Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19–56. The batteries have emfs of $\xi_1 = 9.0 \textrm{ V}$ and $\xi_2 = 12.0 \textrm{ V}$ and the resistors have values of $R_1 = 25 \; \Omega$, $R_2 = 68 \; \Omega$, and $R_3 = 35 \; \Omega$.

a) $I_1 = 0.02 \textrm{ A, right. } I_2 = 0.12 \textrm{ A, left. } I_3 = 0.10 \textrm{ A, up.}$ b) Darn, I forgot to answer this in the video. The process to solve for part b) is exactly the same as what's shown for part a). Since the internal resistances are in series with the resistor in the same branch as the battery, the only difference compared with a) is to add one more ohm to $R_1$ and to $R_3$. $R_1 = 26 \Omega$ and $R_3 = 36 \Omega$. This doesn't make any difference to the final answer after you round to the correct number of significant figures, so the final answer is the same as for part a).