(a) According to the Joule's law of heating, heat produced in a resistor is directly proportional to the :(i) square of current (I) for a given resistance.(ii) resistance (R) for a given current.(iii) the time ( $t$ ) for which the current. flows through the resistor.Mathematical form of Joule's law of heating is :$H = I^2 R t$(b) Given, charge $(q)=96000\ \mathrm{C}$Time $(t)=2\ \mathrm{hrs}=120\ \mathrm{min}=7200\ \mathrm{s}$Potential difference $(V)=40$ voltWe know that,Heat $(H)=V$ It, where $I$ is current...(i) Also,$I = \frac{q}{t}$, where $q$ is charge and $t$ is time in seconds.....(ii)$\therefore$ By putting $I = \frac{q}{t}$ in eqn. (1) we get,$H\; = \left(V \times \frac{q}{t}\right) \times t = V \frac{q t}{t} = V q$$\Rightarrow H\; = 40 \times 96000 \; \text{ joule } \;$$\Rightarrow H\; = 3840000 \; \text{ joule } \;$