(a) Write the mathematical expression for Joule's law of heating.

(b) Compute the heat generated while transferring $96000\text{ coulomb}$ of charge in two hours through a potential difference of $40\text{ V}$.

Joule's law of heating states that the heat generated in a resistor is directly proportional to the square of the current for a given resistance, directly proportional to the resistance for a given current, and directly proportional to the time for which the current flows.

In part (b), we are given the potential difference ($V$) and the total charge ($Q$) transferred. The work done in moving a charge $Q$ through a potential difference $V$ is $W = VQ$. In a purely resistive circuit, this work is entirely converted into thermal energy (heat). Therefore, the heat generated is simply the product of the potential difference and the charge. The time duration of 2 hours is redundant for the direct calculation ($H = VQ$), but if a student chooses to calculate current first ($I = Q/t$) and then use $H = VIt$, the time term cancels out, yielding the same correct result.