The resistance of a wire is $R \; \Omega$. If it is melted and stretched to $n$ times its original length,its new resistance will be

The variation of applied potential and current flowing through a given wire is shown in the figure. The length of the wire is $31.4 \, cm$. The diameter of the wire is measured as $2.4 \, cm$. The resistivity of the given wire is measured as $x \times 10^{-3} \, \Omega \cdot cm$. The value of $x$ is . . . . . . [Take $\pi = 3.14$]

How does the resistivity of a material depend on temperature? Write the empirical formula.

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

The resistance of a platinum wire at $0^{\circ}C$ is $2\,\Omega$ and $6.8\,\Omega$ at $80^{\circ}C$. The temperature coefficient of resistance of the wire 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