$A$ piece of copper is to be shaped into a conducting wire of maximum resistance. If the initial length is $L$ and diameter is $d$,what should be the new length and diameter to achieve maximum resistance?

Equal potentials are applied on an iron and copper wire of the same length. In order to have the same current flow in the two wires, the ratio $r_{\text{iron}} / r_{\text{copper}}$ of their radii must be (Given that specific resistance of iron = $1.0 \times 10^{-7} \, \Omega \cdot \text{m}$ and specific resistance of copper = $1.7 \times 10^{-8} \, \Omega \cdot \text{m}$)

$A$ 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 . . . . . . $\Omega \ m$.

Consider a thin square sheet of side $L$ and thickness $t$,made of a material of resistivity $\rho$. The resistance between two opposite faces,shown by the shaded areas in the figure is

The resistance of a wire is $10\,\Omega$. Its length is increased by $10\%$ by stretching. The new resistance will now be .......... $\Omega$.

At room temperature $(27^{\circ} C)$,the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4} { }^{\circ} C^{-1}$. The temperature of the element,when its resistance is $62 \Omega$,is $\qquad$ ${ }^{\circ} C$.