At room temperature $(27.0^{\circ} C)$,the resistance of a heating element is $100\; \Omega$. What is the temperature (in $^{\circ} C$) of the element if the resistance is found to be $117\; \Omega$,given that the temperature coefficient of the material of the resistor is $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$?

The coefficient of linear expansion of the material of a resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively. Then the correct relation is:

$A$ cylindrical copper rod has length $L$ and resistance $R$. If it is melted and formed into another rod of length $2 L$,then the resistance will be ....... $R$.

$A$ given piece of wire of length $l$ and radius $r$ and resistance $R$ is stretched uniformly to a wire of radius $\frac{r}{2}$. Its new resistance is .................. $R$.

Consider four conducting materials: copper,tungsten,mercury,and aluminium with resistivity $\rho_{C}, \rho_{T}, \rho_{M}$,and $\rho_{A}$ respectively. Then:

This question contains statement-$1$ and statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
statement-$1$: The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100 \; \Omega$ to $150 \; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5 \times 10^{-3} /^{\circ} C$.
statement-$2$: $R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta t$ is small and $\Delta R=(R-R_{0}) << R_{0}$.