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The electrical resistance of a given conductor with regards to a unit of cross-sectional area as well as length seems to be referred to as resistivity. Resistivity seems to be an attribute of a given substance that can be used to compare the potential of different substances in conducting electric currents. Poor conductor materials seem to be usually referred to as materials with high resistance.
In a material like a wire, when the resistance R of the wire seems to be multiplied by the cross-sectional area of the wire, which is represented by A and is then further divided by its own length, is represented by l, the mathematical equation that forms can be written as ρ = RA/l. The ohm seems to be the measurement unit of resistance. The unit of resistivity seems to be referred to as ohm-metre within the metre-kilogram-second scale. Resistivity can also be stated in the form of ohm-centimetre units when the lengths seem to get measured in centimetres.
When at a temperature of 20° C, the resistivity associated with an excellent electrical conductor, as the likes of a hard drawn copper, seems to be 1.77 x 10-8 ohm metres, or 1.77 x 10-6-ohm centimetres. Electrical insulators can exhibit resistivity ranging between 1012–1020 ohm-metre levels.
The amount of resistivity also seems to be affected by the material’s temperature; resistivity tables typically provide values of approximately 20 degrees Celsius. Metal conductors and their resistivity seem to rise with the increase in temperature, but in the case of semiconductors’ resistivity, like carbon or silicon, the resistivity seems to decrease with rising in temperature.
The formula of resistivity
There seem to be four ways the resistivity can be represented in the form of mathematical equations; the details are mentioned below:
- It can be observed that a material’s resistance R seems to be proportional to the length L of that specific material. It is represented as R ∝ L. Further, if the length of the material is increased, let’s say doubled. Its resistance also seems to have increased or doubled.
- In this method, a material’s resistance that is represented by R seems to be inversely proportional with the cross-sectional area, which is represented by A, not that the proportionality seems to be indirect manner, that is, R ∝ 1/A. The material’s resistance value seems to be reduced by half when its cross-sectional area seems to get doubled.
- This rule indicates that a material’s resistance seems to rely on its temperature.
- When the length, as well as cross-sectional areas of two given wires, are the same even though the materials are different from each other, with different properties, their resistance values always seem to be different.
The resistance capacity of a given conductor with a given length of L metres and cross-sectional area that is represented by A can be calculated when an individual utilises all of the above rules.
The mathematical equation for this seems to be R ∝ L/A or R = ρL/A. Here the symbol ρ represents the coefficient resistivity of specific resistance, and hence the electrical resistivity can be represented by ρ = RA/L.
Few uses of resistivity
In the modern world, almost all electrical devices seem to have electrical resistivity. The resistors need to have a balanced resistance, and testing the resistivity of various materials to make resistors seems to be an important part of resistivity.
Other electrical devices rely heavily on resistivity as well. The resistivity of the small chips that are used seems crucial to forming well-integrated circuits. Some materials should contain lower resistance and also have the ability to be able to connect various portions of an IC internally, while others must segregate distinct parts of an IC. This is where the properties of resistivity help.
Materials with low resistance, such as copper and even aluminium, are appropriate for utilising wires as well as cables. Copper seems to be the most popular material used to make wires. Silver, as well as gold, seem to have substantially lower resistivity rates, and they aren’t utilised for regular users because of their higher cost. Nevertheless, silver seems to occasionally get utilised for plating wires when low resistivity is the requirement, and gold flash seems to get utilised to make the most efficient contacts points on the surface of many electronic devices. The gold seems to have no oxidation properties ideal for electrical connections.
Conclusion
The article explains in brief resistivity and its definition. It further talks about how resistivity works and mentions some of its key concepts. resistivity seems to be the electrical resistance regarding a conductor’s cross-sectional area and its overall unit length. This usually helps in determining the conductor and insulator properties of a material. The article also mentions a few terms related to resistivity.
