The resistance of a wire at $50^{\circ}C$ is $5\, \Omega$ and at $100^{\circ}C$ is $6\, \Omega$. The resistance of the wire at $0^{\circ}C$ is ............... $\Omega$.

$A$ $100 \ W$ 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 the following diagram,the lengths of wires $AB$ and $BC$ are equal,but the radius of wire $AB$ is double that of $BC$. The ratio of the potential gradient on wires $AB$ and $BC$ will be (wires are made of the same material):

$A$ wire of circular cross-section has an inner portion of radius $R$ made of a material of resistivity $\rho$ and is surrounded by an outer portion of thickness $R$ made of a material of double resistivity. Find the resistance of a length $l$ of such a wire.

The conductivity of a conductor decreases with temperature because,on heating:

The resistance of a wire at $300 \, K$ is found to be $0.3 \, \Omega$. If the temperature coefficient of resistance of the wire is $1.5 \times 10^{-3} \, K^{-1}$, the temperature at which the resistance becomes $0.6 \, \Omega$ is: (in $K$)