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Solved Problems-6

The figure shows a d.c. network.
  1. Draw a graph of the network. Which elements are not included in the graph and why?
  2. Write a loop incidence matrix and use it to obtain loop equations.
  3. Find branch currents.
Description: 2555.png
  1. The graph is shown below.
The 2 Ω resistor in parallel with voltage source and the 2 A current source have not been included in the graph. This is because of the reason that passive elements in parallel with a voltage source are not included in graph and the current source in parallel with a passive element is open-circuited while drawing graph.
Description: 2562.png
  1. The tie-set matrix for the tree chosen is,
Description: 4985.png
Branch impedance matrix is,
Description: 4995.png
Description: 5006.pngDescription: 5012.png
Description: 5018.png
Description: 5024.png
Description: 5030.png
So, the loop equations are,
Description: 5039.png
Solving these equations, Description: 5045.png 
  1. Putting these values, the branch voltages are
Description: 5051.png 
Thus, the branch currents are
Description: 5057.png
So, the current supplied by the battery = (1.7 + 1.4 + 2.5 – 2) = 4.6 A

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