Answer to Question #190242 in Civil and Environmental Engineering for John Prats

Question

A wire 50 cm long and 1 mm in radius is connected to a battery 9.11 V with a current of 36 A. Taking the temperature at 20°C and using the table of resistivities for some materials above, determine the material of the wire.

Answer 1

V= 9.11 V , I = 36A ,

L length = 50 cm or 0.5 m , radius = 1mm or 0.001 m

R= $\frac{V}{I} = \frac{9.11}{36}= 0. 2531 \Omega$

R= $\frac{pL}{A}$

$p= \frac{AR}{L}$ but area A = $\pi r^2$

$A= \pi\times0.001^2= 3.142 \times 10^{-6} m^2$

$p=\frac{3.142\times10^{-6}\times 0.2531}{0.5}= 1. 5904 \times 10^{-6}\Omega m$

From the table above , there is likely hood that the material is a nichrome that has $1.0 \times 10^{-6} \Omega m$ against calculated resistivity $1.5904\times 10^{-6}\Omega m$