《电路》（英文版）chapter 15 Probler

Basic Circuit Theory 15 Probler I Consider the graph shown in Fig. 15-15. Denote the tree made up of b 6, bs, and b, 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 bs, b2, and b, b Fig 15-15 For prob. 1, 2, 6 Fig15-16 For prob.3,4,5,7,8 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 g, b5, b6, b,, and b 7 5 Write down the fundamental cutest matrix of this graph of Fig. 15-16 corresponding to the tree whose branches are bg, bs, bg, b,, 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 7 Use the results of problems 3 and 4 to show that AB=0 for the graph shown in Fig. 15-16 8 Use the results of problems 5 and 4 to show that BQ =0 for the graph shown in Fig. 15-16 9 The incidence matrix of a network is given by A=000-1 10101 Draw the graph of this network Fig 15-17 For prob. 10 10 Consider the graph shown in Fig. 15-17. choose a tree of this graph and label its branches in such a way that the fundamental cutest matrix corresponding to this tree can be partitioned as in Eq (15-14). Write down the corresponding fundamental cutest matrix DaLian Maritime University

Basic Circuit Theory Chpter15 Problems 1 Consider the graph shown in Fig. 15-15. Denote the tree made up of b 6 , b , and b by T. 5 2 (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 as the datum. 4 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 , and b1 . 2 DaLian Maritime University 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 , b 5 , b , b1 , and b . 9 6 7 5 Write down the fundamental cutest matrix of this graph of Fig. 15-16 corresponding to the tree whose branches are b , b , b , b1 , and b . 9 5 8 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. 7 Use the results of problems 3 and 4 to show that ABT = 0 for the graph shown in Fig. 15-16. f 8 Use the results of problems 5 and 4 to show that B Q = 0 for the graph shown in Fig. 15-16. f T f Fig.15-16 For prob.3,4,5,7,8. b1 b 2 3 b b 4 5 b 6 b 7 b 8 b 9 b n 1 n 2 3 n n 4 n 5 6 n Fig.15-17 For prob.10. b1 b 2 3 b b 4 5 b 6 b n 1 n 2 3 n n 4 Fig.15-15 For prob.1,2 ,6. 9 The incidence matrix of a network is given by A= ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 Draw the graph of this network. 10 Consider the graph shown in Fig. 15-17. choose a tree of this graph and label its branches in such a way that the fundamental cutest matrix corresponding to this tree can be partitioned as in Eq.(15-14). Write down the corresponding fundamental cutest matrix. 1

Basic Circuit Theory Chpter15 Problems Reference answers to Selected Problems 1: (a)[b4, b5, b6l[b,, b2, b5, b6l,[b2, b3,bsI; (b)(b,b4,b6,(b1 b2 b3],[b1,b3,b4,bsI: (e)A=010-110 0、公 00101 00-101 0100 6:M=000-111 DaLian Maritime University

Basic Circuit Theory Chpter15 Problems Reference Answers to Selected Problems 1: (a) [b ,b ,b ], [b1 ,b ,b 5 ,b ], [b ,b ,b 5 ]; 4 5 6 2 6 2 3 (b) [b1 ,b ,b 6 ], [b1 ,b ,b ], [b ,b ,b ,b ]; 4 2 3 1 3 4 5 (c) A = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 2: Q =f ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 6: M= ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 DaLian Maritime University 2