Nodal Analysis: Solving Homework Problem

[Ronaldo95163]

Homework Statement

*Posted in the Screenshot*

Homework Equations

*Posted in the uploaded attachment*

The Attempt at a Solution

*Posted in the uploaded attachment*Hi all.
Our lecturer gave us the question as part of an assignment but I'm not to sure if my approach and answer is correct. I attempted it using a supernode as shown in the picture below:

 

[gneill]

Note that the supernode you've identified is not an essential node -- it's potential is "fixed" by the controlled voltage source tied to the reference node. So you shouldn't write a node equation for it. In fact, there's only one essential node in the whole circuit!
Node v1 is the only essential node.

In your workings you combined the parallel resistors 5||3 at v1. You could also combine the other two 5 and 3 Ohm resistors. Since they are series-connected in a branch, their junction is not an essential node.

Write the node equation for node v1, the only essential node.

 

[Ronaldo95163]

Woa..can't believe I missed those two resistors lol.
Here's my solution.

I used the supernode equations to form relationships with the other node voltages.

 

[Ronaldo95163]

I have another question I got kinda stuck on in the same assignment as well:
*Pics Below*
My first time doing a problem like this so this was my attempt at it.

 

[gneill]

Woa..can't believe I missed those two resistors lol.
Here's my solution.

I used the supernode equations to form relationships with the other node voltages.

No, once again you're trying to write a node equation for the supernode which isn't an essential node. Do NOT write a node equation for a node tied to the reference node by a voltage source. Such a node is only an extension of the reference node, and we do not write an equation for the reference node.

Write only a node equation for the node v1 that I pointed out (post #2). It's the only essential node in the circuit.

 

[gneill]

I have another question I got kinda stuck on in the same assignment as well:
*Pics Below*
My first time doing a problem like this so this was my attempt at it.

You should start a new thread with a new problem. It avoids "crosstalk" that can occur in a thread when more than one problem is being addressed at the same time.

 

[Ronaldo95163]

Oh no probs ill make a new thread for that problem
Wrt the first problem here's what I came up with

Edit
For the second eqn it should be 5Ix-5-V1+5Ix-V1=5

Which simplifies to 10=10Ix-2V1

 

[gneill]

You shouldn't need KVL for this problem. One node equation and the constraint equations imposed by Ix and the controlled source and fixed sources should suffice.

 

[Ronaldo95163]

What I can see from the diagram that the pd across the 20ohm resistor is the same as V1 so 20Ix = V1

So a substitution can be made into the node equation tol solve for either V1 or Ix.

Wrt the kvl approach i took...is it incorrect??
If so then why?

 

[gneill]

What I can see from the diagram that the pd across the 20ohm resistor is the same as V1 so 20Ix = V1

So a substitution can be made into the node equation tol solve for either V1 or Ix.

Yup. And since this is nodal analysis you'll want to solve for V1.

Wrt the kvl approach i took...is it incorrect??
If so then why?

If you want to solve with nodal analysis, then you don't do mesh or loop KVL equations. There's no reason to do so.

 

[Ronaldo95163]

Woa thanks a bunch man!
Gonna go check over that second problem now

 

[Ronaldo95163]

Worked it over and this is my final soln:

 

[gneill]

Check your math on the last two lines of calculating Ix. The setup looks good to me, but your final value for Ix looks much too large.

 

[Ronaldo95163]

Woops divided it wrong on my calculator haha thanks man