In the circuit shown, an ideal battery of constant voltage \(V_0\) is connected in series with an open switch \(S\) and a resistor of resistance \(R\). This combination is connected across a parallel network consisting of a resistor of resistance \(3R\) in one branch and two uncharged, identical capacitors, each of capacitance \(C\), connected in series with each other in the second branch. At time \(t = 0\), switch \(S\) is closed. Which of the following expressions represents the total current \(I(t)\) supplied by the battery as a function of time \(t \ge 0\)?