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Solved Problems-17

Problems-17
Consider the network shown in the figure using loop method of analysis, determine currents in all the branches, indicating their directions. Use graph theory method.
 
Description: 3174.png
Solution
Description: 3181.png
 
The graph of the network is shown below. Also, the tree is selected as shown.
Description: 3189.png Description: 3196.png
 
For the selected tree, the tie-set matrix is given as,
Description: 5564.png 
 
The branch impedance matrix is,
Description: 5571.png
∴ Description: 5579.png
∴ Description: 5585.png
Now,
Description: 5591.png 
 
So, the loop equations become,
Description: 5597.png Description: 3239.png
 
These equations reduce to,
Description: 5603.png 
Description: 5610.png
 
Thus, the branch currents are shown with their directions.
 




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