Analyzing circuit with dependent sources

circuit analysisNetwork

What will be voltage Vz in this circuit

schematic

simulate this circuit – Schematic created using CircuitLab

I have tried to solve the equation using mesh analysis by taking i1 and i2 anti clockwise in upper and lower mesh respectively.

Best Answer

First, see that in the upper wire you have $$I_1=-2 Vx$$ and you can write: $$I_1 = I_2 + I_3$$, where I_2 is the current in the 2nd wire (from left to right) and I_3 is the current in the other one. Now, you have to "decide" where the Ground is and just solve equations.

Note that V_Z has the same voltage that the - of V_x. Using that, I got: $$I_2 = -\frac{V_Z + V_X}{R_2}$$ $$I_3 = \frac{15V - V_Z}{R_3}$$

If you don't know V_X, you can have it using that $$2V_X = I_2 + I_3$$