1. The problem statement, all variables and given/known data The problem is "What is the current through resistor g when switch B has been closed and switch A has been open for a long time?" (see diagram) 2. Relevant equations V = IR I/Reff = 1/R1 + 1/R2 Reff = R1 + R2 3. The attempt at a solution Because f+g are in series, the Reff = 6 ohms. Since f/g is in parallel with c, the new Reff is 4 ohms. Then because f/g/c are in series with a/b, the new total resistance is 10 ohms. As a result, we can find through V = IR that the current is 9A (90 V = I x 10 ohms). So then, if V = IR, to find the current through each respective resistor (in parallel), I did 90 V = I x 12 ohms, and 90 = I 6 ohms, however, this gives me currents that are incorrect. Instead, the answers are 6 A, and 3 A through the 6 ohm resistor and 12 ohm resistor. I understand this conceptually, i.e. yes, the resistor 12 ohm is 2X the resistor 6 ohm, therefore current would be half as large - however, I can't figure this out mathematically. Literally, I have spent an hour on this problem, I've read various tutorials, watched khanacademy, read the solution in the back of the book (which gives a conceptual answer) but I can't figure this out. Please help, because I really want to figure this out and I can't move on until I do.