Question

The resistivity of iron is $2\times {{10}^{-9}}\ ohm\ meter$. The resistance of an iron wire of a particular length and thickness is $1\ ohm$, if the length and the diameter of wire both are double, then the resistivity in ohm meter will be.

Answer 1

Hint: Now, we know that resistance of any wire can be given by the formula, $R=\rho \dfrac{l}{A}$ , where $\rho $ is resistivity and it depends on the material of the wire. Using this property of resistivity of material of the wire we will find the answer.

Formula used: $R=\rho \dfrac{l}{A}$

Complete step by step answer:
In question it is given that the resistivity of iron is $2\times {{10}^{-9}}\ ohm\ meter$. The resistance of an iron wire of a particular length and thickness is $1\ ohm$, so first of all we will understand what is resistivity and then find the answer.
Resistivity is the property of a material to stop or resist the current from passing by through it. The resistivity of wire changes with the changes in material of the wire.
Here, we are given that resistivity of the wire of iron material is $2\times {{10}^{-9}}\ ohm\ meter$ and the resistance is $1\ ohm$, this can be seen mathematically as,
$\rho =2\times {{10}^{-9}}\ ohm\ meter$, $R=1\ ohm$
Now, it is said that the length and diameter of the wire are doubled and we have to find the resistivity of wire, but according to the definition of resistivity i.e. resistivity only changes when material of wire changes and here the material is not changed so it can be said that the resistivity will remain same as before i.e. $\rho =2\times {{10}^{-9}}\ ohm\ meter$.
Thus, the resistivity of the wire will be $2\times {{10}^{-9}}\ ohm\ meter$.

Note: Students might get confused between resistance and resistivity as both look similar in terminology but resistivity of wire changes only when the material of wire changes and resistance of the wire changes with the changes in length and diameter of the wire of same material. So, students should not get confused while solving such problems.