i can see from the result that the way i am trying to solve the problem is wrong can someone tell me why? (see pdf) thank you

 

Your equation correctly sums the currents of the two parallel current sources and subtracting the current through the 10 Ohm resistor should result in 0. The confusing thing is the controlled current source (diamond shape) being controlled by the Vdrop (Vo) of the 10 resistor. In essence this is a non-converging depiction since Vo doubles the output of the controlled source which in turn drives a higher Vo.

I am not sure what this exercise is trying to teach.

 

thank you a lot for your help

 

Your equation correctly sums the currents of the two parallel current sources and subtracting the current through the 10 Ohm resistor should result in 0. The confusing thing is the controlled current source (diamond shape) being controlled by the Vdrop (Vo) of the 10 resistor. In essence this is a non-converging depiction since Vo doubles the output of the controlled source which in turn drives a higher Vo.

I am not sure what this exercise is trying to teach.

Beware of the definition of Vo! Pay close attention to its polarity.

 

ok but can you see the attached pdf the polarity of Vo is how the vccs act on Vo or something else. it is confusing the two current sources send current to the node how on earth i can have current from the loop coming the same way i must loose grasp of something i can not understand please help (see also pdf)

 

ok but can you see the attached pdf the polarity of Vo is how the vccs act on Vo or something else. it is confusing the two current sources send current to the node how on earth i can have current from the loop coming the same way i must loose grasp of something i can not understand please help (see also pdf)

First, do your nodal analysis without thinking too much about how the controlled current source and Vo are interacting. Instead, write definitions for them that you can substitute in later. Don't do the substitutions right away, save that until you've got the node equation nailed down using just the given component values.

Assume a node voltage V1 at the obvious single node:

Clearly Vo is given by Vo = -Io*4Ω. Note the sign. Further, the current in that branch, given the node voltage V1, is given by I = V1/(4Ω + 6Ω); there are TWO resistors in that branch. Note that no mention of Vo is used in that current equation for Io. Vo is incidental at this point.

Finish writing the node equation and only then substitute for Vo using the "definition" of Vo above. Solve for V1. Then you'll have enough information to find Io and hence Vo.

 

In your second PDF you wrote "and the same problem here why 2Vx is
positive in the equation and not negative if the current goes clockwise?". Well, it's for the same reason that you wrote "-15" for the trip through the 15V source; you're summing potential drops, and the 15V source represents a rise while the controlled source represents a drop. So that drop is treated like the drops on the resistors as a positive term.

 

i think i understand i will work with it thank you very much