The temperature dependence of resistances of $Cu$ and undoped $Si$ in the temperature range $300-400 \ K$,is best described by

$A$ cell having an emf $\varepsilon$ and internal resistance $r$ is connected across a variable external resistance $R$. As the resistance $R$ is increased,the plot of potential difference $V$ across $R$ is given by:

In order to determine the $e.m.f.$ of a storage battery,it was connected in series with a standard cell in a certain circuit,and a current $I_1$ was obtained. When the battery is connected to the same circuit opposite to the standard cell,a current $I_2$ flows in the external circuit from the positive pole of the storage battery. What is the $e.m.f.$ $\varepsilon_1$ of the storage battery? The $e.m.f.$ of the standard cell is $\varepsilon_2$.

Which of the following circuits follows Ohm's law?

Match the List-$I$ with the List-$II$ from the combination shown. In the left side (List-$I$) there are four different conditions and in the right side (List-$II$), there are ratios of heat produced in each resistance for each condition:

List-$I$	List-$II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them	$(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $\Omega$ are connected in series and same $P.D.$ is applied across them	$(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them	$(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1:2$ are connected in parallel and same $P.D.$ is applied across them	$(D)$ $2:1$

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 the 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 $D$. $\Delta V$ measured between $B$ and $C$ is