Question

A wire 100 cm long and 2 mm diameter has a resistance of 0.07 ohm, its electrical resistivity of the material is:
A. 2 ohm-m
B. $1\times {{10}^{-6}}$ ohm-m
C. $22\times {{10}^{-6}}$ ohm-m
D. $44\times {{10}^{-6}}$ ohm-m

Answer 1

In this question we are asked to calculate the resistivity of the material. We know that resistance of a material is given by the resistivity of a material per unit length over the area of cross section. Therefore, using this we will calculate the resistivity. Resistivity is the measure of resistance of a given size of object to electrical conduction.
Formula Used:
$R=\rho \dfrac{l}{A}$
Where,
R is the resistance in ohms
L is the length if the wire in meters
A is the area s frock section of the wire in square meters
$\rho$is the resistivity in ohm-meter

Complete answer:
We know that Resistance of a given material is proportional to the length of the conductor but inversely proportional to the area of cross section of the conductor. In terms of equation it can be written as
$R=\rho \dfrac{l}{A}$
Now we have been given resistance as 0.07 ohms and length of wire as 100 cm i.e. 1 m also the diameter of wire is given as 2 mm i.e. 0.002 m
Therefore, after substituting the given values in above equation
We get,
$0.07=\rho \times \dfrac{1}{\left( \pi \times {{0.02}^{2}} \right)}$
Therefore, on solving
We get,
$\rho =22\times {{10}^{-6}}\Omega m$

Therefore, the correct answer is option C.

Note:
Resistance is the quality of material to oppose the flow of current in the circuit. For a material to be a conductor, the resistance of a material should be low. Resistance of a material depends on resistivity of the material, its length and area of cross section. However, resistivity only depends on temperature and nature of material.