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Solved Problems-13

Problems-13
For the network shown in the figure, draw the oriented graph, select a suitable tree and obtain the fundamental cutset matrix. Determine the node equations and find v.
 
Description: 1764.png
Solution
The oriented graph of the network is shown in the figure. Since we have to find v, we take branch (2) in the twig and a possible tree is selected.
 
The fundamental cutsets are identified as
Description: 2933.png
f-cutset-1: [1, 2, 3];
f-cutset-2: [3, 4];
 
The fundamental cutset matrix is given as,
 
The node equations are given as,
[Q][Yb][QT][Vt] = [Q] × {[Yb][VS] – [IS]}
 
Here,
Description: 5372.png
Description: 5381.png 
 
Thus, the KCL equations are
Description: 5387.png 
 
Here, Vt2=v. Putting this in the KCL equations and solving we get,
Description: 5405.png
 




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