INTRODUCTION: This problem has to be answered very specifically. It needs to be

Question

INTRODUCTION: This problem has to be answered very specifically. It needs to be answered as if you were teaching the material to a student that has not learned this type of material yet. Every step and process should be explained in full detail with reasons/definitions of why or why not the process occurs the way it did.

Please include the following to the fullest detail:

Graphs

Step-By-Step Processes/Step-by-Step circuit reductions and expansions

I-V Characteristic Graphs with explanations

Background information on any and all steps possible

Any and all work with KVL, KCL, Node-Voltage Method and Equations, Mesh-Current method and Equations, Superposition, Source Transformations, ETC. (Explanations and background info please)

PROBLEM: Use the node-voltage method to write node-equations, solve for the node volatages, and find vx and ix .

Explanation / Answer

Clearly from figure , we have,
Voltage at node C = Vc = 9 Volts

Also, clearly ,voltage at node A =Va = Vc + 1 = 9 +1 = 10 Volts,

Now at node B, we have,
Using Kirchoff Current law,
we have,
(Va - Vb)/1 = Vb/9 + (Vb-Vc)/9
(10 - Vb)/1 = Vb/9 + (Vb-9)/9
11 = 11Vb/9
Vb = 9 Volts

Hence Voltage at node B = Vb = 9 V

Now, hence,
Vx = Vb = 9 Volts
Ix = (Vb-Vc)/9 = (9-9)/9 = 0 A

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