Nodal Analysis - KVL Loop question.

AI Thread Summary
The discussion focuses on the application of nodal analysis and Kirchhoff's Voltage Law (KVL) in a circuit problem. The user has derived node equations but is uncertain about the correctness of their KVL application in a specific loop involving a 2V source. They confirm the presence of a supernode that includes nodes v1 to v3 and have performed KCL at the relevant nodes. Feedback indicates that their KVL formulation is correct, but a simpler approach could have been used. Overall, the user acknowledges the importance of practice in recognizing efficient problem-solving techniques.
NewtonianAlch
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Homework Statement


I've obtained the node equations that's in the matrix for rows 1, 2, and 4. I got 3 as well but I'm not sure if my analysis was correct.

http://img252.imageshack.us/img252/3151/nodeq.jpg

The Attempt at a Solution



http://img684.imageshack.us/img684/9803/dsc0010van.jpg

So basically this is from the bottom-left of the circuit.

v1 = -2 + Vx, therefore

Vx = v1 + 2 (I wrote -2 in the drawing by mistake)

So doing KVL: -Vx + 2 + 5io + v2 = 0

=> (-v1 -2) + 2 + v3 + v2 = 0

So, -v1 + v2 + v3 = 0 [which is row 3 of the matrix]

Note that io = v3/5, so 5io is just v3.

Is this correct reasoning?
 
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Hmm. Looks to me like you've got a supernode situation since some nodes are directly tied together with voltage sources. Can you identify the boundaries of the supernode? Which nodes are left as independent nodes?
 
I've done all of that, the supernode encompasses everything from v1 to v3. So I did KCL for that supernode and then KCL at node 4.

I just need to know if I've done the KVL for the loop in the bottom-left hand correctly. My answers all work out to the solutions given, but I just had a funny feeling about the KVL as I was struggling to get it initially because of that 2V source and the direction of it.
 
NewtonianAlch said:
I've done all of that, the supernode encompasses everything from v1 to v3. So I did KCL for that supernode and then KCL at node 4.

I just need to know if I've done the KVL for the loop in the bottom-left hand correctly. My answers all work out to the solutions given, but I just had a funny feeling about the KVL as I was struggling to get it initially because of that 2V source and the direction of it.

Okay. Well the KVL you wrote looks fine.

Since you know that 5i0 = v3, would it not have been simpler to just write KVL from node v1 to v2 as:

v2 = v1 - v3

and rearrange?
 
Hmm, you're right! I guess only practice helps recognise things like that easily. Thanks once again.
 

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