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What is Resistivity? - Understand its Definition, Formula & Variation
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Current Electricity
Resistivity
While we’ve read about the limitations of Ohm’s Law, you must have wondered about the concept of resistivity.
Resistivity is a measure of the resisting power of a specified material against the flow of an electric current. Resistivity is the resistance material provides into the cross-sectional area per unit length. Ohmmeter (Ω⋅m) is the S.I. unit of resistivity.
Materials with high resistivity, resist more flow of electrons and hence make bad conductors or insulators. Some examples of insulators are glass, wood, etc. Whereas resistivity of good conductors, such as copper, gold, and aluminum, is low, i.e., they allow more flow of electrons. Semiconductors, as the name suggests, have a resistivity that lies between conductors and insulators. Hence it has high resistivity. Silicon is a semiconductor and allows partial movements of electrons. The resistivity of perfect conductors is zero and of perfect insulators is infinite.
Formula of Resistivity
Let R be the resistance of a conductor of length l, area of cross-section A, and resistivity ρ be given by
But we know that,
R=mlne2A, where is the relaxation time.
When we compare the two equations we get
ρ=mne2
This means, that resistivity, ρ, is independent of the dimensions of the conductor. It does, however, depend on two other factors:
- Number of free electrons per unit of volume, i.e., the electron density of the conductor
- The relaxation time, i.e., the average time between two successive collisions of electrons.
Variation of Resistivity with Respect to Temperature
Since the resistivity of materials depends upon the atomic structure, therefore if the atomic structure changes resistivity can be changed. A change in temperature, causes the atoms to change behavior, and hence there is a change in resistivity.
At room temperature, metals consist of valence electrons which are loosely bound to the nucleus, which conducts electricity. Even though there is a collision between atoms, some electrons move freely causing some resistance. When temperature increases, the metal atoms start to vibrate and take on a random motion. This causes the free atoms to move slower as compared to room temperature. Hence with the increase in temperature, the hindrance in electron flow increases, increasing the resistivity.
In non – metals the electrons are tightly bound to the nucleus. Accordingly, when the temperature increases, the electrons free themselves from the atoms and come out for the conduction, therefore, reducing resistivity and increasing conductivity.
Hope this explanation for the given topic helps with your preparations for the JEE Exam preparations.
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Points to Remember - Resistivity is a measure of the resisting power of a specified material against the flow of an electric current.
- S.I. unit of resistivity is ohm meter ( Ω⋅m ).
- ρ, is independent of the dimensions of the conductor. It depends on the electron density of the conductor and the relaxation time.
- The resistivity of perfect conductors is zero and of perfect insulators is infinite.
- When temperature increases on metals resistivity also increase.
- Resistivity is a measure of the resisting power of a specified material against the flow of an electric current.
- S.I. unit of resistivity is ohm meter ( Ω⋅m ).
- ρ, is independent of the dimensions of the conductor. It depends on the electron density of the conductor and the relaxation time.
- The resistivity of perfect conductors is zero and of perfect insulators is infinite.
- When temperature increases on metals resistivity also increase.
So, this is all about Resistivity. Get some practice of the same on our free Testbook App. Download Now!
Resistivity FAQs
What is resistivity?
Resistivity is a measure of the inherent resistance of a material to the flow of electrical current.
What factors affect resistivity?
Resistivity is affected by the temperature, composition, and structure of the material in question.
How is resistivity different from resistance?
Resistance is a measure of how difficult it is for current to flow through a material of a given length and cross-sectional area, while resistivity is an inherent property of the material itself.
What are some common units of resistivity?
The most common units of resistivity are ohm-meters (Ω·m) and ohm-centimeters (Ω·cm).
How is resistivity used in engineering and technology?
Resistivity is used to determine the suitability of materials for use in electrical and electronic components, and is a critical parameter in the design of circuits and devices.