A circuit consists of an ideal battery with emf \(\mathcal{E}\), a switch \(S\), and two resistors, \(R_1\) and \(R_2\). Resistor \(R_1\) is connected in series with a parallel combination of resistor \(R_2\) and an initially uncharged capacitor \(C\), as shown in the diagram. The switch \(S\) is closed at time \(t = 0\). Which of the following correctly describes the potential difference across resistor \(R_1\), denoted \(V_1\), and the potential difference across the capacitor, denoted \(V_C\), at the instant the switch is closed and after the switch has been closed for a very long time?