Question

What is the multiplication of resistivity and conductivity when the temperature of a metallic resistor is increased?
(A) increases
(B) decreases
(C) may increase or decrease
(D) remains constant

Answer 1

Hint Resistivity is the quantity which opposes the flow of electric current. Conductivity is the measure of how easily the current flows through a material.
The relation between resistivity and conductivity can be explained as
Resistivity is inversely proportional to conductivity.

Complete step-by-step answer:
The ease of flow of electric current through a material is called Conductivity. A conductor is a material which offers very low resistance to flow of an electric current. Electrical conductivity signifies how easily a current will travel through that material. Copper wires are a good example for this.
Thermal conductivity tells us how easily the material will allow thermal energy (heat) through it. Most likely, metals allow the heat to pass through them.
 Resistivity is the measure how easily the material opposes the electricity. Resistivity may also be called as the specific electrical resistance and volume resistivity, but these are not mostly used. The SI unit of electrical resistivity is the ohmmeter \[\left( {\Omega - m} \right)\]. It is commonly represented by the Greek letter, $\rho ,$rho.
The relation between conductivity and resistivity can be stated as,
The conductivity is inversely proportional to resistivity which can be expressed as
$\operatorname{Re} sistivity = \dfrac{1}{{conductivity}}$
The product of resistivity and conductivity is constant because they both are inversely proportional when the temperature of metallic resistor is increased.

Therefore, the option (D) is correct.

Note The electrical resistivity formula can be expressed as
$\rho = R\dfrac{A}{l}$
where, $R$ is the electrical resistance measured in ohms
$l$ is the length of the material measured in metres
$A$ is the cross-sectional area measured in square metres.