The circuit of Fig. $27-75$ shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially $\mathrm{S}$ has been open for a long time. If it is then closed for a long time, what is the change in the charge on the capacitor? Assume $C=10 \mu \mathrm{F}, \quad \mathscr{E}_{1}=1.0 \mathrm{~V}, \quad \mathscr{E}_{2}=3.0 \mathrm{~V}$
$R_{1}=0.20 \Omega,$ and $R_{2}=0.40 \Omega$