Find the current using Nodal Analysis

2 replies · 2K views · last reply
Fatima Hasan
Messages
315
Reaction score
14

Homework Statement


Circuit schematic with nodes V1, V2 and V3 and a 10 V voltage source between V1 and V2, a 5i dependent current source between V2 and V3, resistors 6 Ω, 4 Ω, 3 Ω and 2 Ω, current i labelled in the left branch, and two supernodes outlined by dashed boxes.

Find i using Nodal Analysis.

Homework Equations


V = I * R

The Attempt at a Solution


Handwritten-style equations in LaTeX for nodal analysis: V2 - V1 = 10, V1 = V2 - 10(1), V3 - V2 = 5i, supernode equations (1) to (3) in V1, V2 and V3.

solve (1) , (2) , and (3) to find V1 , V2 ,and V3
V1 = 50/3 = 16.67 V
V2 = 80/3 = 26.67 V
V3 = 40 V
40 - 80/3 = 5i
i = 2.667 A
However , the correct answer is 1.522 A .. I don't know where is my mistake.
 
Attachments
  • Circuit schematic with nodes V1, V2 and V3 and a 10 V voltage source between V1 and V2, a 5i dependent current source between V2 and V3, resistors 6 Ω, 4 Ω, 3 Ω and 2 Ω, current i labelled in the left branch, and two supernodes outlined by dashed boxes.
    screenshot_25.png
    19 KB · Views: 811
  • Handwritten-style equations in LaTeX for nodal analysis: V2 - V1 = 10, V1 = V2 - 10(1), V3 - V2 = 5i, supernode equations (1) to (3) in V1, V2 and V3.
    screenshot_24.png
    12.3 KB · Views: 773
Your first equation should be V1-V2=10, since V1 is at a higher potential than V2.
Where does the first term in your first supernode equation come from?
Hint: Once you fix your first two node equations, you can use the ground node for the third equation.
 
Last edited:
Why did you choose to employ two supernodes when it would seem that a single one would suffice?