The resistance ${R_t}$ of a conductor varies with temperature $t$ as shown in the figure. If the variation is represented by ${R_t} = {R_0}[1 + \alpha t + \beta {t^2}]$,then

Two wires $A$ and $B$ of the same material and same mass have radii $2r$ and $r$,respectively. If the resistance of wire $A$ is $34\,\Omega$,then the resistance of wire $B$ will be ............ $\Omega$.

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. $(\rho_{Al} = 2.63 \times 10^{-8} \; \Omega m, \rho_{Cu} = 1.72 \times 10^{-8} \; \Omega m, \text{Relative density of } Al = 2.7, \text{of } Cu = 8.9.)$

$A$ thick wire is stretched so that its length becomes two times. Assuming that there is no change in its density,what is the ratio of the change in resistance of the wire to the initial resistance of the wire?

The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

$A$ wire of $1 \,\Omega$ has a length of $1\, m$. It is stretched until its length increases by $25\, \%$. The percentage change in resistance to the nearest integer is .....$\%$