Basic Circuit Theory Chpter16 Problems I Find the matrix equation in the circuit of Fig. 16-12 by nodal analysis method. Assume that each branch admittance of the circuit is IS.I,=lA. ca=2A.Va=2V (a) Fig 16-12 For prob. 1 Fig. 16-13 For prob. 2 2 For the circuit of Fig. 16-13a each branch impedance is 1Q, 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 3 For the circuit of Fig. 16-14 determine the nodal voltage equation with the matrix form 831Vr L,4 Fig. 16-14 For prob. 3 Fig. 16-15 For prob. 4 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 200QF 0.5mF 2kQ 20g2 lx 5H (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 5Q2 resistor is part of the tree;(b)assign state variables vc and i, and resistor variables v g and ig;(c) determine the normal-form equations with the state variables ordered vc, iL DaLian Maritime University
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. S1 S 2 S 2 DaLian Maritime University 2 For the circuit of Fig. 16-13a each branch impedance is 1Ω , 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. Vs 2 s1 I s 2 I 1 4 3 + - (a) (b) Fig. 16-13 For prob. 2. s I Vs 1 2 4 3 5 6 7 8 + - I s 4 • R1 L3 C 2 M ∗ 1 4 2 3 5 R4 ∗ L5 V s 2 • s1 i G1 1 2 1 v G 2 G 3 G 4 3 v 23 3 g v 31 1 g v + − + − 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. + - + - + - 0.5mF 4H 5H 1H 2H 2H 20Ω 8Ω 2kΩ 1mF 2000µF s v Li s s i i L 4i 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 . Ω C L R R C L 1
Basic Circuit Theory Chpter l6 Problems F200 5tu(t)vo VR 10Q 300g2 4uF 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 de wn 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 a R R IR6 Fig 16-19 For prob. 9 Rs C L Fig. 16-20 For prob. 10 DaLian Maritime University
Basic Circuit Theory Chpter16 Problems + - + - x 100i 5 t 2 V 200Ω xi 300Ω 3µF 4µF + + - + - - 5 ( ) 2 t u t Li Cv 5Ω Ri R v 10Ω 0.2F V 0.1H 2Ω 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 . + - 1 2 3 4 5 6 7 8 s 4 i C8 L2 M R3 ∗ R4 ∗ L1 R5 R6 R 7 s 7 v (a) (b) Fig. 16-19 For prob.9. - + + - + - Fig. 16-20 For prob.10. L 4 s2 v R 2 C1 R3 1 2 4 3 R5 R6 s3 v 5 v 5 gv s6 i DaLian Maritime University 2
Basic Circuit Theory Chpter l6 Problems Reference answers to Selected Problems 1-14 25-2-31 F。+ s 1-324I 8. -g31-G2-G4G1+G2+G3-g23JVn2L0 6:(b) 081+1.6 =0.1426v2-2451×10315-44lt R 4+Rs+R+ JOL R 2+Rs+jo(L2-M) R4+R5+/(L2-M)R3+R4+R3+R1+jo(L1+L2-2M)R3 R 3 R3 V s7+RaIse R2 R3 R R2 R3 10 R R, Rs jo R Rs R6 DaLian Maritime University
Basic Circuit Theory Chpter16 Problems Reference Answers to Selected Problems 1: = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − − − − − 0 1 1 3 1 1 4 1 1 3 1 1 3 1 1 0 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 2 1 n n n n V V V V ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − 0 4 1 5 2: = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − 1 3 2 4 1 2 3 2 2 5 2 3 3 2 1 1 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 2 1 l l l l I I I I ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − + − S S S S I V I I 0 3: ⎥ = ⎦ ⎤ ⎢ ⎣ ⎡ − − − + + − + + − − + 31 2 4 1 2 3 23 1 2 3 2 4 23 g G G G G G g G G G G G g ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 n n V V ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 0 S1 i 6: (b) dt diL = - 0.8 i +1.6 i . L S 8: dt dv3 = 0.1426v -2.451 -4.41 t . 3 3 1.5 ×10 t 0.5 9: ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + − + + + + + − + + + + + − 3 3 3 4 5 2 3 4 5 7 1 2 3 4 5 6 2 4 5 2 1 0 ( ) ( 2 ) ( ) 0 j C R R R R j L M R R R R j L L M R R R R j L R R j L M ω ω ω ω ω ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ • • • 3 2 1 l l l I I I = ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − + • • • 0 4 4 7 4 4 S S S V R I R I 10: ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − + − + + − − + + − − 5 5 6 3 3 5 4 5 2 3 5 1 1 1 1 0 1 1 1 1 1 1 1 1 R R R R g g R R R j L g R g R R j C ω ω ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ • • • 3 2 1 n n n V V V = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − • • • • 6 3 3 3 3 2 2 S S S S I R V R V R V DaLian Maritime University 3
