$A$ negligibly small current is passed through a wire of length $15 \ m$ and uniform cross-section $6 \times 10^{-7} \ m^2$,and its resistance is measured to be $5 \ \Omega$. The resistivity of the material at the temperature of the experiment is . . . . . . $\Omega \ m$.

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. $(\rho_{Al} = 2.63 \times 10^{-8} \; \Omega m, \rho_{Cu} = 1.72 \times 10^{-8} \; \Omega m, \text{Relative density of } Al = 2.7, \text{of } Cu = 8.9.)$

$A$ wire of resistance $5 \Omega$ is stretched so that its new length is $3$ times its original length. What is the resistance of the new wire?

The alloys constantan and manganin are used to make standard resistance due to they have

$A$ wire of resistance $3 \Omega$ is stretched to twice its original length. The resistance of the new wire will be (in $\Omega$)

The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is