Question

Determine the node voltages \( v_1 \) and \( v_2 \) for the given circuit:

• A. \( v_1 = 10 \, \text{V}, v_2 = 20 \, \text{V} \)
• B. \( v_1 = 20 \, \text{V}, v_2 = 10 \, \text{V} \)
• C. \( v_1 = 20 \, \text{V}, v_2 = 20 \, \text{V} \)
• D. \( v_1 = 10 \, \text{V}, v_2 = 10 \, \text{V} \)

Hint:

When solving for node voltages in electrical circuits, use Kirchhoff's Current Law (KCL) and Ohm’s Law to set up a system of equations. Solve these equations simultaneously to determine the unknown voltages.

Answer 1

The Correct Option is A

Step 1: Implement Kirchhoff's Current Law (KCL) at nodes \( v_1 \) and \( v_2 \).
Ohm's law and KCL are applied to determine the node voltages.

Step 2: Solve the equation system. The KCL equations, combined with the provided current and resistance data, yield the values for \( v_1 \) and \( v_2 \).
The solution is:
\( v_1 = 10 \, \text{V}, v_2 = 20 \, \text{V} \).

Final Answer: \[\boxed{(1) \, v_1 = 10 \, \text{V}, v_2 = 20 \, \text{V}}\]