文档介绍：Basic Circuit Theory
Chpter15 Problems
1 Consider the graph shown in Fig. 15-15. Denote the tree made up of b 6 , b 5 , and b 2 by T.
(a) Find all the fundamental loops of this graph corresponding to T
(b) Find all the fundamental cutsets of this graph corresponding to T
(c) Write the incidence matrix of this graph choose n 4 as the datum.
2 Consider the graph shown in Fig. 15-15. Write down the fundamental cutsets of this graph with
respect to the tree that is made up of branches b 5 , b 2 , and b 1 .
n 3
b 6
b 9
b n b b n 6
n 4 2 5 3 b
1 n 3 2
b 6
b 5
b 2 b
b 3 n
1 4 n 5
b b 4 b
n 7 8
1 n 2
n 4 b 1
-15 For ,2 ,6. -16 For ,4,5,7,8.
3 Write down the augmented incidence matrix of the graph shown in Fig. 15-16.
4 Obtain the fundamental loops of this graph shown in Fig. 15-16 and show that its rank is 4;
choose a tree whose branches are b 9 , b 5 , b 6 , b 1 , and b 7 .
5 Write down the fundamental cutest matrix of this graph of Fig. 15-16 corresponding to the tree
whose branches are b 9 , b 5 , b 8 , b 1 , and b 7 .
6 Choose appropriate meshes for the planar graph of Fig. 15-15 and obtain its mesh matrix M.
Show that M is of rank 3.
T
7 Use the results of problems 3 and 4 to show that AB f = 0 for the graph shown in Fig. 15-16.
T
8 Use the results of problems 5 and 4 to show tha