A capacitor of capacitance \(C_1=1\,\mu\text{F}\) is charged using a \(9\text{ V}\) battery. \(C_1\) is then removed from the battery and connected to capacitors \(C_2\) and \(C_3\) of \(2\,\mu\text{F}\) and \(3\,\mu\text{F}\) respectively as shown in the figure. Find the charge on \(C_3\) after equilibrium has reached.