Originally Posted by
topsquark We know the current in the bottom branch of the circuit (the one with only one 10 Ohm resistor) is 9 A. So what's the potential difference across it? V = IR, so V = (9A)(10 Ohm) = 90 V. (See "Tough circuit4.")
Now take a look at the junction on the left side where the 9 A runs into the 12 A. (The vertical line on the left side.) What is the unknown current running into this junction? Well, by tracing the direction of the currents we know that both the 9 A and 12 A branches have the current flowing upward here. So we have to ADD current to the 9 A to bring it up to the 12 A. Thus the unknown current coming into the junction is 3 A and is flowing to the left. (See "Tough circuit5.")
Finally, let's get the potential across the two 10 Ohm resistors. The two resistors are in series, so the equivalent resistance of the two is 10 Ohm + 10 Ohm = 20 Ohm. The current in this branch is 3 A, so the potential across the resistors is (3 A)(20 Ohm) = 60 V. (See "Tough circuit6.")