Question

A wire of $10\mathrm{\Omega }$ resistance stretched to thrice its original length. What will be its

1. New resistivity
2. New resistance

Answer 1

Step 1: Given data and Formula used

Resistance$=10\mathrm{\Omega }$

Formula used:

$\mathrm{R}\mathrm{\alpha }\frac{\mathrm{l}}{\mathrm{A}}$ and $\mathrm{R}=\frac{\mathrm{\rho l}}{\mathrm{A}}$

Step 2: Explanation

1. The property of a substance that hinders the flow of electrons is called resistance.
2. Temperature, wire length, cross-sectional area of the wire and material type are the four parameters that influence resistance.
3. Wire resistance is proportional to its length and inversely proportional to its cross-sectional area, as we know.
4. A material's resistivity, also known as its specific resistance, is a property that is affected by temperature. It's worth noting that the wire's volume remains constant regardless of its length.

Step 3: Determine the new resistivity and new resistance

New resistivity:

Since resistivity $\mathrm{p}$ is a property of the wire's material, it doesn't change.

New resistance:

The volume of wire is the same in both instances, so,

By using the resistance formula,$\mathrm{R}\propto \frac{\mathrm{l}}{\mathrm{A}}$
$$\begin{gathered} \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{{\mathrm{l}}_1}{{\mathrm{l}}_2},\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1} \\ =\left(\frac{\mathrm{l}}{3\mathrm{l}}\right)\times \left(\frac{\mathrm{A}}{3\mathrm{A}}\right) \\ \frac{10}{{\mathrm{R}}_2}=\frac{1}{9} \\ {\mathrm{R}}_2=90\mathrm{\Omega } \end{gathered}$$

So, resistivity is the property of the body it will not change.

Therefore, the resistivity and resistance will not change and the new resistance of the wire is $90\mathrm{\Omega }$.