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:

The length of a given cylindrical wire is increased by $100 \%$. Due to the consequent decrease in diameter, the change in the resistance of the wire will be .................. $\%$

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

$A$ wire of a certain material is stretched slowly by $10 \%$. Its new resistance and specific resistance become respectively:

The resistance of a resistor wire is $5 \, \Omega$ at $50^{\circ}C$ and $6 \, \Omega$ at $100^{\circ}C$. What is its resistance at $0^{\circ}C$ in $\Omega$?

The resistance of a wire is $2.5 \Omega$ at a temperature $373 \ K$. If the temperature coefficient of resistance of the material of the wire is $3.6 \times 10^{-3} \ K^{-1}$,its resistance at a temperature $273 \ K$ is nearly: (in $Omega$)