Question

Arrange the following materials in the increasing order of their resistivity.
Nichrome, copper, germanium, silicon.
(A) $Copper < nichrome < germanium < silicon$
(B) $Germanium < copper < nichrome < silicon$
(C) $Nichrome < copper < germanium < silicon$
(D) $Silicon < nichrome < germanium < copper$

Answer 1

Hint
Resistivity of material is a characteristic property of a material to determine its ability to conduct electric currents. It is denoted by ρ. It can be calculated by knowing the resistance, length and the area of the cross section of the material.

Complete step by step answer
We know that both resistance and resistivity of a material helps to determine the ability of the material to allow the electric current to pass through it. But, resistivity is an intrinsic property, which means that the resistivity of a material is constant for the material, irrespective of its shape and size. But the resistance changes for thick and thin forms of the same material.
Now, we know that the conductors allow the electric current to pass through them easily that semiconductors and insulators. Thus, the resistivity of the conductors is the least, when compared to insulators and semiconductors.
Here in the question, the copper is a good conductor of electricity, Nichrome is an alloy, and germanium and silicon are semiconductors. The conductivity of a semiconductor lies between the conductivity of a conductor and an insulator.
Thus, the order of conductivity comes as,
$copper > nichrome > germanium > silicon$
Here, the conductivity of silicon is less than that of the conductivity of germanium. It is because, at room temperature, silicon has fewer free electrons compared to germanium. Thus the conductivity becomes less.
Now, we know that, if the conductivity is high, the resistivity becomes low. Thus, the order of resistivity of the given materials comes as,
$Copper < nichrome < germanium < silicon$
Hence, the correct answer is option (A).

Note
To calculate the resistivity of a material, we know that, the resistance of a material is given by,
$\Rightarrow R = \rho \dfrac{l}{A}$
Where, R is the resistance of the material; ρ is the resistivity of the material; l is the length and A is the cross sectional area of the given material.
To find the resistivity of the material, it becomes as,
$\Rightarrow \rho = \dfrac{{RA}}{l}$
Its SI unit is “ohm-metre”.