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 b 1 . 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 , b 1 , 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 , b 1 , 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 AB T = 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. 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 1 n 2 n 3 n 4 n 5 n 6 n Fig.15-17 For prob.10. 1 b 2 b 3 b 4 b 5 b 6 b 1 n 2 n 3 n 4 n Fig.15-15 For prob.1,2 ,6. 9 The incidence matrix of a network is given by A= ? ? ? ? ? ? ? ? ? ? ?? ?? 10101 11000 01110 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) [b ,b ,b ], [b 1 ,b ,b 5 ,b ], [b ,b ,b 5 ]; 4 5 6 2 6 2 3 (b) [b 1 ,b ,b 6 ], [b 1 ,b ,b ], [b ,b ,b ,b ]; 4 2 3 1 3 4 5 (c) A = ? ? ? ? ? ? ? ? ? ? ?? ? 110100 011010 101001 2: Q = f ? ? ? ? ? ? ? ? ? ? ? ?? 110100 101110 101001 6: M= ? ? ? ? ? ? ? ? ? ? ? ? 010110 111000 001011 DaLian Maritime University 2