Cutset Matrix Concept of Electric CircuitPublished on 24/2/2012 & updated on Thursday 21st of June 2018 at 08:45:18 PM
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Example of Cutsets Matrix of a Circuit
Two sub-graphs are obtained from a graph by selecting cut-sets consisting of branches [1, 2, 5, 6].Thus, in other words we can say that fundamental cut set of a given graph with reference to a tree is a cut-set formed with one twig and remaining links. Twigs are the branches of tree and links are the branches of co-tree. Thus, the number of cutset is equal to the number of twigs. [Number of twigs = N - 1] Where, N is the number of nodes of the given graph or drawn tree. The orientation of cut-set is the same as that of twig and that is taken positive.
Steps to Draw Cut Set MatrixThere are some steps one should follow while drawing the cut-set matrix. The steps are as follows-
- Draw the graph of given network or circuit (if given).
- Then draw its tree. The branches of the tree will be twig.
- Then draw the remaining branches of the graph by dotted line. These branches will be links.
- Each branch or twig of tree will form an independent cut-set.
- Write the matrix with rows as cut-set and column as branches.
Orientation in Cut Set MatrixQij = 1; if branch J is in cut-set with orientation same as that of tree branch. Qij = -1; if branch J is in cut-set with orientation opposite to that of branch of tree. Qij = 0; if branch J is not in cut-set. Example 1 Draw the cut-set matrix for the following graph. Answer: Step 1: Draw the tree for the following graph. Step 2: Now identify the cut-set. Cut-set will be that node which will contain only one twig and any number of links. Here C2, C3 and C4 are cut-sets. Step 3: Now draw the matrix.
- In cutset matrix, the orientation of twig is taken positive.
- Each cut-set contains only one twig.
- Cut-set can have any number of links attached to it.
- The relation between cut-set matrix and KCL is that
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