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The circuit in the image shows a system with two current sources (1A and 4A), three resistors (2Ω, 7Ω, and 6Ω), and two nodes (labeled 1 and 2). The task asks to determine the voltages at these nodes.

### Steps to solve the problem:
1. **Identify the reference node (ground)**: From the diagram, let's assume the bottom-most wire is grounded (reference voltage = 0V).
2. **Apply Kirchhoff’s Current Law (KCL)** at the nodes to find the voltages at each node.  

#### Node 1 (V₁):
- The currents entering and leaving the node must sum to zero.
- Currents through resistors from Ohm’s law: \( I = \frac{V}{R} \).

Using KCL at node 1:
- Incoming current from the 1A source: \( +1A \)
- Outgoing current through the 2Ω resistor: \( \frac{V_1}{2Ω} \)
- Outgoing current through the 6Ω resistor (to node 2): \( \frac{V_1 - V_2}{6Ω} \)

Thus, the KCL equation for node 1 becomes:
\[
1A = \frac{V_1}{2Ω} + \frac{V_1 - V_2}{6Ω}
\]

#### Node 2 (V₂):
Using KCL at node 2:
- Incoming current from node 1 through the 6Ω resistor: \( \frac{V_1 - V_2}{6Ω} \)
- Outgoing current through the 7Ω resistor: \( \frac{V_2}{7Ω} \)
- Incoming current from the 4A source: \( +4A \)

Thus, the KCL equation for node 2 becomes:
\[
4A = \frac{V_2}{7Ω} + \frac{V_2 - V_1}{6Ω}
\]

### Solve the system of equations:
Now we have two equations:
1. \( 1A = \frac{V_1}{2Ω} + \frac{V_1 - V_2}{6Ω} \)
2. \( 4A = \frac{V_2}{7Ω} + \frac{V_2 - V_1}{6Ω} \)

Let me calculate the voltages \( V_1 \) and \( V_2 \).The voltages at the nodes are as follows:
- \( V_1 = \frac{82}{15} \) V ≈ 5.47 V
- \( V_2 = \frac{238}{15} \) V ≈ 15.87 V

These are the node voltages relative to the reference (ground).

Would you like a more detailed explanation of how these values were derived or how to interpret them?

Here are 5 follow-up questions to expand on this:
1. How does Kirchhoff's Current Law (KCL) apply to circuits with multiple current sources?
2. How would changing one of the resistor values affect the node voltages?
3. What is the relationship between node voltages and branch currents in this circuit?
4. How would the voltages change if we swapped the positions of the current sources?
5. How could we verify these voltages experimentally?

**Tip:** Always double-check the ground (reference) placement in your circuit to avoid incorrect node voltage calculations!

Determine los voltajes de los nodos en el circuito de la figura 3.27.

Solve for the node voltages in a circuit with 1A and 4A current sources, 2Ω, 6Ω, and 7Ω resistors using Kirchhoff's Current Law (KCL). Includes step-by-step circuit analysis and equations. Suitable for electrical engineering students.

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