1) First of all, let's find the resistance of the wire by using Ohm's law:
[tex]V=IR[/tex]
where V is the potential difference applied on the wire, I the current and R the resistance. For the resistor in the problem we have:
[tex]R= \frac{V}{I}= \frac{5.70 V}{17.6 A}=0.32 \Omega [/tex]
2) Now that we have the value of the resistance, we can find the resistivity of the wire [tex]\rho[/tex] by using the following relationship:
[tex]\rho = \frac{RA}{L} [/tex]
Where A is the cross-sectional area of the wire and L its length.
We already have its length [tex]L=2.90 m[/tex], while we need to calculate the area A starting from the radius:
[tex]A=\pi r^2 = \pi (0.654\cdot 10^{-3}m)^2=1.34 \cdot 10^{-6}m^2[/tex]
And now we can find the resistivity:
[tex]\rho = \frac{RA}{L}= \frac{(0.32 \Omega)(1.34 \cdot 10^{-6}m^2)}{2.90m}= 1.48 \cdot 10^{-7}\Omega \cdot m[/tex]
