Two wires of equal length and equal diameter and having resistivities $\rho_1$ and $\rho_2$ are connected in series. The equivalent resistivity of the combination is . . . . . . .

Two wires of equal length,one of aluminium and the other of copper,have the same resistance. Which of the two wires is lighter? Hence,explain why aluminium wires are preferred for overhead power cables. $(\rho_{Al} = 2.63 \times 10^{-8} \; \Omega m, \rho_{Cu} = 1.72 \times 10^{-8} \; \Omega m, \text{Relative density of } Al = 2.7, \text{of } Cu = 8.9.)$

In an experiment,the resistance of a material is plotted as a function of temperature. As shown in the figure,the plot of $\ln R(T)$ versus $1/T^2$ is a straight line. One may conclude that:

Why does the resistivity of metals increase with an increase in temperature?

Constantan wire is used in making standard resistances because its

$A$ wire of resistance $160\,\Omega$ is melted and drawn into a wire of one-fourth of its original length. The new resistance of the wire will be $......\Omega$.