Question

What is meant by resistivity? The electrical resistivity of silver is $1.6 \times {10^{ - 6}}\Omega m$. What will be the resistance of a silver wire of length 100m and cross – sectional area $2 \times {10^{ - 3}}{m^2}$?

Answer 1

Hint: Resistivity of a material is defined as the measure of the ability of the material to oppose the flow of the current through it. In order to find the solution of the given question write down all the given physical quantities and then apply the formula of resistivity.
Formula Used: $R = \dfrac{{\rho l}}{A}$

Complete answer:
Electrical resistivity of a material is defined as the reciprocal of the electrical conductivity. The unit of electrical resistivity is expressed in ohm metre. The resistivity of conductors having a uniform cross – section and uniform flow of electric current is given as,
$R = \dfrac{{\rho l}}{A}$
Where ‘$\rho $’ is expressed as the resistivity of the material, ‘R’ is expressed as the electrical resistance of the uniform cross – sectional material, ‘l’ is the length of the material and ‘A’ is denoted as the cross – sectional area of the material.
Now, $R = \dfrac{{\rho l}}{A}$
$ \Rightarrow R = \dfrac{{1.6 \times {{10}^{ - 6}} \times 100}}{{2 \times {{10}^{ - 3}}}}$
$\therefore R = 8 \times {10^2}\Omega $
Hence, resistivity is defined as the measure of the resistance of a given size of a specific to the electrical conduction. It is also referred to as the specific electrical resistance or volume resistivity.
Hence, the resistance of a silver wire is $8 \times {10^2}\Omega $.

Additional Information:
Specific resistance of a material is defined as the resistance which is offered per unit length and cross – sectional area when a known amount of voltage is applied to it.
$ \Rightarrow \rho = \dfrac{{RA}}{l}$
Since, A $ = 1{m^2}$ and l $ = 1m$
Then, $\rho = R$

Note:
Materials which conduct electricity are known as conductors of electricity and are said to have a low resistivity. While insulators which are bad conductors of electricity have high resistivity. Resistivity of materials defends upon several factors such as the nature of the material and the temperature.