The specific resistance (resistivity) of material $B$ is twice that of material $A$. Two wires are prepared from these materials having the same resistance. If the diameter of wire $B$ is twice the diameter of wire $A$,then the ratio of the lengths of the two wires $l_B / l_A$ is equal to ......

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?

An electric toaster has a resistance of $60 \ \Omega$ at room temperature $\left(27^{\circ} C\right)$. The toaster is connected to a $220 \ V$ supply. If the current flowing through it reaches $2.75 \ A$,the temperature attained by the toaster is around: (given $\alpha = 2 \times 10^{-4} /{ }^{\circ} C$) (in $^{\circ} C$)

The lead wires should have

Silicon and copper are cooled from $300 \ K$ to $100 \ K$. What happens to their specific resistance (resistivity)?

$A$ rectangular carbon block has dimensions $1.0 \ cm \times 1.0 \ cm \times 50 \ cm$. The resistance is to be measured first between the two square ends and then between the two rectangular ends. If the resistivity of carbon is $3.5 \times 10^{-5} \ \Omega \cdot m$,find the values of the resistances in both cases respectively.