Three resistors $R_1=80\mathrm{.}2,R_2=22\mathrm{.}6,R_3=70\mathrm{.}0,$ and two batteries ${}_1=40\mathrm{.}0V,$ and ${}_2=358V$ are connected as shown in the diagram below.

$($a$)$ What current flows through $R_1,R_2,$ and $R_3?$

$I_1=$

$$ Did you choose directions for each of the three currents? Given that you have three unknowns to solve for, how many equations, at the least, will you need? A $I_2=-5\mathrm{.}6$ Did you choose directions for each of the three currents? Given that you have three unknowns to solve for, how many equations, at the least, will you need? A $I_3=3$ Did you choose directions for each of the three currents? Given that you have three unknowns to solve for, how many equations, at the least, will you need? A

$($b$)$ What is the absolute value of the potential difference across $R_1,R_2,$ and $R_3?$

$|V_{R1}|=1$

How is the potential difference related to the current and the resistance? V

$|V_{R2}|=$

$q,$ How is the potential difference related to the current and the resistance? $V$

$|V_{R3}|=$

$q,$ How is the potential difference related to the current and the resistance? $V$