The value of the unknown node voltage V₁ in the given circuit is to be determined...

Question

The value of the unknown node voltage V₁ in the given circuit is to be determined.

Given:

• Resistors: 3Ω, 4Ω, 1Ω, 5Ω
• Voltage source: 22V between V₂ and V₃
• Current sources: -3A, -8A, -25A

Step-by-Step Solution

Step 1: Define Node Voltages

Let the node voltages be:

• V₁
• V₂
• V₃

The bottom node is taken as the reference (ground).

Step 2: Voltage Source Constraint

Since there is a 22V source between V₂ and V₃:

V₃ − V₂ = 22

Step 3: Apply KCL at Node V₁

Applying Kirchhoff’s Current Law:

(V₁ − V₂)/3 + (V₁ − V₃)/4 + 3 + 8 = 0

Step 4: Supernode (V₂ and V₃)

Because of the voltage source, treat V₂ and V₃ as a supernode.

KCL for supernode:

(V₂ − V₁)/3 + (V₃ − V₁)/4 + V₂/1 + V₃/5 − 3 − 25 = 0

Step 5: Substitute V₃

Using: V₃ = V₂ + 22

Step 6: Solve Equations

Solving the system of equations:

• V₂ = 10.5 V
• V₁ = 1.071 V

Final Answer: V₁ = 1.071 V
Correct Option: B