Electrical Engineering (Nodal analysis problem)

[sykoh2]

Homework Statement

Using Nodal analysis, find Vo in the circuit of Fig. 3.56

http://img233.imageshack.us/img233/7080/74830694.png

Homework Equations

1. KCL and KVL
2. Supernode?

The Attempt at a Solution

http://img560.imageshack.us/img560/8250/16133010.png




Hi, I'm stuck with this question, I'm not sure to use supernode to solve it or not. Pleaae help me. Thanks in advance. :)

 

[gneill]

Hi sykoh2. Welcome to Physics Forums.

You should be able to complete the problem with the nodes you've chosen, provided that you make sure to include all the branches! (In the "@Node 1" equation you started with, you failed to include in the sum the current through the branch with B1 and R4).

You might also note that V2, the voltage at node 2, is identical to Vo which you're trying to find.

 

[sykoh2]

Hi gneill, just to confirm with you what is the current through the voltage of the 3V source and the 1 ohm resistor, is it (3V - 0V) / 1 ohm?

 

[gneill]

Hi gneill, just to confirm with you what is the current through the voltage of the 3V source and the 1 ohm resistor, is it (3V - 0V) / 1 ohm?

Nope. The voltage at the top of R4 will be V1 - B1. Think of a branch as a stack of component from the ground (reference) node up to the node that you're writing the node equation for. Essentially you're doing a KVL pass through those components with an assumed current value and direction for the branch. So for this branch you have:

V1 - B1 - I*R4 = 0

which gives I = (V1 - B1)/R4 for the branch current.

 

[uart]

Hi sykoh2. It usually makes nodal analysis much easier if you replace the voltage sources with their Nortons equivalents. Doing this makes your problem quite a lot easier.

 

[sykoh2]

http://img40.imageshack.us/img40/7184/46842948.png

Hi all, I had try to solve it, but no matter how I try to solve i just can;t get the correct answer. The ans is Vo = 2.778V. Any guide? Thanks.

 

[gneill]

Hi all, I had try to solve it, but no matter how I try to solve i just can;t get the correct answer. The ans is Vo = 2.778V. Any guide? Thanks.

In your Node 1 equation you're not being consistent in your current directions.

When you write (V2 - V1)/3 that's the current flowing from node 2 INTO node 1. When you write (4V2 - V1)/5 that's the current flowing from the controlled source INTO node 1. When you write (V1 - 3)/1, that's the current flowing OUT of node 1 to the ground node. Surely this latter current must EQUAL the sum of the other two.

If you want to make the equation consistent and sum to zero, change the sign of the the last term.

 

[sykoh2]

okay, Thanks for the guidance, I get a clearer pictures of how to solve it. Thanks. :)