$A$ 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 thermo emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is:

$A$ silver voltmeter and a copper voltmeter are connected in parallel to a $12\ V$ battery. In $30\ minutes$,$1\ g$ of silver and $1.8\ g$ of copper are deposited. The power supplied by the battery is .... $(Z_{Cu} = 6.6 \times 10^{-4}\ g/C$ and $Z_{Ag} = 11.2 \times 10^{-4}\ g/C)$ (in $J/s$)

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

Given below are two statements:
Statement $I$: $A$ uniform wire of resistance $80\,\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\,\Omega$.
Statement $II$: Two resistances $2\,R$ and $3\,R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3\,R$ and $2\,R$ will be in the ratio $3:2$.
In the light of the above statements,choose the most appropriate answer from the options given below.

$A$ silver and a copper voltameter are connected in parallel across a $6\,V$ battery of negligible resistance. In half an hour,$1\,g$ of copper and $2\,g$ of silver are deposited. The rate at which energy is supplied by the battery will approximately be ............... $W$ (Given $E.C.E.$ of copper $= 3.294 \times 10^{-4}\,g/C$ and $E.C.E.$ of silver $= 1.118 \times 10^{-3}\,g/C$).