The specific resistance of a wire is $\rho$,its volume is $3\,m^3$ and its resistance is $3\,\Omega$. Then its length will be:

$A$ wire of resistance $4 \,\Omega$ is stretched to twice its original length. The resistance of the stretched wire would be ........... $\Omega$.

If $n, e, \tau$ and $m$ represent electron density,charge,relaxation time,and mass of an electron respectively,then the resistance of a wire of length $l$ and cross-sectional area $A$ is given by:

Explain how the resistance of a conductor depends on its dimensions.

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

The new resistance of a wire of $R \, \Omega$,whose radius is reduced to half,is