Column $- I$ gives certain physical terms associated with the flow of current through a metallic conductor. Column $- II$ gives some mathematical relations involving electrical quantities. Match Column $- I$ and Column $- II$ with appropriate relations.

Column $- I$	Column $- II$
$(A)$ Drift Velocity	$(P)$ $\frac{m}{n e^{2} \rho}$
$(B)$ Electrical Resistivity	$(Q)$ $n e v_{d}$
$(C)$ Relaxation Period	$(R)$ $\frac{e E}{m} \tau$
$(D)$ Current Density	$(S)$ $\frac{E}{J}$

At time $t = 0$,terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and alternating current $I(t) = I_0 \cos(\omega t)$,with $I_0 = 1 \text{ A}$ and $\omega = 500 \text{ rad s}^{-1}$ starts flowing in it with the initial direction shown in the figure.
At $t = \frac{7\pi}{6\omega}$,the key is switched from $B$ to $D$. Now onwards only $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C = 20 \mu\text{F}$,$R = 10 \Omega$ and the battery is ideal with emf of $50 \text{ V}$,identify the correct statement$(s)$.
$(A)$ Magnitude of the maximum charge on the capacitor before $t = \frac{7\pi}{6\omega}$ is $1 \times 10^{-3} \text{ C}$.
$(B)$ The current in the left part of the circuit just before $t = \frac{7\pi}{6\omega}$ is clockwise.
$(C)$ Immediately after $A$ is connected to $D$,the current in $R$ is $10 \text{ A}$.
$(D)$ $Q = 2 \times 10^{-3} \text{ C}$.

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	$(D)$ $2:1$

$A$ battery of $emf$ $E$ is being charged from a charger such that the positive terminal of the battery is connected to terminal $A$ of the charger and the negative terminal of the battery is connected to terminal $B$ of the charger. The internal resistance of the battery is $r$.

If the internal resistance of a cell is proportional to the current drawn from the cell,then the best representation of the terminal potential difference of the cell with respect to the current drawn from the cell will be:

Which of the following statements is true regarding the thermo $e.m.f.$ of a thermocouple?