Feeling Stuck? Help with This Example Problem!

[wencme]

I can't tell you how many attempts I've had at this. I must be following the current wrong, or something...

PLEASE HELP.. this is an example from the chapter! I feel very stupid...

 

[donpacino]

You are forgetting about the current through that dependent source.
To easily solve this you can use a method that my basic EE proffesor called supernodes. You can use a supernode whenever two node are directly linked by a voltage source.

First define V3 and V2 in respect to V1.

then write 1 equation for the current leaving all three nodes and solve.

Show me some work or an attempt!

 

[wencme]

I already found those values. I have 3 of the 4 equations I need and I can't understand how to find the formula for the V1 node. there is i4 and i1 coming out, but nothing going into the node. Here are the formulas I already found:
V2=V1-25
V3=V2+2.5V1
2V1-3V2-6V3=0

 

[donpacino]

the current going into the node is the current that goes through the voltage source.

The current that goes through the voltage source is the current through the 4 ohm resistor and the dependant voltage source.

The current through the dependant voltage source is the current through the 6 ohm resistor and the current through the 3 ohm resisitor

 

[donpacino]

If you use true nodal analysis it all has to be solved as one node

 

[wencme]

I used the formulas you suggested and still cannot get the correct answer. The book says v1=7.608 v2=-17.39 v3=1.6035

Any further help will be greatly appreciated - I have spent hours on this problem

 

[gneill]

Hi wencme. Let's see if we can't get you a satisfactory solution.

My suggestion is to begin by writing the single supernode equation making use of the voltages as labelled. Then write out the relationships between the voltages as you've doe above, and substitute them into the supernode equation leaving only one voltage variable.

Here's your circuit redrawn to indicate the supernode. Your supernode equation will contain terms for each node where the supernode "bubble" cuts a conductor.

Can you write out the supernode equation, first using V1, V2, and V3 to begin with?

 

[wencme]

None of this helps. I have tried this problem 11 ways to Sunday and still cannot arrive at the correct answer! This is a chapter intro PRACTICE problem and is not for homework or for a grade. I simply want to know how to solve this thing.

 

[The Electrician]

I already found those values. I have 3 of the 4 equations I need and I can't understand how to find the formula for the V1 node. there is i4 and i1 coming out, but nothing going into the node. Here are the formulas I already found:
V2=V1-25
V3=V2+2.5V1
2V1-3V2-6V3=0

You only need 3 equations, not 4.

These 2 equations are correct:

V2=V1-25
V3=V2+2.5V1

The three nodes V1, V2 and V3 form a supernode. The 6 ohm resistor is just connected from one node of the supernode to another node of the supernode; whatever current passes through it enters the supernode at one end and leaves the supernode at the other end--you can ignore it.

Treating V1, V2 and V3 as if they were all one node, sum the currents leaving it:

V1/2 + V2/4 + V3/3 = 0

That's the additional equation you need--the supernode equation. What do you get if you solve all three equations?