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 = $1.7 \times 10^{-8} \, \Omega \cdot \text{m}$)

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:

Choose the correct alternative:
$(a)$ Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
$(b)$ Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
$(c)$ The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
$(d)$ The resistivity of a typical insulator (e.g.,amber) is greater than that of a metal by a factor of the order of $(10^{22}/10^{23}).$

$A$ uniform wire of length $l$ and radius $r$ has a resistance of $100\, \Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of the new wire will be ............... $\Omega$.

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled,then

We have two wires $A$ and $B$ of the same mass and same material. The diameter of wire $A$ is half that of wire $B$. If the resistance of wire $A$ is $24 \, \Omega$,then the resistance of wire $B$ will be ................ $\Omega$.