To solve this problem, we need to determine:

1. Currents $i_1, i_2, i_3, i_4,$ and $i_5$ in the circuit.
2. Voltages at nodes $A$, $B$, and $C$.

Let's break down each part of the problem:

Step 1: Analyze Currents

We'll use Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) along with Ohm's law to find the unknown currents in each branch of the circuit.

Known Values:

• $V_1 = 8 \, \text{V}$
• $V_2 = 12 i_5$ (controlled source)
• $V_4 = 15 \, \text{V}$
• $I_1 = 3 \, \text{A}$

Step 1.1: Node $B$

Since $I_1 = 3 \, \text{A}$ flows downward through $R_1$, the current $i_1$ flowing from node $A$ to node $B$ and the current $i_2$ flowing from node $B$ to node $C$ can be related using Kirchhoff's Current Law at node $B$: $i_1 + i_2 = I_1 = 3 \, \text{A}$

Step 1.2: Write Equations for Each Current

1. For $i_3$: Apply KVL in the left loop (containing $V_1$, $R_2$, $R_4$, and the dependent source $V_2 = 12 i_5$).

2. For $i_4$: Apply KVL in the right loop (containing $R_3$, $R_5$, $R_6$, and $V_4$).

3. For $i_5$: Note that $V_2 = 12 i_5$, which will help solve for $i_5$ when we set up equations in each loop.

Step 2: Determine Voltages at Nodes $A$, $B$, and $C$

Using the known voltages $V_1$, $V_4$, and the relationships derived from the currents, we can find the voltages at nodes $A$, $B$, and $C$ with respect to ground.

Would you like me to proceed by calculating each current and voltage in detail, or is there a specific part of the question you'd like to focus on?