$A$ 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 .............. $^{\circ}C$.

In order to increase the resistance of a given wire of uniform cross-section to four times its value,a fraction of its length is stretched uniformly until the full length of the wire becomes $\frac{3}{2}$ times the original length. What is the value of this fraction?

The resistances of a carbon filament lamp and a tungsten filament lamp are measured individually when the lamps are lit and compared with their respective resistances when cold. Which one of the following statements will be true?

What is the resistance of a cubic block of length $50 \, cm$ having a resistivity of $50 \times 10^{-8} \, \Omega m$?

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 $\Delta R=(R-R_{0}) << R_{0}$.

For wiring in the home,one uses $Cu$ wires or $Al$ wires. What considerations are involved in this?