Question

Which of the following materials has lowest resistivity?
A) Manganin
B) Copper
C) Constantan
D) Silver

Answer 1

Hint: Conductivity is inversely proportional to resistivity $C\propto \dfrac{1}{\rho }$. Material which has lower resistivity is a good conductor of electricity. Alloy are the mixtures of elements, therefore alloy has higher resistivity. Element silver has lowest resistivity and hence has higher conductivity.
Complete step by step answer
Resistivity - Resistivity is equal to the resistance of a given conductor having a unit volume.
$\rho =\dfrac{RA}{l}$
$\rho =$ Resistivity of the conductor
$R=$ Resistance of the conductor
$A=$Area of cross section of the conductor
$l=$ length of the conductor
Resistivity only depends on
Nature of material
Temperature
Resistivity is also given by,
$\rho =\dfrac{m}{n{{e}^{2}}\tau }$
Where,
$m=$ mass of electron
$n=$ number of electrons per unit volume in the conductor
$e=$ charge of electron
$\tau =$Relaxation Time
Relaxation Time - The average time interval between two successive collisions for the free electron drifting within the conductor due to the action of the applied electric field is called the relaxation time.
From the above relation of resistivity to the number of electrons in the conductor. It is clear that resistivity is inversely proportional to the number of free electrons per unit volume in the conductor.
$\rho \propto \dfrac{1}{n}$
Silver has more free electrons per unit volume than copper. Therefore the resistivity of silver is less than that of copper.
Hence, the correct answer is option D.
Additional Information
Metal has low resistivity and it lies in the range of \[{{10}^{-8}}\Omega m\] to \[{{10}^{-6}}\Omega m\] and on the other hand insulators has resistivities \[{{10}^{18}}\] times greater than metals or more.
There is another type of material known as semiconductor, which has resistivity in between metals and insulators.
Resistivity of some metals, insulators and semiconductor are given below
Conductors Resistivity\[(\Omega m)\]
Silver \[1.6\times {{10}^{-8}}\]
Copper \[1.7\times {{10}^{-8}}\]
Aluminium \[2.7\times {{10}^{-8}}\]
Manganin (alloy) \[48\times {{10}^{-8}}\]
Semiconductors
Carbon \[3.5\times {{10}^{-5}}\]
Insulators
Glass \[{{10}^{10}}-{{10}^{14}}\]
Hard Rubber \[{{10}^{13}}-{{10}^{16}}\]
Note: Resistivity is the characteristic property of the material and it only depends on the nature of the material and temperature.
Students must remember that resistivity is independent of length and area of the cross section of material.