Question

A magnin wire of length 2m has a diameter of 0.4mm with a resistance of $70 \Omega$. Find the resistivity of the material.

Answer 1

Hint: We know the Resistivity of a material is equal to the resistance of an object in the form of the unit cube. Resistance depends upon the nature of the material, length, Area of cross-section, and also the dimensions and temperature.

Complete step by step answer:
Given length of wire ($l$) $ = 2m$
Radius of the cross section($r$)$ = \dfrac{{0.4}}{2} = 0.2mm = 0.2 \times {10^{ - 3}}m$
Here the resistance of a wire$ = 70\Omega $
Therefore resistivity of the material $\rho = {\text{R}}\left( {\dfrac{A}{L}} \right)$
$ \Rightarrow \rho = 70\left( {\dfrac{{\pi \times {{(0.2 \times {{10}^{ - 3}})}^2}}}{2}} \right) = 4.4 \times {10^{ - 6}}\Omega m$( here $\pi = \dfrac{{22}}{7}$ )

$\therefore$ The resistivity of material $ = 4.4 \times {10^{ - 6}}\Omega m$

Additional information:
The resistivity of a conductor also depends upon the temperature of the conductor. If the temperature of a conductor increases. Its resistivity also increases. If the temperature decreases, resistivity also decreases. Resistivity is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.

Note:
The electrical resistivity of particular conductor material is a measure of how strongly the material opposes the flow of electric current through it. Then the factors which affect the resistance (R) of a conductor in ohms can be listed as The resistivity (ρ) of the material from which the conductor is made. That is, resistivity affects resistance. Resistivity is also known as specific resistance.