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: Apply KCL (Kirchhoff's Current Law) at node \( v_1 \) and \( v_2 \).
Using Ohm’s law and KCL, we can solve for the node voltages.

Step 2: Solve the system of equations. We can substitute the given current and resistance values into the KCL equations to find the values of \( v_1 \) and \( v_2 \).
After solving, we get:
\( v_1 = 10 \, \text{V}, v_2 = 20 \, \text{V} \).

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