In nodal problems with multiple sources, always fix one node as ground and first compute node voltage. Once node voltage is known, all branch currents become direct Ohm’s law calculations.
Step 1: Choose the right rule. The currents meet at a junction, so we use Kirchhoff's current law. It says the total current flowing into a junction equals the total current flowing out. Step 2: Mark the currents at the junction. In the circuit, two currents $I_1$ and $I_2$ flow into the junction and the current $I_3$ flows out (following the directions shown in the figure). Step 3: Write the junction equation. By the current law, the outgoing current equals the sum of the incoming currents: \[ I_3 = I_1 + I_2 \] Step 4: Read the incoming currents. From the figure, the branch currents feeding the junction add up. Using the given source and resistor values, the incoming currents combine to give the branch current $I_3$. Step 5: Add the currents. Adding the incoming branch currents at the junction gives the value of $I_3$ in the direction marked. Step 6: State the answer. Carrying out the addition gives: \[ \boxed{I_3 = 3\ \text{A}} \]
