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Solved Problems-14

Problems-14
For the resistive network, write a cutset schedule and equilibrium equations on voltage basis. Hence obtain values of branch voltages and branch currents.
 
Description: 2970.png
Solution
The graph of the network is shown in the figure. A suitable tree is shown.
Description: 2977.pngDescription: 2984.png
 
The fundamental cutsets are identified as,
f-cutset-1: [1, 2, 6];
f-cutset-2: [3, 5, 6];
f-cutset-3: [1, 4, 5]
 
The fundamental cutset matrix is given as,
 
The node equations are given as,
[Q][Yb][QT][Vt] = [Q] × {[Yb][VS] – [IS]} = [Q] [Yb][VS] {since IS = 0 here}
 
Here,
Description: 5411.png 
Description: 5417.png 
Description: 5423.png
 
Thus, the KCL equations are
Description: 5429.png
 
Solving by Cramer’s rule, we get the tree-branch voltages as,
Description: 5435.png




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