A circuit contains an ideal battery of potential difference \(\Delta V\), an open switch \(S\), and two parallel branches. Branch 1 contains a resistor of resistance \(R\). Branch 2 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\). Switch \(S\) is closed at time \(t = 0\). Which of the following claims and justifications correctly describes the current in Branch 2 a long time after the switch is closed?