The thermoelectric electromotive force $e$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$. If the temperature of the cold junction is $0 \, ^\circ C$,find the temperature of inversion $t_i$. (Given: $\alpha = 500.0 \, \mu V/^\circ C$,$\beta = 5.0 \, \mu V/^\circ C^2$)

$A$ cable consists of a copper wire of radius $9 \, mm$ having a resistance of $5 \, \Omega$. If this cable is replaced by $6$ copper wires each of radius $3 \, mm$,what will be the new resistance of the cable in $\Omega$?

Find the percentage error in the reading of the voltmeter shown in the circuit. (in $\%$)

Consider the four circuits shown below. In which circuit is the power dissipated the maximum? (Neglect the internal resistance of the applied power source $E$)

In an experiment, a graph is plotted between the potential difference across the terminals of a battery and the current in the circuit. The internal conductance of the battery will be:

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?