Statement $(I)$: The temperature coefficient of resistance for most metals in pure form is positive.
Statement $(II)$: $A$ metal wire $2 \ mm$ in diameter carries a charge of $360 \pi \ C$ in two hours. If the metal contains $5 \times 10^{22}$ free electrons $/ cm^3$, then the drift velocity of the electrons in the wire is $6.25 \times 10^{-6} \ m/s$.
Statement $(III)$: Semiconductors like pure germanium do not obey Ohm's law for all ranges of electric field values. Which of the following is correct?

Two wires with resistances $R$ and $2R$ are connected in parallel. The ratio of heat generated in $2R$ and $R$ is:

If for a thermocouple ${T_n}$ is the neutral temperature,${T_c}$ is the temperature of the cold junction,and ${T_i}$ is the temperature of inversion,then:

The direction of current in an iron-copper thermocouple is

$A$ battery of $e.m.f.$ $E$ is connected in series with a resistor $R$ and a voltmeter $V$. An ammeter $A$ is connected in parallel with the battery. Then:

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 $10 \text{ A}$.
$(D)$ $Q = 2 \times 10^{-3} \text{ C}$.