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Solved Problems-20

For the network shown in the figure, write the tie-set matrix and determine the loop currents and branch currents.
Description: 3431.png
The graph and a suitable tree for the network are shown in the figure.
The tie-set matrix is given as,
Description: 5792.pngDescription: 6194.png
The branch impedance matrix is given as,
Description: 5798.png
∴ Description: 5804.png
∴ Description: 5810.png
Description: 5816.png
Thus, the loop equations are given as,
Description: 5825.png
Solving by Cramer’s rule, we get the loop currents as,
Description: 5831.png 
Description: 5839.png 
Description: 5845.png 
Also, the branch currents are given as, Description: 5864.png
∴  Description: 5853.png
Description: 5870.png

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