Question

A 0.20 m long metal wire has a radius of 1 cm and a resistance of 3.2x10-5 Ω. What is the resistivity of the metal?Group of answer choices5.0x10-8 Ωm16x10-8 Ωm1.6x10-8 Ωm160x10-8 Ωm

Answer 1

Given that the length of the wire is l = 0.2 m

The radius of the wire is r = 1 cm = 0.01 m

The resistance of the wire is

$R\text{ = 3.2}\times10^{-5}\Omega$

We have to find the resistivity of the metal.

Resistivity can be calculated by the formula,

$\begin{gathered} \rho=\text{ }\frac{Resis\tan ce\text{ }\times Area}{length} \\ =\frac{R\pi r^2}{l} \end{gathered}$

Substituting the values, the resistivity will be

$\begin{gathered} \rho\text{ =}\frac{3.2\times10^{-5}\times\pi\times(0.01)^2}{0.2} \\ =5.0\text{ }\times10^{-8}\Omega\text{ m} \end{gathered}$

Thus, the resistivity of the metal is 5.0 x 10^(-8) ohm-meter.