it varies for conductors, insulators, and semiconductors.
Variation in Conductors
We have seen that resistivity is very less for conductors. Because of the least resistance, they offer high conductance of flow of charges. At normal temperature, there is no gap between the valence band and conduction band for a conductor. Each conductor, based on the atomic number has a free electron in outermost orbit. And hence ready to donate easily.
With the increase in temperature, the atomic structure of the elements gets disturbed. It causes a collision between free electrons and other electrons. Due to which, the movement of free electrons is restricted. Hence the free electron is not able to move freely. This implies that the flow of charges is decreased, and hence it is increased. Such elements are said to have a positive temperature coefficient of resistance. The linear relationship between temperature and resistivity is valid up to 500 K.
Variation in Semi-Conductors
Semi-conductors have exactly four free electrons in their outermost orbit. Silicon and Germanium are mostly used in semi-conductor elements. For semiconductor elements, the gap between the valence band and conduction band is small. With an increase in temperature, the electrons move from valence band to conduction band. This implies that, with an increase in temperature conductivity increases, and hence resistivity decreases. Such elements are said to have a negative temperature coefficient of resistance. The curve between resistivity and temperature is nonlinear up to 300 K.
Variation in Insulators
For insulator, the gap between the valence band and the conduction band is high. Hence, with an increase in temperature, electrons easily move towards the conduction band and therefore flow of charges increases. This implies that with an increase in temperature, conductivity increases, and hence resistivity decreases. Therefore, insulators have a negative temperature coefficient of resistance.
Apart from conductors, insulators, and semiconductors, there is one more group of elements for which resistivity is independent of temperature. With an increase in temperature, there is no effect on it. These are used in applications that are highly sensitive to temperature. Examples of such elements are manganin, constantan, etc.
Electrical Resistivity Method
This method has a different meaning in different contexts. It is mostly used in the field of geophysics. In geophysics, it deals with measuring the resistivity of soils and rock as a function of the depth of the soil or position. The resistivity of soil is a function of soil properties like porousness, moisture, etc. This method also involves calculating the horizontal and vertical discontinuities in the soil.
In this method, the current is injected into the soil by two electrodes, and based on potential drop across the electrodes, soil resistivity is evaluated. The process is repeated at different depth and for the different texture of the soil. Different factors like moisture content, permeability, ionic content, etc. are considered while evaluating. Further, based on the results computer modeling of soil characteristics is done for further analysis.
1). How does resistivity vary with temperature?
It varies with temperature based on the element. For a conductor, it increases with an increase in temperature. Such elements are said to have a positive coefficient of temperature resistance. For insulators and semiconductors, with an increase in temperature, resistivity decrease. Such elements are said to have a negative coefficient.
2). On what factors resistivity depends?
It depends on the length of the element, cross-sectional area, and temperature.
3). Which material has the highest resistivity?
Glass has the highest resistivity like up to 1-10000*10 to the power 9
4). What is Ohm’s Law used for?
Ohm’s Law is used for measuring the current through an element for an increase in potential difference or voltage. As per Ohm’s law, voltage is directly proportional to the current flowing through an element, and the resistance the element is proportionality constant. V = IR
5). Does resistivity depend on shape?
Yes, it depends on the shape. Since the shape of the element or material determines its length and cross-sectional area, it also depends on the shape of the material.
Hence, we have seen the definition and units of resistivity. We have also seen the factors on which the resistivity varies. This also depends on a lot on temperature and some special materials like manganin etc. resistivity does not vary with an increase in temperature. The reader may find out, how resistivity varies for superconductors?