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?

$(A)$ When a steady current flows in a metallic conductor of non-uniform cross-section, the current $(I)$ flowing through the conductor remains constant because charge cannot accumulate at any point. Since $I = J A = n e v_d A$, where $J$ is current density, $A$ is cross-sectional area, and $v_d$ is drift speed, $J$, $E$ (electric field), and $v_d$ are inversely proportional to $A$. Thus, they vary with the cross-section.
$(b)$ No, Ohm's law is not universally applicable. Elements that do not obey Ohm's law are called non-ohmic conductors. Examples include vacuum diodes, semiconductors, and junction diodes.
$(c)$ According to the relation $I = \frac{\varepsilon}{R + r}$, where $\varepsilon$ is the electromotive force and $r$ is the internal resistance, to obtain a high current $(I)$ from a low voltage source $(\varepsilon)$, the internal resistance $(r)$ must be very low.
$(d)$ $A$ high tension $(HT)$ supply must have a very large internal resistance to limit the current to a safe value. If the internal resistance were low, a short circuit would cause an extremely high current to flow, which could be dangerous and damage the equipment.