Which solution is correct for finding Vth and Rth?

[sciman]

hello!
can you tell me please which solution is correct:

We need to find the Vth and Rth. Rth is easily 4Ohms, but what about Vth?

1st solution:
Calculate Vth, by doing 10A=I1+I2 and 4V+2xI1=2xI2, where you find I1=6A and I2=4A, so Vth=12V

2nd solution:
Calcullate Vth, by transforming the voltage source into current source and then apply KCL, so Vth=8V

which is the correct?thanks!

 

[AlexCaledin]

Perhaps, in this case, it's good to apply the theorem thrice, in 3 easy steps... - that would help to choose the values of the resistors if you're doing a real practical circuit.

 

[gneill]

Hi sciman.

In future be sure to use the homework template when you post a problem here in the homework sections! It's in the rules.

I can see by the result that your first method is incorrect, but it is also incorrect because you haven't defined I1 and I2 so your equation doesn't mean anything!

Your second approach is much better, but you need to be careful about the polarities of things. What direction will the net current be flowing through the combined resistance?