# Nodal Analysis

Discussion in 'Homework Help' started by jumbo16, Sep 24, 2013.

1. ### jumbo16 Thread Starter New Member

Sep 24, 2013
3
0
Hey guys,
having trouble with this nodal analysis question for my weekly tutorial and was wondering if anyone could help me out. Here's the question below and the circuit is attached.

The circuit shown in Figure 3, has an independent voltage source, an independent current source and current controlled dependent current source.
(i) Write a set of NODAL equations that mathematically describes the circuit;
(ii) Show these Nodal equations in MATRIX form;
(iii) Using Cramers Rule and Circuit Theory solve for the voltages at the numbered NODES 1 to 4;
(iv) Using the voltages at each node calculate the current for nodes 2 & 4 and show Kirchhoffs Current Law (KCL) holds for each of these nodes.

Any help or pointers would be great

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2. ### jumbo16 Thread Starter New Member

Sep 24, 2013
3
0
Have already attempted the problem with V1 and V2 forming a supernode (is this correct?) but not sure if the rest of calculations are right as i am left with a matrix that, as far as i can tell, is un-solveable using cramers rule

3. ### WBahn Moderator

Mar 31, 2012
17,719
4,788
How can we tell if you are doing it right unless you show us how you are trying to do it?

You need to post your best attempt at a solution.

4. ### jumbo16 Thread Starter New Member

Sep 24, 2013
3
0
So far i hav

Ia=V1/2x10^3 so Ia/5= V1/10x10^4

Super node: V2 = V1-12

Node 2: (V2-V4/4x10^3) + (V2-V3/5x10^3) + (V2/1x10^3) = 0
29(V2) - 4(V3)-5(V4) = 0
Node 3: (-Ia/5) + (V3-V1/2x10^3) + (V3-V2/5x10^3) = 0
(V1/10x10^3) + (V3-V1/2x10^3) + (V3-V2/5x10^3) = 0
-4(V1) - 2(V2) + 7(V3) = 0
Node 4: (V4/2x10^3) + (2x10^-3) + (V4-V2/4x10^3) = 0
-V2 + 3(V4) = -8

Not sure if this is correct and dont really know where to go from here

5. ### WBahn Moderator

Mar 31, 2012
17,719
4,788
You are being very sloppy with your math. When you say

(V2-V4/4x10^3)

this means

(V2) - (V4/4x10^3)

which is not what YOU mean.

The sloppier you are with your notation, the more absolute the guarantee that you will screw of the arithmetic at some point.

Also, you need to track your units properly.

What happened to the negative sign on Ia in your Node 3 equation?

In your equation for Node 4, what is the basis upon which you concluded that V4 was the voltage across the 2kΩ resistor?

After you come up with your equations, you need to develop the habit of then looking them over critically and asking if they truly make sense. A big part of this is asking if the units actually work out properly and you can't do this unless you properly track units.

jumbo16 likes this.
6. ### tongang New Member

Sep 23, 2013
1
0
i need help with my homework but i couldn't post it here..

Mar 31, 2012
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