Question

Resistance of a metal wire of length 1 m in 26 ? at 20? C. If the diameter of the wire is 0.7 mm,
what will be the resistivity of the metal of the wire at the same temperature? If the length of the wire is
cut into two halves and connected with the source in parallel to each other how does its resistance and
resistivity change?

Answer 1

Dear Student
$$\begin{gathered} R=\rho \frac{L}{A} \\ 26=\rho \frac{\left(1\right)}{{\mathrm{\pi r}}^2} \\ \rho =26{\mathrm{\pi r}}^2=26\times 3.14\times \frac{0.7\times {10}^{-3}}{2}\times \frac{0.7\times {10}^{-3}}{2} \\ \rho =10.00\times {10}^{-6}ohm.m \end{gathered}$$
If the length of the wire is cut into two halves then as R is directly proportional to length so for each part resistance is R/2
and as both part is connected with the source in parallel to each other
so
$$\begin{gathered} \frac{1}{R_{eff}}=\frac{1}{R/2}+\frac{1}{R/2} \\ \frac{1}{R_{eff}}=\frac{4}{R} \\ {R}_{eff}=\frac{R}{4} \end{gathered}$$
Resistivity is a property of a material, so unless you change the material of the wire, resistivity will remain same.

Regards