Two conductors have the same resistances at $0^{\circ} C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :

Choose the correct alternative:
$(a)$ Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
$(b)$ Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
$(c)$ The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
$(d)$ The resistivity of a typical insulator (e.g.,amber) is greater than that of a metal by a factor of the order of $(10^{22}/10^{23}).$

The conductivity of a superconductor is

Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the voltage $\Delta V$ developed between $B$ and $C$. The calculation is done in the following steps:
$(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculate field $E(r)$ at distance $r$ from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at $r$.
$(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i)$,$(ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$.
For current entering at $A$,the electric field at a distance $r$ from $A$ is

If the length of a wire is increased by $10\%$ by stretching it,the percentage increase in its resistance is ..............$\%$

The resistivity of alloys is $\rho_{\text{alloy}}$ and the resistivity of constituent metals is $\rho_{\text{metal}}$. Then,usually: