Question

A wire 75m long and 3.38cm in diameter is connected to a source of power with a potential difference of 18.25v and a current flowing of 28.92A. Assume the temperature remains constant. Calculate the resistivity of the metal.

Answer 1

Let $\rho$ be the resistivity, l be the length of the wire, S be the cross-section of the wire. Therefore, the resistance of the wire is $R = \rho\cdot \dfrac{l}{S} = \rho\cdot \dfrac{l}{\pi D^2/4}$ .

According to Ohm's law, $R = \dfrac{U}{I}.$

Finally,

$\dfrac{U}{I} = \rho\cdot \dfrac{l}{\pi D^2/4} , \\ \rho = \dfrac{\pi D^2\cdot U}{4lI} = \dfrac{\pi \cdot(33.8\,\mathrm{mm})^2\cdot 18.25\,\mathrm{V}}{4\cdot75\,\mathrm{m}\cdot28.92\,\mathrm{A}} = 7.5\,\mathrm{Ohm\cdot mm^2/m}.$