When a current $I$ is passed through a wire of constant resistance,it produces a potential difference $V$ across its ends. The graph drawn between $\log I$ and $\log V$ will be:

$A$ cell of emf $E$ has an internal resistance $r$ and is connected to a rheostat. When the resistance $R$ of the rheostat is changed,which is the correct graph of the potential difference $V$ across it?

Four equal resistances dissipate $5 \, W$ of power together when connected in series to a battery of negligible internal resistance. The total power dissipated in these resistances when connected in parallel across the same battery would be ........... $W$.

Shown in the figure is a semicircular metallic strip that has thickness $t$ and resistivity $\rho$. Its inner radius is $R_1$ and outer radius is $R_2$. If a voltage $V_0$ is applied between its two ends,a current $I$ flows in it. In addition,it is observed that a transverse voltage $\Delta V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)-
$(A)$ $I = \frac{V_0 t}{\pi \rho} \ln \left(\frac{R_2}{R_1}\right)$
$(B)$ the outer surface is at a higher voltage than the inner surface
$(C)$ the outer surface is at a lower voltage than the inner surface
$(D)$ $\Delta V \propto I^2$

$A$ $100 \ W$ bulb is rated at $200 \ V$ and a $200 \ W$ bulb is rated at $100 \ V$. Then:

$A$ thermocouple produces $200\,\mu V$ between $0\,^oC$ and $100\,^oC$. If it produces $64\,\mu V$ and $76\,\mu V$ for temperature ranges $(0\,^oC - 32\,^oC)$ and $(32\,^oC - 70\,^oC)$ respectively,then the thermo $emf$ produced between $70\,^oC$ and $100\,^oC$ will be ........... $\mu V$.