Simple Nodal Analysis: Solving Homework

[ravenprp]

Homework Statement

http://img258.imageshack.us/img258/2152/screenshot01kf5.th.jpg

Homework Equations

KCL
KVL
V = IR

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.

 

[mjsd]

your image is too small to be legible

 

[doodle]

So far it's correct.

your image is too small to be legible

Try clicking on the (thumbprint) image to view a larger one.

 

[ravenprp]

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?

 

[ravenprp]

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.

 

[doodle]

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.

 

[ravenprp]

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.

 

[ravenprp]

Nevermind, it's correct. I just checked.

Thanks for all those that helped :)