The resistance of a wire is $5 \Omega$. Its new resistance in ohm,if stretched to $5$ times of its original length,will be:

In the given circuit,the lengths of $AB$ and $BC$ are equal. The radius of $AB$ is three times that of $BC$. What is the ratio of the potential difference across $AB$ to that across $BC$?

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

$A$ rod of a certain metal is $1.0 \, m$ long and $0.6 \, cm$ in diameter. Its resistance is $3.0 \times 10^{-3} \, \Omega$. Another disc made of the same metal is $2.0 \, cm$ in diameter and $1.0 \, mm$ thick. What is the resistance between the round faces of the disc?

One $kg$ of copper is drawn into a wire of $1 \ mm$ diameter and a wire of $2 \ mm$ diameter. The resistance of the two wires will be in the ratio:

At what temperature $(^{\circ} C)$ will the resistance of a copper wire become $3$ times its resistance at $0^{\circ} C$? (Given: Temperature coefficient of resistance $\alpha = 4 \times 10^{-3} {}^{\circ} C^{-1}$)