Answer
a). The answer is (1) a greater diameter, because aluminium has a higher value of resistivity. Its area must be greater, if the length of the wire is the same, to have the same resistance as copper. The relationship $R=p\frac{L}{A}$ shows this. [$p$ being the resistivity]
b). $1.29$
Work Step by Step
a). The answer is (1) a greater diameter, because aluminium has a higher value of resistivity. Its area must be greater, if the length of the wire is the same, to have the same resistance as copper. The relationship $R=p\frac{L}{A}$ shows this. [$p$ being the resistivity]
b). $R_{Al}=R_{Cu}$
or, $p_{Al}\frac{L_{Al}}{A_{Al}}=p_{Cu}\frac{L_{Cu}}{A_{Cu}}$
${L_{Al}}={L_{Cu}}$
So, $\frac{{A_{Al}}}{{A_{Cu}}}=\frac{{p_{Al}}}{{p_{Cu}}}$
Since, Area is directly proportional to square of radius,
$\frac{r_{Al}^{2}}{r_{Cu}^{2}}=\frac{2.82}{1.7}=1.6588$
Thus, $\frac{r_{Al}}{r_{Cu}}=1.29$
