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 $\text{ m}$)

$A$ $100 \ W$ 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 resistance of a wire at $0^{\circ} C$ is $20 \Omega$. If the temperature coefficient of resistance is $5 \times 10^{-3} {}^{\circ} C^{-1}$,the temperature at which the resistance will be double that at $0^{\circ} C$ is: (in $^{\circ} C$)

$A$ wire of aluminium and a wire of germanium are cooled to a temperature of $77 \,K$. Then

If a wire is stretched to make it $0.1 \%$ longer,its resistance will.......

There are two wires of the same length and of the same material and radii $r$ and $2r$. The ratio of their specific resistance is