A circuit contains an ideal battery of electromotive force \(\mathcal{E}\), an open switch, a resistor of resistance \(R\), and an initially uncharged capacitor of capacitance \(C\) connected in series. At time \(t = 0\), the switch is closed and the capacitor is allowed to charge completely until current ceases. If the experiment is repeated using an identical battery and capacitor but with a resistor of resistance \(2R\), how does the total thermal energy dissipated in the resistor compare to that in the original circuit, and why?