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

$A$ wire of resistance $3 \Omega$ is stretched to twice its original length. The resistance of the new wire will be (in $\Omega$)

Two different conductors have the same resistance at $0\,^{\circ}C$. The resistance of the first conductor at $t_1\,^{\circ}C$ is equal to the resistance of the second conductor at $t_2\,^{\circ}C$. What is the ratio of their temperature coefficients of resistance $\alpha_1 / \alpha_2$?

$A$ $100 \ W$ tungsten light bulb has a resistance of $250 \ \Omega$ when it is turned $ON$ and $25 \ \Omega$ when turned $OFF$. The ambient room temperature is $25^{\circ} C$. Find the temperature of the filament when the bulb is turned $ON$. (Let $\alpha_{\text{tungsten}} = 4.5 \times 10^{-3} /^{\circ} C$) (in $^{\circ} C$)

In order to quadruple the resistance of a uniform wire,a part of it is uniformly stretched so that the final length of the wire becomes $1.5$ times the original length. The fractional length of the stretched part is

Resistance of the wire is measured as $2\,\Omega$ and $3\,\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. The temperature coefficient of resistance of the material of the wire is............$^{\circ}C^{-1}$.