# Need Help With Anaylsis of Circuit

Discussion in 'Homework Help' started by Mawangs1, Apr 28, 2012.

1. ### Mawangs1 Thread Starter New Member

Mar 26, 2012
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0
My book states that voltage at v1, v2, and v3 are 3.043V, -6.956V, and 0.6522V respectively.

I want to analyze this circuit by use of superposition. When I use superposition, I create a supernode out of the row where the 10V source as well as the dependent voltage source are at.

After this, I arbitrarily assigned current directions through the 3, 6, and 4 ohm resistors.

From here, I arrived at one equation by use of KCL and then 2 equations by use of KVL in the loop on the bottom left with the 10V source and KVL in the loop on the bottom right with the 5i dependent source.

I then plugged three values into a 3x4 matrix in my calculator from the following equations:

8v1 + 3v2 + 2v3 = 0

-1v1 + 1v2 + 0v3 = -10

-5v1 - 2v2 + 2v3 = 0

Next, I did rref and my calculator showed

v1 = 2.778

v2 = -7.222

v3 = -0.278

I just don't understand where I could be going wrong here....

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2. ### WBahn Moderator

Mar 31, 2012
23,381
7,095
So, you have two sets of answers: Your's and the book's. Which is correct? Is either of them correct? One of the nice things about analyzing circuits like this is that you can almost always determine whether your answer is correct or not regardless of whether you have solutions available.

There's no way to tell where you went wrong because you haven't shown your work in sufficient detail. At the very least, include the initial equations that your application of KVL and KCL gave you. From there we should at least be able to determine if your setup was correct. If so, then it is most likely an algebra error. If not, then we can work on the getting the concepts corrected.

Keep in mind that superposition is used by turning off all the independent sources and then turning them on (usually one at a time, but at least so that each is on exactly once) and performing separate analyses for each one and summing the result. In each analysis, all of the dependent sources need to be active. So, in this case, you only have one independent source and hence only one configuration to analyze -- in other words, superposition is useless here.

Before jumping in and throwing a bunch of equations at your calculator, examine the circuit and see what simplifications you can make. In this case, consider:

1) What effect on the three node voltages will removing the 6ohm resistor have?
2) Fundamentally, how many unknowns do you have?
3) Can you come up with a very simple relationship between v1 and v2?
4) Can you come up with a very simple relationship between v2 and v3?
5) Can you come up with a very simply relationship between v1 and i?

Answer these questions, and you should be able to write down a single equation that will give you one of the voltages (your pick) almost by inspection.

Now, before you solve for anything, look at what the answers will have to exhibit in order for them to make sense.

6) Can the voltages on v1, v2, and v3 all be positive?
7) What sign must i have?
8) Can you determine what sign must v1, v2, and/or v3 must have?