At room temperature $(27^{\circ} C)$,the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4} { }^{\circ} C^{-1}$. The temperature of the element,when its resistance is $62 \Omega$,is $\qquad$ ${ }^{\circ} C$.

If copper and silicon are cooled from $300 \, K$ to $60 \, K$,their resistivity will:

Two wires of equal length,one of aluminium and the other of copper,have the same resistance. Which of the two wires is lighter? Hence,explain why aluminium wires are preferred for overhead power cables. $(\rho_{Al} = 2.63 \times 10^{-8} \; \Omega m, \rho_{Cu} = 1.72 \times 10^{-8} \; \Omega m, \text{Relative density of } Al = 2.7, \text{of } Cu = 8.9.)$

$A$ cylindrical wire $P$ has resistance $10 \ \Omega$. $A$ second wire $Q$ has length and diameter half that of $P$. If the material of both the wires is same,then the resistance of wire $Q$ is (in $Omega$)

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?

The specific resistance (resistivity) of manganin is $50 \times 10^{-8} \, \Omega \cdot m$. The resistance of a cube of length $50 \, cm$ will be: