R2 is gone now because V2=R2*gv
now i dont know what i should do to calculate Vab :/

When you transform a Norton equivalent circuit (current source in parallel with a resistance) it becomes a Thevenin equivalent circuit (voltage source in series with a resistance). The resistance does NOT go away.

 

okay! now the circuit is like this?

 

Topologically that is correct. You still need to show what V2 is equal to (namely gv*R2) and what v is.



So now the next step is to find Voc (open-circuit voltage) and Iss (short-circuit current).

 

V= - (V1*R2)/(R1+R2) + (V1*R)/(R+R3) ???

 

V= - (V1*R2)/(R1+R2) + (V1*R)/(R+R3) ???

It looks like you are just throwing the voltage divider formula at anything that has a voltage supply and two resistors.

For the open-circuit voltage, what is the current in R1 and R2?

Given the answer to the above, what is the voltage, relative to node B, of the junction between R1 and R2?

Given the answer to the above, what is the voltage, v, across the gap?

Given the answer to the above, what is the voltage of the V2 supply?

Given the answer to the above, what is the voltage Vab?

 

there is no current in R1 and R2?? and V=VR ?? i am confused! this is So haaard!!

 

but i'm not gonna give up!!

 

there is no current in R1 and R2?? and V=VR ?? i am confused! this is So haaard!!

Correct that there is no current in R1 and R2.

I'm not sure what you mean by V=VR. Let's rename the little v (the voltage across the gap) to Vgap, making our dependent current source gVgap and our dependent voltage source gVgapR2. Let's also rename R to R0. I'm making those changes so that unadorned variables, such as V and R, can stand for generic variables in formulas such as Ohm's Law and not be mistaken for specific variables in this problem.

Since we haven't been explicit before now, let's call the bottom node (Node B) our ground, making it 0V.

What is the voltage at the junction between R0 and R3 (the + side of Vgap)?

If there is no current in R1, what is the voltage at the junction between R1 and R2 (the - side of Vgap)?

So what is Vgap?

Given Vgap, what is V2 (the output voltage of the dependent voltage source)?

If there is no current in R2, what is the voltage across R2?

Given the voltage at the - side of Vgap, the voltage across R2, and the voltage output of the dependent voltage source, what is Va (the voltage at Node A)?

What is Vab?