$A$ 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

$A$ metal wire of circular cross-section has a resistance $R_{1}$. The wire is now stretched without breaking, so that its length is doubled and the density is assumed to remain the same. If the resistance of the wire now becomes $R_{2}$, then $R_{2}: R_{1}$ is

If the resistance of a conductor is $5\,\Omega$ at $50\,^{\circ}\text{C}$ and $7\,\Omega$ at $100\,^{\circ}\text{C}$,then the mean temperature coefficient of resistance of the material is ............... $^{\circ}\text{C}^{-1}$.

Write the equation representing the relation between resistivity and temperature.

$A$ $100 \ W$ 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 $^{\circ} C$)

The variations of resistivity $\rho$ with absolute temperature $T$ for three different materials $X, Y$ and $Z$ are shown in the graph below. Identify the materials $X, Y$ and $Z$.