The resistance of a wire is $2.5 \Omega$ at a temperature $373 \ K$. If the temperature coefficient of resistance of the material of the wire is $3.6 \times 10^{-3} \ K^{-1}$,its resistance at a temperature $273 \ K$ is nearly: (in $\Omega$)

Equal potentials are applied on an iron and copper wire of the same length. In order to have the same current flow in the two wires, the ratio $r_{\text{iron}} / r_{\text{copper}}$ of their radii must be (Given that specific resistance of iron = $1.0 \times 10^{-7} \, \Omega \cdot \text{m}$ and specific resistance of copper = $1.7 \times 10^{-8} \, \Omega \cdot \text{m}$)

$A$ 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

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

$A$ metal wire of $1 \text{ cm}$ length and $1 \text{ mm}$ radius has a resistance of $3 \times 10^{-3} \Omega$. If a wire of the same metal of length $3 \text{ cm}$ and radius $0.5 \text{ mm}$ is drawn,what is the resistance of the new wire (in $\Omega$)?

$A$ platinum resistance thermometer has a resistance of $50\,\Omega$ at $20\,^{\circ}C$. When dipped in a liquid,the resistance becomes $76.8\,\Omega$. The temperature coefficient of resistance for platinum is $\alpha = 3.92 \times 10^{-3}\,^{\circ}C^{-1}$. The temperature of the liquid is .............. $^{\circ}C$.