$A$ given piece of wire of length $l$ and radius $r$ and resistance $R$ is stretched uniformly to a wire of radius $\frac{r}{2}$. Its new resistance is .................. $R$.

The figure shows a rectangular block with dimensions $x, 2x$ and $4x$. Electrical contacts can be made to the block between opposite pairs of faces (for example,between the faces labelled $A-A, B-B$ and $C-C$). Between which two faces would the maximum electrical resistance be obtained? ($A-A$: Top and bottom faces,$B-B$: Left and right faces,$C-C$: Front and rear faces)

$A$ wire of a certain material is stretched slowly by $10 \%$. Its new resistance and specific resistance become respectively:

An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $\text{ m}$)

The temperature coefficient of resistance for a wire is $0.00125\,^{\circ}C^{-1}$. At $300\,K$ its resistance is $1\,\Omega$. The temperature at which the resistance becomes $2\,\Omega$ is .......... $K$.

$A$ silver wire has a resistance of $2.1 \Omega$ at $27.5^{\circ} C$ and a resistance of $2.7 \Omega$ at $100^{\circ} C$. Then the temperature coefficient of the resistivity of silver will be . . . . . . .