$A$ cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6\%$. The percentage increase in its length is (in $\%$)

$A$ metal rod of length $10 \text{ cm}$ and a rectangular cross-section of $1 \text{ cm} \times 0.5 \text{ cm}$ is connected to a battery across opposite faces. The resistance will be

$A$ cylindrical metal wire of length $l$ and cross-sectional area $S$ has resistance $R$,conductance $G$,conductivity $\sigma$,and resistivity $\rho$. Which one of the following expressions for $\sigma$ is valid?

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

$A$ rectangular carbon block has dimensions $1.0 \ cm \times 1.0 \ cm \times 50 \ cm$. The resistance is to be measured first between the two square ends and then between the two rectangular ends. If the resistivity of carbon is $3.5 \times 10^{-5} \ \Omega \cdot m$,find the values of the resistances in both cases respectively.

Two copper wires $A$ and $B$ have the same diameter and lengths of $3 \ cm$ and $5 \ cm$ respectively. If their resistances are $R_A$ and $R_B$ and their resistivities are $\rho_A$ and $\rho_B$,then which of the following is correct?