Superposition Diagram Reduction

[Mesmer]

Please click the image to enlarge it

http://img237.imageshack.us/img237/3605/untitlednu9.th.jpg


I'm having trouble seeing how this circuit was reduced. Can anyone shed some light on it for me?

My question pertains to the second solution in the image. I see that the 12k and 4k resistors are in parallel and that leads to the second diagram on the bottom. Why is the 6k resistor drawn up there? When I try to redraw the circuit, I keep it just like the first one- with the exception that the 12k and 4k resistors are combined on the rightmost branch- with the 6k and the current source in the same place. When the 6V source is shorted out why is there a need to redraw that branch?

 

[interested_learner]

I thought about your problem today while at work and realized that the 4K Ohm resistor and the 12K Ohm resistor on the right are in parallel. Look at them, both resistors connect at both ends (directly and through the short): The definition of parallel. Once they are combined in parallel, you can twist the circuit around and get the final result without much effort.

(If you still have trouble seeing it, pull the upper ends of the two resistors until they touch and then yank them over to one side. Keep in mind that the 6K resistor is connected to both ends of the current source and the parallel resistors connected on only one end as is the other 12K. Twist it around. You'll see it.)

(I deleted my original solution because it is too complicated -- this is simplier)

 

[piercas]

I would like to clarify that the process shown in the diagram is not a reduction, but rather a simplification of the original circuit. This technique is known as superposition, which involves analyzing the circuit by considering one independent source at a time and then combining the individual solutions to obtain the final solution.

In this particular case, the 6V source is shorted out in the second solution, which means that it is not contributing to the circuit. Therefore, it is not necessary to redraw that branch with the 6k resistor and the current source. The 6k resistor is included in the first solution because it is part of the original circuit and contributes to the overall solution.

To further explain, when the 6V source is shorted out, it creates a parallel connection between the 12k and 4k resistors. This results in an equivalent resistance of 3k, which is why the 6k resistor is not included in the second solution.

I hope this clarifies the process for you. Superposition is a useful technique in circuit analysis, but it is important to keep in mind that it is not a reduction or simplification of the circuit, but rather a method of solving it.