If a battery of voltage $V$ is connected across terminals $I$ of the black box shown in the figure,an ideal voltmeter connected to terminals $II$ gives a reading of $V/2$. While if the battery is connected to terminals $II$,a voltmeter across terminals $I$ reads $V$. The black box may contain:

Identify the correctness of the following statements:
$(1)$ The product of a volt and a coulomb is a joule.
$(2)$ The product of a volt and an ampere is a joule/second.
$(3)$ The product of a volt and a watt is a horsepower.
$(4)$ $A$ watt-hour can be measured in terms of an electron volt.

Consider the following two statements $A$ and $B$,and identify the correct choice out of the given answers:
$A$. Thermo $e.m.f.$ is minimum at the neutral temperature of a thermocouple.
$B$. When two junctions made of two different metallic wires are maintained at different temperatures,an electric current is generated in the circuit.

In a copper voltameter,the mass deposited in $6 \text{ min}$ is $m \text{ g}$. If the current-time graph for the voltameter is as shown in the figure,then the $E.C.E.$ of the copper is:

$A$ battery is charged at $15\,V$ for $8\,h$ with a current of $10\,A$. During discharge, the battery supplies a current of $5\,A$ for $15\,h$. The terminal voltage during discharge is $14\,V$. Find the watt-hour efficiency of the battery in percentage.

In the circuit shown in the figure,the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition,a current of $1 \,A$ flows through the $1 \,\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1}=0.36$]
$(A)$ The value of the resistance $R$ is $3 \,\Omega$.
$(B)$ The current through the $3 \,\Omega$ resistor (connected in parallel to the $1 \,\Omega$ and $R$ branches) is $2 \,A$ when $K$ is open.
$(C)$ At $t=t_0+7.2 \,\mu s$,the current in the capacitor branch is $0.6 \,A$.
$(D)$ For $t < \infty$,the charge on the capacitor is $12 \,\mu C$.