Basic Circuit Theory Chpter16 Problems 1 Find the matrix equation in the circuit of Fig. 16-12 by nodal analysis method. Assume that each branch admittance of the circuit is 1S, I =1A, I =2A, V =2V. 1S 2S 2S DaLian Maritime University 2 For the circuit of Fig. 16-13a each branch impedance is 1? , if choose branches 1, 2, 6, and 7 as a tree in the corresponding graph (see Fig. 16-13b), write down the matrix equation by loop analysis method. 3 For the circuit of Fig. 16-14 determine the nodal voltage equation with the matrix form. + - Fig. 16-12 For prob. 1. 2s V 1s I 2s I 1 4 3 + - (a) (b) Fig. 16-13 For prob. 2. s I s V 12 34 5 6 7 8 + - 4sI ? 1 R 3 L 2 C M ? 1 23 4 5 4 R ? 5 L 2sV ? 1s i 1 G 1 2 1 v 2 G 3 G 4 G 3 v 323 vg 131 vg + ? + ? 2 (a) (b) Fig. 16-15 For prob.4. Fig. 16-14 For prob. 3. 4 For the circuit of Fig. 16-15a whose direct graph in the Fig. 16-15b write down the loop current equation with the matrix form using the phasor notation. 5 Draw a normal tree for the circuit shown in Fig. 16-16a, b, c. + - + - + - mF5.0 H5 H4 H1 H2 H2 ?20 ?8 ?k2 mF1 F2000μ s v L i s is i L i4 s v (a) (b) (c) Fig. 16-16 For prob.5 and 6. 6 Write a set of normal-form equation for the circuit shown in Fig. 16-16a, b, c. 7 For the circuit illustrated in Fig. 16-17 (a) draw a normal tree in which the 5 resistor is part of the tree; (b) assign state variables v and i and resistor variables v and i ; (c) determine the normal-form equations with the state variables ordered v , i . ? C L R R C L 1 Basic Circuit Theory Chpter16 Problems + - + - x i100 V 2 5 t ?200 x i ?300 F3μ F4μ + + - + - - )(5 2 tut L i C v ?5 R i R v ?10 F2.0 V H1.0 ?2 Fig. 16-17 For prob.7. Fig. 16-18 For prob.8. 8 determine a suitable tree for the circuit shown in Fig. 16-18, select a state variable, and write the corresponding normal-form equation. 9 For the circuit of Fig. 16-19a if choose branches 1, 2, 3, 4, and 5 as a tree in the corresponding graph (see Fig. 16-19b), write down the matrix equation by loop analysis method. 10 For the circuit of Fig. 16-20 if choose node ④ as the datum write down the nodal voltage equation with the matrix form. Assume the radian frequency of source is ω . + - 12 3 4 5 6 7 8 4s i 8 C 2 L M 3 R ? 4 R ? 1 L 5 R 6 R 7 R 7s v (a) (b) Fig. 16-19 For prob.9. -+ + - -+ Fig. 16-20 For prob.10. 4 L 2s v 2 R 1 C 3 R 1 2 4 3 5 R 6 R 3s v 5 v 5 gv 6s i DaLian Maritime University 2 Basic Circuit Theory Chpter16 Problems Reference Answers to Selected Problems 1: = ? ? ? ? ? ? ? ? ? ? ? ? ?? ??? ??? ?? 3110 1411 1131 0113 ? ? ? ? ? ? ? ? ? ? ? ? 4 3 2 1 n n n n V V V V ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0 4 1 5 2: = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ??? ? 4231 2321 3252 1123 ? ? ? ? ? ? ? ? ? ? ? ? 4 3 2 1 l l l l I I I I ? ? ? ? ? ? ? ? ? ? ? ? +? ? S SS S I IV I 0 3: = ? ? ? ? ? ? ?++??? +??++ 233214231 2342321 gGGGGGg gGGGGG ? ? ? ? ? ? 2 1 n n V V ? ? ? ? ? ? 0 1S i 6: (b) dt di L = - 0.8 i +1.6 i . L S 8: dt dv 3 = 0.1426v -2.451 -4.41 t . 3 5.13 10 t× 5.0 9: ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ?+++++?++ ?+++++ 3 33 3217543254 2542654 1 0 )2()( 0)( Cj RR RMLLjRRRRMLjRR MLjRRLjRRR ω ωω ωω ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 2 1 l l l I I I = ? ? ? ? ? ? ? ? ? ? ? ? ? ? +? ?? ? 0 4 4 7 4 4 SS S IRV IR 10: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? +? ??++? ??++ 655 54533 532 1 111 0 11111 111 RRR R gg LjRRR g R g RR Cj ω ω ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 2 1 n n n V V V = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? 6 3 3 3 3 2 2 S S SS I R V R V R V DaLian Maritime University 3