The thermo emf of a thermocouple is given by $E = aT + bT^2$,where $\frac{a}{b} = -200^{\circ}C$. If the cold junction is kept at $30^{\circ}C$,then the inversion temperature is ($\varepsilon$ in volt,$T$ in centigrade). (in $K$)

For ensuring the dissipation of the same energy in all three resistors $({R_1}, {R_2}, {R_3})$ connected as shown in the figure,their values must be related as:

The expression for thermo $e.m.f.$ in a thermocouple is given by the relation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference of two junctions. For this,the neutral temperature will be ................... $^oC$.

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?

The battery shown in the figure has an $e.m.f.$ $E$ and internal resistance $r$. The current in the circuit can be varied by sliding the contact $J$. If at any instant the current flowing through the circuit is $I$,the potential difference between the terminals of the cell is $V$,and the thermal power generated in the cell is equal to $\eta$ fraction of the total electrical power generated in it,then which of the following graphs is correct?

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