$(a)$ Why are copper or aluminium wires generally used for electrical transmission and distribution purposes?
$(b)$ Two wires,one of copper and the other of manganin,have equal lengths and equal resistances. Which wire is thicker? Given that the resistivity of copper is lower than that of manganin.

(B) Copper and aluminium are used because they have low electrical resistivity,which results in low resistance and minimal energy loss during transmission. Additionally,they are highly ductile,allowing them to be easily drawn into thin wires.
$(b)$ The resistance of a wire is given by the formula $R = \frac{\rho L}{A}$,where $\rho$ is resistivity,$L$ is length,and $A$ is the cross-sectional area.
Since $R$ and $L$ are equal for both wires,we have $A = \frac{\rho L}{R}$,which implies $A \propto \rho$.
Given that the resistivity of manganin is higher than that of copper $(\rho_{\text{manganin}} > \rho_{\text{copper}})$,it follows that the cross-sectional area of the manganin wire must be greater than that of the copper wire $(A_{\text{manganin}} > A_{\text{copper}})$.
Therefore,the manganin wire is thicker.