Question

A wire 6.50 m long with diameter of 2.05 mm has a resistance of 0.0290 Ω. What material is the wire most likely made of?

Short answer

Silver is most likely the material used to make the wire.

Step-by-step solution

Step 1:

Given data:

$$\begin{gathered} L=6.50m \\ d=2.05mm=2.05\times {10}^{-3}m \\ R=0.0290\Omega \end{gathered}$$

The cross-sectional area of the wire is:

$$\begin{gathered} A=\frac{\mathrm{\pi }}{4}{d}^2 \\ =\frac{\mathrm{\pi }}{4}\times {\left(2.05\times {10}^{-3}m\right)}^2 \\ =3.3\times {10}^{-6}{m}^2 \end{gathered}$$

Step 2:

The material used to make wire is:

$$\begin{gathered} \rho =\frac{RA}{L} \\ =\frac{\left(0.0290\Omega \right)\left(3.3\times {10}^{-6}{m}^2\right)}{6.50m} \\ =1.47\times {10}^{-8}\Omega .m \end{gathered}$$

Hence, silver is most likely the material used to make the wire.