Question

for the network shown in the figure below draw the oriented graph develop the incidence matrix,choose a tree and considering the tree develop the tie-set matrix ​

Answer 1

Question:⤵

For the network shown in the figure below draw the oriented graph develop the incidence matrix, choose a tree and considering the tree develop the tie-set matrix ​

Answer:⤵

2.1 Introduction

An important step in the procedure for solving any circuit problem consists first in selecting a  number of independent branch currents as (known as loop currents or mesh currents) variables,

and then to express all branch currents as functions of the chosen set of branch currents. Alternately a number of independent node pair voltages may be selected as variables and then express

all existing node pair voltages in terms of these selected variables.

For simple networks involving a few elements, there is no difficulty in selecting the independent branch currents or the independent node-pair voltages. The set of linearly independent

equations can be written by inspection. However for large scale networks particularly modern

electronic circuits such as integrated circuits and microcircuits with a larger number of interconnected branches, it is almost impossible to write a set of linearly independent equations by

inspection or by mere intuition. The problem becomes quite difficult and complex. A systematic and step by step method is therefore required to deal with such networks. Network topology

(graph theory approach) is used for this purpose. By this method, a set of linearly independent

loop or node equations can be written in a form that is suitable for a computer solution.

2.2 Terms and definitions

The description of networks in terms of their geometry is referred to as network topology. The

adequacy of a set of equations for analyzing a network is more easily determined topologically

than algebraically.

Graph (or linear graph): A network graph is a network in which all nodes and loops are retained but its branches are represented by lines. The voltage sources are replaced by short circuits

and current sources are replaced by open circuits. (Sources without internal impedances or admittances can also be treated in the same way because they can be shifted to other branches by

Explanation:⤵

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