An ideal battery of voltage \(\varepsilon\) is connected in series with a switch \(S\) and a resistor of resistance \(R\). This series combination is connected to a parallel network consisting of a second resistor of resistance \(R\) and an initially uncharged capacitor of capacitance \(C\). At time \(t = 0\), the switch \(S\) is closed. Which of the following correctly pairs the current \(I_0\) supplied by the battery immediately after the switch is closed and the charge \(Q_{\infty}\) on the capacitor after the switch has been closed for a long time?

Choice	\(I_0\)	\(Q_{\infty}\)
(A)	\(\dfrac{\varepsilon}{R}\)	\(\dfrac{C\varepsilon}{2}\)
(B)	\(\dfrac{\varepsilon}{2R}\)	\(\dfrac{C\varepsilon}{2}\)
(C)	\(\dfrac{\varepsilon}{R}\)	\(C\varepsilon\)
(D)	\(\dfrac{\varepsilon}{2R}\)	\(C\varepsilon\)