$A$ battery consists of a variable number $n$ of identical cells (each having electromotive force $\varepsilon$ and internal resistance $r$) which are connected in series. The terminals of the battery are short-circuited and the current $I$ is measured. Which of the graphs shows the correct relationship between $I$ and $n\,?$

For a given temperature difference,which of the following pairs will generate maximum thermo $e.m.f.$?

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.

The temperature of the cold junction of a thermocouple is $0\,^oC$ and the temperature of the hot junction is $T\,^oC$. The thermo e.m.f. is given by the relation $E = AT - \frac{1}{2}BT^2$ (where $A = 16$ and $B = 0.08$). The temperature of inversion is ............... $^oC$.

Answer the following questions:
$(a)$ $A$ steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?
$(b)$ Is Ohm's law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm's law.
$(c)$ $A$ low voltage supply from which one needs high currents must have very low internal resistance. Why?
$(d)$ $A$ high tension $(HT)$ supply of, say, $6 \ kV$ must have a very large internal resistance. Why?

Three wires of copper,iron,and nickel are joined to form three junctions as shown in the figure. When the temperature of junction $1$ is kept at $50\,^{\circ}\text{C}$ with the other two junctions at $0\,^{\circ}\text{C}$,the sensitive galvanometer gives a deflection of $14$ divisions. When the temperature of junction $3$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,the galvanometer gives a deflection of $11$ divisions. Then the deflection given by the galvanometer,when the temperature of junction $2$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,will be (in $div$)