Given:
The length of the wire is,
[tex]l=433\text{ feet}[/tex]The diameter of the wire is,
[tex]d=4\text{ mm}[/tex]The resistance of the wire is,
[tex]R=1.24\text{ ohms}[/tex]To find:
The length of the wire whose resistance is,
[tex]R^{\prime}=1.49\text{ ohms}[/tex]diameter is,
[tex]d^{\prime}=5\text{ mm}[/tex]Explanation:
The resistance of a conductor is,
[tex]R\propto\frac{l}{d^2}[/tex]We can write,
[tex]\begin{gathered} \frac{R}{R^{\prime}}=\frac{l}{l^{\prime}}\times\frac{d^{\prime2}}{d^2} \\ \frac{1.24}{1.49}=\frac{433}{l^{\prime}}\times\frac{5^2}{4^2} \\ l^{\prime}=433\times\frac{25}{16}\times\frac{1.49}{1.24} \end{gathered}[/tex]The length is,
[tex]l^{\prime}=813\text{ feet}[/tex]Hence, the required length is 813 feet.