Nodal Analysis - KVL Loop question.

[NewtonianAlch]

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?

 

[gneill]

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?

 

[NewtonianAlch]

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.

 

[gneill]

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?

 

[NewtonianAlch]

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