$A$ wire has a resistance of $3.1 \Omega$ at $30^{\circ} C$ and $4.5 \Omega$ at $100^{\circ} C$. The temperature coefficient of resistance of the wire is

$A$ wire of resistance $2 R$ is stretched such that its length is doubled. Then the increase in its resistance is (in $R$)

$A$ hollow cylindrical conductor has a length of $3.14 \, m$, while its inner and outer diameters are $4 \, mm$ and $8 \, mm$ respectively. The resistance of the conductor is $n \times 10^{-3} \, \Omega$. If the resistivity of the material is $2.4 \times 10^{-8} \, \Omega \, m$, the value of $n$ is $..........$

$A$ wire $100\,cm$ long and $2.0\,mm$ diameter has a resistance of $0.7\,\Omega$. The electrical resistivity of the material is ...........$ \times 10^{-6}\,\Omega \cdot m$.

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

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is: