Determine the current in each segment of the circuit, starting from point 'a' and working left, utilizing Kirchhoff's Current Law.

Step 1: Determine the current in each segment of the circuit.
We will trace the current from right to left, starting from point 'a'.
The 3A current is flowing into point 'a'. This means the current through the 4Ω resistor and the 1Ω resistor (to its left) is $I_3 = 3\text{A}$.
At the node to the left of the 1Ω resistor (right of 12V source), a 1A current flows downwards. By Kirchhoff's Current Law, the current flowing into this node from the left must be $I_2 = I_3 + 1A = 3A + 1A = 4