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Here is my problem from Hayt Fig 5.7

I am trying to solve applying superposition principle, but I am not getting anywhere close to the correct answer.

As the first step I eliminated 2A current source. omit 2A

I tried to solve it using mesh analysis. In the first loop I introduced clockwise current called i_1, in the second loop I introduced clockwise current called i_2. Here are the equations that I wrote for it.

-3 + 7i_1+15i_1 + 5(i_1-i_2) = 0

i_2 = -4i

i_1-i_2 = i

I solved it and got i = -1/61 and v_2 = -5/61 which is far off from stated answer: -0.246V

What did I miss?

Then I short-circuited 3V voltage source:

Omit 3V

I solved it using node analysis. Nodes are labelled in the main picture. Here are my equations:

2= v_1/7 + (v_1 + v_2)/15

4i = (v_2 - v_1)/15 + v_2/5

v_2 = 5i

I solved it and got v_2 = -546, which is again far off from -1.148.

I double checked my calculations. Could somebody confirm that I got correct equations?

user1700890
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2 Answers2

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In your mesh equations, you wrote i_1-i_2 = i. I think you meant i_2-i_1 = i. Your diagram didn't clearly show the directions of i_1 and i_2, so you made it hard for yourself to debug your own equations. I infer their directions from the two loop equations.

You appear to have declared the current from the dependent source to be 0 A. This is not valid unless current i is 0 A. When using superposition the procedure calls for killing independent sources, not dependent sources.

Charles B. Cameron
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  • Thank you! I should have created better diagram. I should have added arrow indicating i_1 and i_2 direction instead of writing that they are clockwise. 0A dependent source is just artifact of multisim diagram, I had to put some value there. So I have chosen 0A, but I am not using this value anywhere. – user1700890 Dec 07 '23 at 12:50
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Please see the answer below.Do not kill dependent sources while applying SPST.

enter image description here

Hari
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  • Thank you so much! I found my computational error. I did not kill dependent source. It is present in my system (i_2 = -4i). I like how you express current in terms of dependent current source. – user1700890 Dec 07 '23 at 12:48
  • If it solves your problem, please accept the answer – Hari Dec 07 '23 at 13:24