Question

Mention the factor on which resistance of a conductor depends and hence define resistivity.

Answer 1

Hint: The electrical resistivity or specific electrical resistance is used to find selective materials for the construction of electrical wires. From the equation\[R=\rho \dfrac{l}{A}\], we can say that resistance depends on length, cross-sectional area and the properties of the material.

Complete step by step answer:
Resistance of a conductor depends upon the following factors.
1. Length of conductor: The resistance \[(R)\] of a conductor is directly proportional to its length \[(l)\].
\[R\propto l\]
If we increase the length of a conductor, its resistance increases since only less amount of current can pass through it. If we reduce the length of a conductor, the resistance decreases since more current can pass through it.
2. Area of cross-section: Area of the cross-section is inversely proportional to the resistance.
\[R\propto \dfrac{1}{A}\]
If we double the area of cross-section, the resistance will be half. So, electricity can. That's why we are using thick wires for the heavy electrical loads.
3. Nature of material: Conductors offer less resistance compared to insulators. That’s why we are using plastic materials for electrical insulation purposes like switches, coatings etc.
Effect of temperature: Resistance of pure metals are showing a direct relationship with temperature. But generally, alloys like nichrome won’t show that much change in resistance with respect to the temperature. The resistance of semiconductors decreases with increasing temperature.
From these conclusions, we can conclude that,
\[R\propto \dfrac{l}{A}\]
The proportionality constant is known as resistivity \[(\rho )\].
\[R=\rho \dfrac{l}{A}\]
Resistivity is a measurable property that quantifies how strongly a given material opposes the electric current flow. It depends upon the dimension of the material. It is also known as specific electrical resistance. It is inverse to conductivity. Its unit is \[\Omega m\]
If we are considering unit measurements, we can say that; the electrical resistivity of a material is the resistance of the material per unit length and per unit cross-sectional area at a specified temperature.

Note: \[\rho \] tells about the material properties and their relation towards the resistance. Normally metals have lower resistivity, thus they can conduct electrical current easily. Insulators have large resistivity; thus, they cannot conduct electrical current easily.