Question

An engineer cuts a $1.0m$long, $0.33mm$diameter piece of wire, connects it across a $1.5\mathrm{V}$battery, and finds that the current in the wire is$8.0\mathrm{A}$. Of what material is the wire made?

Short answer

The material of the wire is silver.

Step-by-step solution

Given information

Wire length$=1.0m$

Wire diameter$=0.33mm$

Battery$=1.5V$

Current$=8.0A$

Explanation 

In this part of the experiment, we will determine the resistivity (or conductivity) of various materials and compare them to the values given in the book. Resistance takes the form of:

$R=\rho \frac{L}{A}\Rightarrow \rho =\frac{AR}{L}$

In addition, given that the wire is conductive and that the current flowing in it is constant, we can find the resistance by applying Ohm's law.

$R=\frac{U}{I}$

Substituting the second expression into the first one,

$\rho =\frac{AU}{LI}$

The cross-section area is a circle,

We can substitute $A=\frac{\pi D^2}{4}$to find

$\rho =\frac{\pi U{D}^2}{4LI}$

Substitute the values,

role="math" localid="1648976871881" $\rho =\left(\frac{\pi \times 1.5V\times 0.00033m{m}^2}{4\times 8A\times 1m}\right)$

role="math" localid="1648977110953" $=1.6\times {10}^{-8}\Omega m$

Final Answer

Hence, by checking this value in our table provided in the book, we find that the material is silver.