Hi
I have two problem both dealing with finding voltage using nodal anaylsis. When you have two dependant or independant voltage sources, Is the supernode equation determine identifying the node points separately for each voltage source or together as one?

For instance in the first question (refer to attachment doc)
View attachment tut2qns.doc
First SuperNode independent voltage source 3V : i1 = i3

Second SuperNode dependent voltage source 4Vo : i1 + i2

KVL for 4Vo - V = 0

rest of the equations

i1= (Vo-V)/3
i2= -3+V
i3= 4Vo-V

P.S

 

Well simply you start with equations for the current that enter the V node

I1 = (Vo - V)/3Ω
I2 = (0 - (V - 3))/1Ω
I3 = (4Vo - V)/5Ω

(Vo - V)/3Ω - (0V - (V - 3V))/1Ω - (4Vo - V)/5Ω = 0

Now we write equation for Vo node

(0V - Vo)/2 - ( Vo - V)/3 = 0

And now we can solve for Vo and V
Vo = 10/9 ; V = 25/9

 

One thing i don't understand when using nodal analysis with voltage source aren't you suppose to create a supernode?

 

according to your equations i have tried it a number of times and i cannot get the answer that you have got.
This is what i got from your equations:

1) -7Vo+13V = 45
2) -5Vo+2V=0

 

One thing i don't understand when using nodal analysis with voltage source aren't you suppose to create a supernode?

In your circuit we have only one supernode.

\( I1 = \frac{V_B - V_A}{3\Omega}\)

\( I2 = \frac{0V - V_D}{1\Omega}\)

\( V_D = V_A - 3V\) (supernode)

\( I3 = \frac{V_C - V_A}{5\Omega}\)

So for node A we can write from KCL.

\( I1 + I2 + I3 = 0\)

All current entry the A node, no current (0A) leaves the node.

according to your equations i have tried it a number of times and i cannot get the answer that you have got.
This is what i got from your equations:

1) -7Vo+13V = 45
2) -5Vo+2V=0

Well, yes because I made the mistake in the first equation when I rewriting the equation.