Given $R_1 = 3.0\ \Omega,$ $R_2 = 6.0\ \Omega,$ $R_3 = 6.0\ \Omega,$ $R_4 = 12.0\ \Omega,$ $R_5 = 8.0\ \Omega,$ $R_6 = 4.0\ \Omega,$ $R_7 = 2.0\ \Omega$ and $R_8 = 4.0\ \Omega.$ Find the charge of the capacitor in the circuit shown in the figure. The capacitance of the capacitor is $C= 2 \text{ F},$ and the voltage of the ideal battery is given by $V= 54 \text{ V}.$