(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 ( $\mathit{t}$ ) for which the current. flows through the resistor.
Mathematical form of Joule's law of heating is :
$\mathrm{H}={\mathrm{I}}^2\mathrm{R}\mathit{t}$
(b) Given, charge $\left(\mathit{q}\right)=96000\mathrm{C}$
Time $\left(\mathit{t}\right)=2\mathrm{hrs}=120\min =7200\mathrm{}\mathit{s}$
Potential difference $\left(\mathrm{V}\right)=40$ volt
We know that,
Heat $\left(\mathrm{H}\right)=\mathrm{V}$ It, where $\mathrm{I}$ is current...(i)
Also,
$\mathit{I}=\mathit{q}∕\mathit{t}$, where $\mathit{q}$ is charge and $\mathit{t}$ is time in seconds.....(ii)
$\therefore$ By putting $\mathrm{I}=\mathit{q}∕\mathit{t}$ in eqn. (1) we get,
$\mathrm{H}=\left(\mathrm{V}\times \mathit{q}∕\mathit{t}\right)\times \mathit{t}=\mathrm{V}\mathit{q}\mathit{t}∕\mathit{t}=\mathrm{V}\mathit{q}$