There are two wires of the same length and of the same material and radii $r$ and $2r$. The ratio of their specific resistance is

Two wires of the same radius having lengths $l_{1}$ and $l_{2}$ and resistivities $\rho_{1}$ and $\rho_{2}$ are connected in series. The equivalent resistivity will be

If the length of a wire is increased by $0.1\%$,what is the percentage increase in its resistance (in $\%$)?

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

$A$ metal wire of circular cross-section has a resistance $R_{1}$. The wire is now stretched without breaking, so that its length is doubled and the density is assumed to remain the same. If the resistance of the wire now becomes $R_{2}$, then $R_{2}: R_{1}$ is

$A$ copper wire of length $L$ and diameter $D$ is to be reshaped into another wire so as to have minimum resistance. For this,we should: