An ideal battery with emf \(\mathcal{E} = 18\text{ V}\) is connected in a circuit with three resistors (\(R_1 = 3\text{ }\Omega\), \(R_2 = 6\text{ }\Omega\), and \(R_3 = 6\text{ }\Omega\)), an initially uncharged capacitor \(C = 4.0\text{ }\mu\text{F}\), and an open switch \(\text{S}\), as shown in the schematic diagram. Switch \(\text{S}\) is closed at time \(t = 0\). What is the potential difference across resistor \(R_1\) a long time after switch \(\text{S}\) is closed?