A circuit consists of an ideal battery of electromotive force \(\mathcal{E}\), a resistor of resistance \(R\), two initially uncharged capacitors of capacitances \(C_1\) and \(C_2\), and an open switch, all connected in series. At time \(t = 0\), the switch is closed. Which of the following expressions represents the potential difference \(V_1(t)\) across capacitor \(C_1\) as a function of time \(t\)?