A circuit contains an ideal battery of emf \(\mathcal{E}\), two open switches \(S_1\) and \(S_2\), two resistors of resistances \(R_1\) and \(R_2\), and an initially uncharged capacitor of capacitance \(C\). Switch \(S_1\) and resistor \(R_1\) are in series with the battery in the main loop, while the capacitor \(C\) is connected in parallel with a branch containing switch \(S_2\) and resistor \(R_2\). At time \(t = 0\), switches \(S_1\) and \(S_2\) are closed simultaneously. Which of the following correctly identifies the initial current \(I_0\) supplied by the battery immediately after the switches are closed, the time constant \(\tau\) of the charging circuit, and the steady-state charge \(Q_{\infty}\) stored on the capacitor as \(t \to \infty\)?