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Solved Problems-16

Determine the currents in all branches of the network shown in the figure using node analysis method. Use graph theory method.
Description: 3091.png
Here, the 1Ω resistance in parallel with the 2V voltage source can be ignored. Also, there is no passive element in parallel with 1A current source. We assume a resistance R in parallel with 1A current source and finally let R → ∞. Therefore, the graph of the network is shown in the figure.
Description: 3098.png Description: 3105.png
The complete incidence matrix is,
Description: 5503.png 
Reduced incidence matrix is,
Description: 5509.png 
Branch admittance matrix is,
Description: 5518.png
∴ Description: 5524.png
∴ Description: 5530.png
Description: 5536.png 
Thus, node equations are,
Description: 5542.png 
With R → ∞, the equations become
Description: 5552.png 
Solving equations, we get,
Description: 5558.png 
Hence, the currents in different branches are shown in the figure.
Description: 3167.png

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