17.3 KIRCHHOFF'S LAWS IN INCIDENCE MATRIX FORMULATION

17.3.1 KCL Equations from A Matrix

Kirchhoff's Current Law states that the sum of currents leaving a node in a network is zero on an instant-to-instant basis at all nodes in the network. The orientation of a particular branch in the graph of a network was taken to be the same as the reference direction for current in that branch. The incidence matrix entry is +1 if a branch is incident at a node with orientation away from the node. It is – 1 if a branch is incident at a particular node and is oriented towards it. Therefore, the KCL equation at a node can be obtained by multiplying the entries in the row of A corresponding to that node by the elements of a column vector of branch currents. ...

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