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

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:

When the temperature of a conductor increases, the ratio of conductivity and resistivity . . . . . . .

The coefficient of linear expansion of the material of a resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively. Then the correct relation is:

$A$ 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.

The length of a given cylindrical wire is increased by $100\,\%$. Due to the consequent decrease in diameter,the percentage change in the resistance of the wire will be ................ $\%$.