A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 36.0 A. Find the resistivity of the material.

ρ = 1.6*10⁻⁸ Ω/m.

Explanation:

Applying Ohm's Law to the wire, assuming that it can be treated as a pure resistance, the resistance of the wire can be obtained as follows:

       

At the same time, we know that there exists a relationship between the resistance, the resistivity ρ, the length L and the area A of the wire, that is given for the following expression:

       

The area of the circular section of the wire, can be expressed as a function of the diameter d, as follows:

     

Replacing  the left side of (2) by (1), and (3) on the right side, we can solve for the resistivity ρ as follows:

       

ρ = 1.6*10⁻⁸ Ω/m