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 $\alpha_1 / \alpha_2$?

$A$ cylindrical resistor is connected to a battery with emf $5 \ V$. The resistance per unit length varies as $\rho(x) = \rho_0 \left(\frac{x}{L}\right)^\alpha$,where $\rho_0$ and $\alpha$ are constants and $x$ is the distance from one end of the resistor. The product $\rho_0 L$ is $10 \ \Omega$,where $L$ is the length of the resistor. If the thermal power generated by the resistor is $20 \ W$,then the value of $\alpha$ is:

If a wire of resistance $R$ is melted and recasted to half of its length,then the new resistance of the wire will be

$A$ conductor has resistance values of $2.71 \ \Omega$ and $3.70 \ \Omega$ at $10^{\circ}C$ and $100^{\circ}C$ respectively. The temperature at which the resistance is $3.26 \ \Omega$ is .......... $^{\circ}C$.

$A$ and $B$ are two square plates of the same metal and same thickness,but the length of $B$ is twice that of $A$. The ratio of the resistances of $A$ and $B$ is

At what temperature $(^{\circ} C)$ will the resistance of a copper wire become $3$ times its resistance at $0^{\circ} C$? (Given: Temperature coefficient of resistance $\alpha = 4 \times 10^{-3} {}^{\circ} C^{-1}$)