Question

Specific resistance of a conductor increases with
(A) Increase in temperature
(B) Increase in cross section area
(C) Increase in cross section area and decrease in length
(D) Decrease in cross-section area

Answer 1

Hint : Resistivity is the resistance of a material of unit cross-sectional area and unit length. Resistivity is a constant value for different materials. It is like the specific heat capacity. Resistivity does not depend on the geometry.

Complete step by step answer
The resistivity of a material is defined as the resistance offered by a material of unit length and unit cross section area. Since it is always in terms of unit cross section area and length it is a fixed value based on the type of material.
It doesn’t depend on geometry which means it doesn’t depend on the length and cores section of the conductor.
With an increase in temperature of the material, the ions of the conductor vibrate with greater amplitude making the resistance increase. Hence, we can say that the resistivity of a material increases with an increase in temperature.

Additional Information
A conductor is a material or object that permits an electric current to flow easily. An insulator is a material or object that permits an electric current to flow easily.

Note
If we take the formula of resistivity in terms of resistance to find the solution for this question, we might presume that resistivity depends on length and cross-section area, which is wrong. It depends only on temperature.
The temperature coefficient of resistivity is the factor that changes the value of resistivity at a particular temperature. The resistivity-change factor per degree Celsius of temperature change is called the temperature coefficient of resistivity. The same applies to resistance.