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

Copper and silicon are cooled from $300 \ K$ to $60 \ K$. The specific resistance:

If a conducting wire of length $L$ is uniformly stretched to double its length, then its conductivity becomes . . . . . . .

The cross-sections of wires made of the same material and having the same length are shown in the figure. What can be said about their resistances?

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?

Two square-shaped metal plates $A$ and $B$ of the same thickness $(t)$ and of the same material are connected as shown in the figure. The side of $B$ is twice that of $A$. If the resistances of $A$ and $B$ are $R_A$ and $R_B$ respectively, then $\frac{R_A}{R_B}$ is: