Question

At what temperature will aluminum have a resistivity that is three times the resistivity of tungsten at room temperature? (Assume room temperature is 20° C.)

Answer 1

Explanation:

At room temperature, resistivity of tungsten is $5.6 \times 10^{-8}$ and the resistivity of aluminium is $2.8 \times 10^{-8}$.

Temperature coefficient of aluminium ($\alpha$) = $3.9 \times 10^{-3}$

$R_{a} = 3R_{c} = 5.1 \times 10^{-8} \ohm m$

and,      $R_{a} = R_{o}(1 + \alpha \times \Delta T)$

                       = $2.82 \times 10^{-8} (1 + 3.9 \times 10^{-8} \times \Delta T)$

                  $\Delta T = 207.3^{o}C$

                             T = $(207.3 + 20)^{o}C$

                                 = $227.3^{o}C$

So, at $227.3^{o}C$ aluminium has resistivity which is three times the resistivity of tungsten at room temperature.