An engineer cuts a 1.0-m-long, 0.33-mm-diameter piece of wire, connects it across a 1.5 V battery, and finds that the current in the wire is 8.0 A. Find the resistitvity rho of the piece of the wire.

The resistivity of the wire is:

Explanation:

Recall the formula that connects resistance R with the material's resistivity :

where A stands for the cross-sectional area of the wire, and L for the wire's length.

In our case, the cross-sectional area of a 0.33 mm wire is the area of a circle of 0.165 mm radius (0.000165 m) which we can calculate as:

Since we don't have the actual resistance, but the information on the current on the wire when applying a potential difference, we use Ohm's Law to get the resistance R of the wire:

Now, using the resistance formula shown at the beginning, we solve for the resistivity :

the plateau is likely to turn into a desert do to corrosion.