# Simple Nodal Analysis

1. Homework Statement

http://img258.imageshack.us/img258/2152/screenshot01kf5.th.jpg [Broken]

2. Homework Equations

KCL
KVL
V = IR

3. The Attempt at a Solution

I used 4 nodes at the top, one reference node at the bottom.

I have it labeled V1, V2, V3, V4, starting from the far left -> right.

My nodal equations are:

At v1:

+ 7V

At v2:

0 = (v2-v1) / 2 + v2 / 4 + (v2 - v3) / 4

At v3:

(v3-v2) / 4 + v3 / 8 + (v3 - v4) / 8 = 0

At v4:

0 = (v4-v3)/ 8 - 1mA

so we know V0 is v2-v3 = v0.

I'm not sure if this is correct so far.

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mjsd
Homework Helper
your image is too small to be legible

So far it's correct.

your image is too small to be legible
Try clicking on the (thumbprint) image to view a larger one.

For v4, is it 8V in my case? I'm stuck with the simult. equations, and I'm just curious. I have a 1mA current going through the 8k resistor, so i'm believing its 8V? Can anyone verify this?

I have simplified it to this:

V1 = 7V (like before)

for node at V2...

4V_2 - 2V_1 - V_3 = 0

for node at V3...

4V_3 - 2V_2 - V_4 = 0

for node at V4...

V_3 - V_4 = 8

So, all of the eq put together...

4V_2 - 2V_1 - V_3 = 0
4V_3 - 2V_2 - V_4 = 0
V_3 - V_4 = 8
V_0 = V_2 - V_3

I'm not sure what to do after here.

For v4, is it 8V in my case? I'm stuck with the simult. equations, and I'm just curious. I have a 1mA current going through the 8k resistor, so i'm believing its 8V? Can anyone verify this?
No, v4 is not 8V, but either one of (v4-v3) or (v3-v4) is and it is not difficult to figure out which one is.

I have simplified it to this:

V1 = 7V (like before)

for node at V2...

4V_2 - 2V_1 - V_3 = 0

for node at V3...

4V_3 - 2V_2 - V_4 = 0

for node at V4...

V_3 - V_4 = 8

<snip>

I'm not sure what to do after here.
The nodal equation for node 4 is incorrect. Please check that against your first post. You have above 3 equations with 3 unknowns (v2, v3, v4). It becomes thus a mathematical problem now to resolve the 3 unknowns. The final step, of course, would be to put these values into finding v0 = v2-v3.

Oh, woops, it should be v_4 - v_3 = 8, as in my first post.

Its this math part that kills me, I'll be back in a few:)

Thanks so far, doodle.

Nevermind, it's correct. I just checked.

Thanks for all those that helped :)