$A$ torch bulb rated as $4.5\, W$,$1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ................ $V$.

The bulb which glows with maximum intensity in the given circuit is

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

For a thermocouple,the neutral temperature is $270^{\circ}C$ when its cold junction is at $20^{\circ}C$. What will be the neutral temperature and the temperature of inversion when the temperature of the cold junction is increased to $40^{\circ}C$?

Column-$I$ gives certain physical quantities 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.

$A$. Mobility	$P$. $\frac{m}{ne^2 \rho}$
$B$. Electrical conductivity	$Q$. $neAv_{d}$
$C$. Relaxation period	$R$. $\frac{v_{d}}{E}$
$D$. Current	$S$. $\frac{J}{E}$

The cold junction of a thermocouple is maintained at $10\,^{\circ}C$. No thermo $e.m.f.$ is developed when the hot junction is maintained at $530\,^{\circ}C$. The neutral temperature is ................ $^{\circ}C$.