$45M$ In Fig. $27\mathrm{.}37,$ the resistances are $R_1=1\mathrm{.}0$ and $R_2=2\mathrm{.}0,$ and the ideal batteries have emfs $E_1=2\mathrm{.}0V$ and $E_2=C_3=4\mathrm{.}0V.$ What are the $($a$)$ size and $($b$)$ direction $($up or down$)$ of the current in battery $1,$ the $($c$)$ size and $($d$)$ direction of the current in battery $2,$ and the $($c$)$ size and $($f$)$ direction of the current in battery $3?($g$)$ What is the potential difference $V_a-V_b?$