c 2009 i - PDF 無料ダウンロード

I 2009

c 2009 i 0 1 0.0................................... 1 0.1.............................. 3 0.2.............................. 5 1 7 1.1................................. 7 1.2.............................. 8 1.3.................................... 9 1.4.......................... 11 1.5................................... 14 1.6................................. 23 2 30 2.1.............................. 30 2.2.................................... 32 2.3................................... 35 2.4................................ 40 2.5.............................. 46 3 51 3.1................................... 51 3.2......................... 56 3.3.................................... 60 4 65 4.1....................... 65 4.2.................................... 69 4.3.................... 71

ii c 2009 4.4.................................... 79 4.5.................................... 88 4.6................................... 97 4.7................................. 105 5 109 6 119 6.1.............................. 119 6.2................................... 121 6.3................................... 129 6.4................... 133 6.5............................... 135 7 139 7.1......................... 139 7.2.............................. 145 7.3...................................... 147 8 154 8.1................................. 154 8.2....................... 157 8.3.............................. 162 8.4.................................... 165 9 167 9.1.............................. 167 9.2........................... 171 9.3................................. 177 9.4................................... 179 10 184 10.1............................ 184 10.2........................... 188 10.3..................... 192 11 195 11.2 K................................ 195

c 2009 iii 11.4 T π...................... 200 12 202 12.2............................... 202 12.3........................... 208 12.4.............................. 211 A 217

c 2009 1 0 0.0 0.1 (1) 2.1 3.0 (2) 2.5 4.0 (3) 1.45 2.4 (4) 4.7 3.1 (5) 7.0 5.0 (6) 6.0 2.0 (7) 26 24 (8) 2.2 + 3.7 (9) 1.7 + 2.3 (10) 7.2 + 2.8 (11) 3.5 1.2 (12) 10.5 3.3 (13) 23 1.5 (14) 3.2 0.123 (15) 6.2 (2.3 + 1.2) (16) 1.3 (1.23 0.12) 0.1

2 c 2009 0 (1) 2.1 3.0 = 6.3 (2) 2.5 4.0 = 8.0 (3) 1.45 2.4 = 3./4 5 /8 = 3.5 (4) 4.7 3.1 = 1/4 5./5/7 = 15 (5) 7.0 5.0 = 1.4 (6) 6.0 3.0 = 2.0 (7) 26 24 = 1./0 1 /8 3 = 1.1 (8) 2.2 + 3.7 = 5.9 (9) 1.7 + 2.3 = 4.0 (10) 7.2 + 2.8 = 10.0 (11) 3.5 1.2 = 2.3 (12) 10.5 3.3 = 7.2 (13) 23 1.5 = 2/1 2./5 = 22 (14) 3.2 0.123 = 3.2 0.12 3 = 3.2 0.12 = 3./0 1 /8 = 3.1 (15) 6.2 (2.3 + 1.2) = 6.2 3.5 = 2/1 2./7 = 22 (16) 1.3 (1.23 0.12) = 1.3 1.11 = 1.4/4/3 = 1.4 0.1 (1) 1.5 4.2 (2) 1.41 2.83 (3) 9.3 6.2 (4) 2.97 1.5 (5) 1.2 + 7.1 (6) 1.5 + 1.52 (7) 2.3 + 0.15 (8) 3.5 1.1 (9) 14.1 5.5 (10) 3.72 0.184 (11) 1.6 (10.2 + 2.3) (12) 1.5 (1.33 + 2.35) 0.2 x 10 n x 1 x < 10 n

0.1 c 2009 3 (1) 150 Ω (2) 4.7 kω (3) 20 mh (4) 5.0 µh (5) 150 pf (6) 2.5 nf 0.2 (1) 1.50 10 2 Ω (2) 4.7 10 3 Ω (3) 2.0 10 2 H(= 20 10 3 H) (4) 5.0 10 6 H (5) 1.50 10 10 F(= 150 10 12 F) (6) 2.5 10 9 F 0.2 x 10 n x 1 x < 10 n (1) 300 Ω (2) 1.5 MΩ (3) 3.0 mh (4) 100 µh (5) 15 pf (6) 0.15 µf 0.1 0.3 1 (1) i a 2.3 A i b 5.7 A i (2) i 7.7 A i a 2.7 A i b

4 c 2009 0 i ia ib a b 1 0.3 0.3 (1) i = i a + i b = 2.3 A + 5.7 A = 8.0 A (1) (2) i b = i i b = 7.7 A 2.7 A = 5.0 A (2) 0.3 1.6 10 19 C (1) 1.0 C (2) 1.5 A 2.0 s (3) 8.0 s 5.0 10 16 0.4 2 I 1 1.2 A I 2 2.3 A I 4 1.5 A I 3 I 5 2 0.4 0.5 3

0.2 c 2009 5 3 0.5 (1) v ac 2.3 V v ab 4.5 V v bc (2) v ab 1.50 V v bc 0.72 V v ac 0.6 4 v ab 6.0 V v bc 1.5 V v ad 9.0 V v ac v dc 4 0.6 0.2 0.4 (1) 3.3 kω R 3.0 ma i v (2) 4.2 ma i 0.21 µwb L (3) 15 V v 4.5 10 11 C q C

6 c 2009 0 0.4 (1) v = Ri = 3.3 kω 3.0 ma = (3.3 10 3 Ω) (3.0 10 3 A) = 9.9 V (3) (2) L = φ i = 0.21 µwb 4.2 ma = 0.21 10 6 Wb 4.2 10 3 A = 5.0 10 5 H = 50 µh (4) (3) C = q v = 4.5 10 11 C 15 V = 3.0 10 12 F = 3.0 pf (5) 0.7 (1) 5.0 kω R 12 V i (2) L 30 mh φ 0.60 mwb i (3) C 4.8 nf q 1.2 10 8 C v

c 2009 7 1 1.1 1.1 1.1 E R 1.1 1.1 (1) R 5.0 Ω 0.30 A I E (2) E 10 V 2.5 A I R 1.1 (1) E = RI = 5.0 Ω 0.30 A = 1.5 V (1.1) (2) R = E I = 10 V = 4.0 Ω (1.2) 2.5 A

8 c 2009 1 1.1 (1) 2.0 kω 7.0 V (2) 1.3 kω 3.0 ma (3) 1.20 V 0.60 A 1.2 1.2 E r R 1 R 2 1.2 1.2 1.2 (1) 1.2 (a) V 1.20 V E (2) 1.2 (b) 2.20 Ω R 1 I 500 ma r (3) 1.2 (c) R 2 I 600 ma R 2 (4) 1.2 (c) V 1.2

1.3 c 2009 9 (1) E = 1.20 V (1.3) (2) (3) (4) I = E r + R 1 (1.4) r = E I R 1 = 1.20 V 2.20 Ω = 2.40 Ω 2.20 Ω = 0.20 Ω (1.5) 500 ma I = E r + R 2 (1.6) R 2 = E I r = 1.20 V 0.20 Ω = 2.00 Ω 0.20 Ω = 1.80 Ω (1.7) 600 ma V = E ri = 1.20 V 0.20 Ω 600 ma = 1.20 V 0.12 V = 1.08 V (1.8) 1.2 1.50 V 0.20 Ω 3.0 A 1.3 1.40 V 0.15 Ω 1.22 V 1.4 1.3 E r R V R 3.0 Ω 9.0 V R 5.0 Ω 10.0 V E r 1.3 1.3

10 c 2009 1 1.3 1.4 (1) 100 V V 5.00 A I P (2) 15 Ω R I 2.0 A P (3) 16 Ω R 24 V V P 1.3 (1) P = V I = 100 V 5.00 A = 500 W (1.9) (2) P = RI 2 = 15 Ω (2.0 A) 2 = 60 W (1.10) (3) P = E2 R = (24 V)2 16 Ω = 36 W (1.11) 1.5 (1) 1.5 V 30 ma (2) 100 V 1.0 kw (3) 3.0 kω 12 V (4) 500 ma 1.0 W (5) 10 V 1.5 A (6) 100 V 1.2 kw (7) 120 V 60 W (8) 60 W 5

1.4 c 2009 11 1.6 1.4 E r R R [1] [6] 1.4 1.6 R I [1] R V [2] R P [3] P = 2 a, b ( [4] ) a + b 2 ab a = b P [5] R = [6] E2 1.4 1.4 1.5 R 0 I V 1, V 2, V 3 R 1 2.0 Ω R 2 3.0 Ω R 3 7.0 Ω E 24 V 1.5 1.4 1.4

12 c 2009 1 R 0 = R 1 + R 2 + R 3 = 2.0 Ω + 3.0 Ω + 7.0 Ω = 12.0 Ω (1.12) I = E = 24 V = 2.0 A R 0 12.0 Ω (1.13) V 1 = R 1 I = 2.0 Ω 2.0 A = 4.0 V (1.14) V 2 = R 2 I = 3.0 Ω 2.0 A = 6.0 V (1.15) V 3 = R 3 I = 7.0 Ω 2.0 A = 14 V (1.16) 1.7 1.6 1.6 1.7 (1) R 1 2.0 Ω R 2 3.0 Ω a b V ab 15 V V 1 V 2 (2) R 1 7.0 Ω R 2 3.0 Ω R 2 V 2 1.5 V a b V ab 1.5 1.7 R 1 2.0 Ω R 2 3.0 Ω E 2.4 V I 1 I 2 I 1.7 1.5

1.4 c 2009 13 1.5 I 1 = E = 2.4 V = 1.2 A R 1 2.0 Ω (1.17) I 2 = E = 2.4 V = 0.80 A R 2 3.0 Ω (1.18) I = I 1 + I 2 = 1.2 A + 0.80 A = 2.0 A (1.19) 1.8 1.8 1.8 1.8 (1) R 1 2.0 Ω R 2 1.0 Ω a b I 3.0 A I 1 I 2 (2) R 1 2.0 Ω R 2 3.0 Ω R 2 I 2 1.0 A a b I 1.9 1.9 R 1 2.0 Ω R 2 4.0 Ω R 3 4.0 Ω a b I 9.0 A (1) a b R ab (2) R 1 I 1 1.10 (1) 11.3 Ω 2.7 Ω (2) 1.6 Ω 2.4 Ω (3) 1.2 Ω 2.7 Ω 14.5 Ω 3 (4) 3.0 Ω 4.0 Ω 12 Ω 3

14 c 2009 1 1.9 1.9 1.11 1.10 2 (1) P 1 (2) P 2 P 1 : P 2 k 1.10 1.11 1.5 1.6 1.11 (a) (d) R a, R b, R c, R d 1.6 (a) R 1, R 2 R 1 R 2 R 1 + R 2 (1.20)

1.5 c 2009 15 1.11 1.6 (b) R 1 (R 2 + R 3 ) (c) (R 1 + R 2 ) R 3 (d) R a = R 1R 2 R 1 + R 2 + R 3 = R 1R 2 + R 2 R 3 + R 3 R 1 R 1 + R 2 (1.21) R d = R b = R 1(R 2 + R 3 ) R 1 + R 2 + R 3 (1.22) R c = (R 1 + R 2 )R 3 R 1 + R 2 + R 3 (1.23) 1 R d = 1 R 1 + 1 R 2 + 1 R 3 (1.24) R 1 R 2 R 3 R 1 R 2 + R 2 R 3 + R 3 R 1 (1.25) 1.12 5.0 Ω R 1 10 Ω R 2 15 Ω R 3 1.12 (a) (d)

16 c 2009 1 1.12 1.12 1.13 1.13 1.13 1.13 A B R AB C D R CD 1.7 1.14 a b 92 V R L 20 V r R 12 Ω R L 10 Ω 1.7 R L 20 V = 2.0 A (1.26) 10 Ω

1.5 c 2009 17 1.14 1.7 R 92 V 20 V 12 Ω = 72 V = 6.0 A (1.27) 12 Ω r 6.0 A 2.0 A = 4.0 A (1.28) r 20 V 4.0 A = 80 W (1.29) 1.14 1.15 E 9.0 V R 1 1.0 Ω R 2 6.0 Ω R 3 3.0 Ω 1.15 1.14 (1) R (2) R 1 I 1 (3) R 2 I 2 (4) R 3 I 3 (5) R 1 P 1 (6) R 2 P 2

18 c 2009 1 (7) R 3 P 3 1.15 1.16 R 2 3.0 Ω R 3 7.0 Ω a b V ab 144 V R 3 V 3 84 V 1.16 1.15 (1) R 3 I 3 (2) R 2 I 2 (3) R 1 I 1 (4) R 1 V 1 (5) R 1 1.16 1.17 R 2 1.2 Ω R 3 1.8 Ω E 6.8 V R 3 P 3 7.2 W 1.17 1.16 (1) R 3 I 3 (2) R 2 V 2 (3) R 2 I 2 (4) R 1 I 1 (5) R 1 V 1 (6) R 1

1.5 c 2009 19 1.17 1.18 I, I 1, I 2, I 3, I 4 V 1, V 2 R 1 16 Ω R 2 40 Ω R 3 60 Ω R 4 8.0 Ω E 40 V 1.18 1.17 1.18 1.19 R, I, I 1, I 2, I 3, I 4 V ac V bc R 0 1.0 Ω R 1 1.6 Ω R 2 12 Ω R 3 4.0 Ω R 4 6.0 Ω E 4.0 V 1.19 1.18

20 c 2009 1 1.19 1.20 V R 1.20 1.19 (1) a b I (2) d b V db (3) c I c (4) a c V ac (5) c d V cd 1.20 R 1, R 2, R 3 J 1.21 I 1 I 2, I 3 V 1, V 2, V 3 1.21 1.20 1.21 1.22 R 1 2.0 Ω R 2 8.0 Ω SW

1.5 c 2009 21 1.00 V SW 0.96 V E r 1.22 1.21 1.22 1.23 R 1 0.90 Ω R 2 0.72 Ω SW1 SW2 1.20 V SW1 1.20 A 1.23 1.22 (1) E (2) r (3) SW1 SW2 (4) SW1 SW2 1.23 1.24 C D A B R AB A B C D R CD 1.24 1.25 a V a b V b c V c d V d E

22 c 2009 1 1.24 1.23 1.25 1.24 1.25 1.26 I R E 1.26 1.25 1.26 1.27 r R 1 R 2 1.27 1.26

1.6 c 2009 23 1.27 1.28 1.28 1.27 (1) A B R AB (2) R AB R 0 R 0 R 1 R 2 (3) (2) R 0 R 2 R 1 R 2 1.28 1.29 R 0 : R 1 : R 2 = 1 : 2 2 : ( 3 2 2 ) 1.29 1.28 (1) A B R AB R AB/R 0 (2) R 1 V 1 A B V AB V 1/V AB (3) R 0 V 0 A B V AB V 0 /V AB 1.29 1.30 A B R 0 V = 2V R 1 R 2 R 0 1.6

24 c 2009 1 1.30 1.29 1.8 1.31 a b R ab R 1 2.0 Ω R 2 8.0 Ω R 3 3.0 Ω R 4 12 Ω R 5 6.0 Ω 1.31 1.8 1.8 R 1 R 4 = R 2 R 3 (1.30) R 5 R 1 + R 3 = 5.0 Ω (1.31) R 2 + R 4 = 20 Ω (1.32) R ab = 5.0 Ω 20 Ω = 4.0 Ω (1.33) 5.0 Ω + 20 Ω 1.30 1.32 R 5 R 1 2.0 Ω R 2 4.0 Ω R 3 3.0 Ω R 5 1.0 Ω E 1.8 V

1.6 c 2009 25 1.32 1.30 (1) R 4 (2) A 1.31 1.33 R 16 Ω 1.33 1.31 (1) a b R ab (2) c d R cd (3) a d R ad 1.32 1.34 R 1 4.0 Ω R 2 6.0 Ω R 3 3.0 Ω R 4 2.0 Ω R 5 5.0 Ω (1) a b R ab (2) a c R ac (3) a d R ad (4) b c R bc (5) c d R cd

26 c 2009 1 1.34 1.32 1.33 1.35 A B R 1 10 Ω R 2 12 Ω R 3 6.0 Ω R 4 5.0 Ω R 5 6.0 Ω 1.35 1.33 (1) SW1 SW2 (2) SW1 SW2 (3) SW1 SW2 (4) SW1 SW2 1.34 1.36 SW I 25 A R 3 R 4 R 1 1.0 Ω R 2 4.0 Ω E 100 V 1.35 1.37 R 1, R 2, R 3, R 4 R x E A R 1R 4 R 2R 3 (1) R x A R x R 1 R 4 (2) (1) I 1 I 2 I 3 R 1 R 4 E

1.6 c 2009 27 1.36 1.34 1.37 1.35 1.36 1.38 SW V V ON SW V V OFF V ON = 2V OFF R r 1.38 1.36 (1) V ON E

28 c 2009 1 (2) V OFF E, R, r (3) r R 1.37 1.39 1.39 1.37 (1) 1.39 (a) A B 2R I (2) 1.39 (b) A B r I = 0 r R 1.38 1.40 R 2 7.0 Ω R 4 1.0 Ω R 5 1.0 Ω E 8.0 V I 4 2.0 A I 5 1.0 A I 5 0 1.40 1.38 (1) c d V cd (2) c b V cb (3) a c V ac (4) R 1 I 1

1.6 c 2009 29 (5) R 1 (6) d b V db (7) a d V ad (8) R 2 I 2 (9) R 3 I 3 (10) R 3 1.39 1.41 b c I 0 b c 1.41 1.39 0 Ω I 0 b c 0 Ω I 0 = 0 V I 0 (1) a d (2) I (3) I a I 1 I 2 R 1 I 1 (4) d I 3 I 4 I R 3 I 3 (5) b I 1 I 0 I 3 I 0

30 c 2009 2 2.1 2.1 2.1 I V 1, V 2 E 1 20 V E 2 5.0 V E 3 10 V R 1 20 Ω R 2 30 Ω 2.1 2.1 2.1 E 1 E 2 + E 3 = R 1 I + R 2 I (2.1) I = E 1 E 2 + E 3 R 1 + R 2 = 20 V 5.0 V + 10 V 20 Ω + 30 Ω = 25 V = 0.50 A (2.2) 50 Ω

2.1 c 2009 31 V 1 = R 1 I = 20 Ω 0.50 A = 10 V (2.3) V 2 = R 2 I = 30 Ω 0.50 A = 15 V (2.4) 2.1 2.2 2.2 2.1 2.2 2.3 (1) a b c (2) 2.3 2.4 A B C

32 c 2009 2 2.3 2.2 2.4 2.3 2.2 2.2 2.5 I 1, I 2, I 3 2.2 I 1 I 2 I 3 = 0 (2.5) E 1 = R 1 I 1 + R 3 I 3 (2.6) E 2 = R 2 I 2 R 3 I 3 (2.7)

2.2 c 2009 33 2.5 2.2 (2.5) (2.6) (2.7) E 1 = (R 1 + R 3 ) I 1 R 3 I 2 (2.8) E 2 = R 3 I 1 + (R 2 + R 3 ) I 2 (2.9) I 1 = (R 2 + R 3 ) E 1 + R 3 E 2 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.10) I 2 = R 3E 1 + (R 1 + R 3 ) E 2 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.11) R 2 E 1 R 1 E 2 I 3 = I 1 I 2 = R 1 R 2 + R 2 R 3 + R 3 R 1 (2.12) 2.4 2.6 I 1, I 2, I 3 E 1 12 V E 2 30 V R 3.0 Ω r 5.0 Ω 2.6 2.4

34 c 2009 2 2.5 2.7 V o a b I 0 = 0 2.7 2.5 (1) I 1 I 2 (2) V 1 V 2 (3) V 1 E 1, R 1, I 1 (4) V 2 E 2, R 2, I 2 (5) I 1, I 2 (6) V o 2.6 2.8 I 1, I 2, I 3 2.8 2.6 (1) I 1, I 2, I 3 (2) A B (3) I 1, I 2, I 3

2.3 c 2009 35 2.3 2.3 2.9 2.9 2.3 (1) I A, I B (2) I A, I B (3) R 2 2.3 (1) I A E 1 E 2 = (R 1 + R 2 ) I A + R 2 I B (2.13) I B E 3 E 2 = R 2 I A + (R 2 + R 3 ) I B (2.14) (2) [ (2.13) (R 2 + R 3 ) (2.14) R 2 ] I A = (R 2 + R 3 ) (E 1 E 2 ) R 2 (E 3 E 2 ) (R 1 + R 2 ) (R 2 + R 3 ) R 2 2 = (R 2 + R 3 ) E 1 R 3 E 2 R 2 E 3 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.15) [ (2.13) R 2 (2.14) (R 1 + R 2 )] I B = R 2 (E 1 E 2 ) (R 1 + R 2 ) (E 3 E 2 ) R 2 2 (R 1 + R 2 ) (R 2 + R 3 ) = R 2E 1 R 1 E 2 + (R 1 + R 2 ) E 3 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.16)

36 c 2009 2 (3) R 3 R 3 I A + I B = R 3E 1 (R 1 + R 3 ) E 2 + R 1 E 3 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.17) R 3 E 1 + R 1 E 3 = (R 1 + R 3 ) E 2 (2.18) 2.7 2.10 R 1 5.0 Ω R 2 10 Ω R 3 5.0 Ω E 1 10 V E 2 15 V I a I b 2.10 2.7 2.8 2.11 2.11 2.8 (1) I a, I b (2) I a, I b

2.3 c 2009 37 2.4 2.12 I 1, I 2, I 3 R 1 10 Ω R 2 30 Ω R 3 20 Ω R 4 5.0 Ω R 5 10 Ω E 1 10 V E 2 40 V 2.12 2.8 2.4 E 1 = (R 1 + R 4 ) I 1 R 4 I 2 (2.19) 0 = R 4 I 1 + (R 2 + R 4 + R 5 ) I 2 + R 5 I 3 (2.20) E 2 = R 5 I 2 + (R 3 + R 5 ) I 3 (2.21) 10 = 15I 1 5.0I 2 (2.22) 0 = 5.0I 1 + 45I 2 + 10I 3 (2.23) 40 = 10I 2 + 30I 3 (2.24) (2.23) I 3 = 0.50I 1 4.5I 2 (2.25) (2.25) (2.24) 40 = 15I 1 125I 2 (2.26) [ (2.26) (2.22)] 30 = 120I 2 (2.27) I 2 = 0.25 A (2.28) [25 (2.22) (2.26)] 210 = 360I 1 (2.29) I 1 = 0.58/3 = 0.58 A (2.30)

38 c 2009 2 (2.25) I 3 = 0.50I 1 4.5I 2 = 1.4/1 = 1.4 A (2.31) I 1 = 0.58 A, I 2 = 0.25 A, I 3 = 1.4 A (2.32) 2.9 2.13 E 1 12.0 V E 3 4.0 V, R 1 1.0 Ω R 2 1.0 Ω R 3 2.0 Ω R 4 1.0 Ω R 5 2.0 Ω 2.13 2.9 (1) (2) I 1, I 2, I 3 2.10 2.14 2.14 2.10 (1)

2.3 c 2009 39 (2) I a I b I c 2.11 2.15 2.15 2.11 (1) I a, I b, I c (2) E 1 1.0 V E 2 2.0 V R 1 R 3 R 4 3 1.0 Ω R 2 2.0 Ω I a I b 2.12 2.16 2.16 2.12 (1) (2) R 1 1.0 Ω R 2 2.0 Ω R 3 1.0 Ω R 4 1.0 Ω R 5 2.0 Ω E a 2.1 V E b 4.2 V I a, I b, I c 2.13 2.17

40 c 2009 2 2.17 2.13 (1) I a I b I c (2) R a, R b, R c, R d R I a, I b, I c E 1, E 2, E 3, R 2.14 R E a E b 2.18 I 1 I 2 I 3 I 4 2.18 2.14 (1) (2) 2.4 2.5 2.19 R 2 I (1) E 1 R 2 I 1

2.4 c 2009 41 2.19 2.5 (2) E 2 R 2 I 2 (3) E 3 R 2 I 3 (4) I 2.5 1 2.20 2.20 2.5 (1) (2) (3) I 1 = E 1 R 1 + R 2R 3 R 2 + R 3 I 2 = E 2 R 2 + R 1R 3 R 1 + R 3 R 3 R 2 + R 3 = R 3 E 1 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.33) (R 1 + R 2 ) E 2 = (2.34) R 1 R 2 + R 2 R 3 + R 3 R 1 I 3 = E 3 R 3 + R 1R 2 R 1 + R 2 R 1 R 1 + R 2 = R 1 E 3 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.35)

42 c 2009 2 (4) I = I 1 + I 2 + I 3 = R 3E 1 + R 1 E 3 (R 1 + R 2 ) E 2 R 1 R 2 + R 2 R 3 + R 3 R 1 (2.36) 2.15 2.21 I 2.21 2.15 2.16 2.22 I E 1, E 2 R 2.22 2.16 2.17 2.23 R 2 I R 1 4.0 Ω R 2 2.0 Ω R 3 3.0 Ω R 4 6.0 Ω E 1 8.0 V E 2 6.0 V 2.18 2.24 a V a

2.4 c 2009 43 2.23 2.17 2.24 2.18 2.19 2.25 R 3 V 2.25 2.19 2.20 2.26 a 2.26 2.20

44 c 2009 2 2.21 2.27 V 2.27 2.21 2.22 2.28 V 2.28 2.22 2.23 2.29 I E 1 9.0 V E 2 4.4 V R 1 3.0 Ω R 2 2.0 Ω R 3 6.0 Ω R 4 4.0 Ω R 5 4.0 Ω 2.24 2.30 I E 1, E 2 R 2.25 2.31 I E 1 4.8 V E 2 1.6 V R 1 6.0 Ω R 2 2.0 Ω R 3 3.0 Ω R 4 6.0 Ω R 5 2.0 Ω R 6 4.0 Ω

2.4 c 2009 45 2.29 2.23 2.30 2.24 2.31 2.25

46 c 2009 2 2.5 2.6 2.32 (a) (c) E 0 R 0 E 1 2.4 V E 2 1.1 V R 1 2.0 Ω R 2 6.0 Ω R 3 1.2 Ω 2.32 2.6 2.6 2.32 (a) E 0 = R 2E 1 6.0 Ω 2.4 V = R 1 + R 2 2.0 Ω + 6.0 Ω R 0 = R 1R 2 R 1 + R 2 = 2.32 (b) 2.32 (c) = 1.8 V (2.37) 2.0 Ω 6.0 Ω = 1.5 Ω (2.38) 2.0 Ω + 6.0 Ω E 0 = R 2E 1 6.0 Ω 2.4 V = = 1.8 V (2.39) R 1 + R 2 2.0 Ω + 6.0 Ω R 0 = R 1R 2 R 1 + R 2 + R 3 = 1.5 Ω + 1.2 Ω = 2.7 Ω (2.40) E 0 = R 2E 1 R 1 + R 2 + E 2 = 1.8 V + 1.1 V = 2.9 V (2.41) R 0 = R 1R 2 R 1 + R 2 + R 3 = 1.5 Ω + 1.2 Ω = 2.7 Ω (2.42) 2.26 2.33 E 3.0 V R 1 3.0 Ω R 2 2.0 Ω B

2.5 c 2009 47 2.33 2.26 (1) E 0 R 0 (2) J 0 G 0 2.27 2.34 E 0 R 0 B 2.34 2.27 2.28 2.35 E 0 R 0 B 2.35 2.28 2.29 2.36 E 0 R 0 B

48 c 2009 2 2.36 2.29 2.30 2.37 E 0 R 0 B 2.37 2.30 2.31 B 2.38 2.31 (1) 2.38 E 0 R 0 (2) 2.38 J 0 G 0 2.32 2.39 (1) E 0 R 0

2.5 c 2009 49 2.39 2.32 (2) A B I 0 2.33 2.40 2.40 2.33 (1) E 0 R 0 (2) A B I 0 2.34 2.41 E 0 R 0 E 1 = 1.5 V, E 2 = 2.0 V, E 3 = 1.2 V, R 1 = 1.5 Ω, R 2 = 1.0 Ω, R 3 = 0.40 Ω 2.41 2.34 2.35 2.42 E 0 R 0

50 c 2009 2 2.42 2.35 2.36 E r 2.43 (a) (e) 2.43 (a) (e) E 0 R 0 2.43 2.36

c 2009 51 3 3.1 3.1 (1) f 1.6 khz ω (2) T 2.5 µs f (3) I e 17 ma I m (4) V m 3.5 V V e (5) f 50 Hz C 64 µf X C (6) f 3.2 khz L 50 mh X L 3.1 (1) (2) ω = 2πf = 2π ( 1.6 10 3 Hz ) = 1.0/0 10 4 rad/s = 1.0 10 4 rad/s = 10 krad/s (3.1) f = 1 T = 1 2.5 10 6 s = 4.0 105 Hz = 0.40 MHz (3.2)

52 c 2009 3 (3) (4) I m = 2I e = 2 ( 17 10 3 A ) = 24./0 10 3 A = A = 24 ma (3.3) V e = Vm 2 = 3.5 V 2 = 2./4 5 /7 V = 2.5 V (3.4) (5) X C = 1 ωc = 1 2πfC = 1 2π 50 Hz (64 10 6 F) = /4 5 /9 0./7 Ω = 50 Ω (3.5) (6) X L = ωl = 2πfL = 2π ( 3.2 10 3 Hz ) ( 50 10 3 H ) = 1.0/0 10 3 Ω = 1.0 10 3 Ω = 1.0 kω (3.6) 3.1 3.1 50 µs/div 2 V/div f V m 2 3.1 3.1 3.2 (1) 1.6 khz (2) 8.00 khz

3.1 c 2009 53 (3) 2.5 µs (4) 220 rad/s (5) 17 ma (6) 110 V (7) 212 V (8) 3.5 V (9) 17.0 ma (10) 71 ma 3.3 50 V 100 rad/s π rad t v(t) 3 3.4 ω i(t) i(t) = 2 sin(ωt + π ) [A] (3.7) 3 t i(t) T (1) t = T/12 (2) t = 5T/24 (3) t = 2T/3 (4) t = 2T (5) t = 7T/3 3.5 50.0 Hz 100 V π rad t = 0.833 ms 6 3 3.6 v(t) v(t) = 70.7 sin(629t + 1.57) [V] (3.8) π 3.14 (1) V m (2) V e (3) ω (4) f (5) θ (6) t 2.50 ms v(t) 3.7

54 c 2009 3 i(t) v(t) C 3.2 3.2 (1) 5.0 mh 2.0 krad/s (2) 25 pf 2.0 Mrad/s (3) 13 mh 60 Hz (4) 10 nf 0.80 khz (5) 2.0 mh 44 Ω (6) 0.10 µf 4.0 kω (7) 4.0 µf 60 Hz (8) 50 mh 3.2 khz (9) 50 Hz 100 V 47 ma (10) 1.5 khz 50 V 76 ma 3.2 3.2 500 µf C v(t) v(t) = 49.2 sin(250t 30 ) [V] (3.9) (1) ω (2) V e (3) X C (4) I e (5) i (t) 3.2 (1) ω = 250 rad/s (3.10)

3.1 c 2009 55 3.3 3.8 (2) 49.2 V (3) X C (4) V e = X C I e V e = 49.2 V 2 = 34./7 8 /8 V = 34.8 V (3.11) X C = 1 ωc = 1 = 8.00 Ω (3.12) 250 rad/s 500 µf I e = V e = 34.8 V = 4.35 A (3.13) X C 8.00 Ω (5) π 2 = 90 i (t) = 2I e sin (250t 30 + 90 ) = 6.15 sin (250t + 60 ) [A] (3.14) 3.8 3.3 5.0 Ω R v ( v(t) = 10 sin 200t + π ) 3 [V] (3.15) v (1) ω (2) V e (3) I e (4) i (t) 3.9 3.4 20 mh L i ( i (t) = 8 sin 300t + π ) [A] 6

56 c 2009 3 3.4 3.9 (1) ω (2) I e (3) X L (4) V e (5) v (t) 3.10 L 450 mh v(t) = 141 sin (314πt + 0.785) [V] (3.16) π = 3.14 2 = 1.41 (1) (2) (3) (4) (5) i (t) 3.11 v(t) = 212 sin (785t 30.0 ) [V] (3.17) 12.5 A π = 3.14 2 = 1.41 (1) V e (2) f (3) X C (4) C (5) i (t) 3.2 3.3

3.2 c 2009 57 z 1 = 1 j z 2 = 3 + j (1) z 1 + z 2 (2) z 1 z 2 (3) z 1 z 2 (4) z 1 z 2 (5) z 1 (6) z 2 (7) z 1 z 2 (8) z 1 z 2 3.3 (1) z 1 + z 2 = (1 j) + ( 3 + j) = 1 3 (3.18) (2) z 1 z 2 = (1 j) ( 3 + j) = (1 + 3) j2 (3.19) (3) z 1 z 2 = (1 j) ( 3 + j) = (1 3) + j(1 + 3) (3.20) (4) (5) (6) z 1 = z 1 = 1 j z 2 3 + j = 1 j 3 + j 3 j 3 j = ( 1 3) + j( 1 + 3) 4 1 2 + ( 1) 2 1 1 tan 1 = ( 2 π ) 4 ( z 2 = ) 2 3 + 12 tan 1 1 3 = 2 5π 6 (3.21) (3.22) (3.23)

58 c 2009 3 (7) (8) z 1 z 2 = ( 2 π ) 4 = z 1 z 2 = ( 2 2 ) ( 2 π ) 4 2 5π 6 2 5π ( 6 π 4 + 5π 6 = = 1 ( 13π ) 2 12 θ π θ π ) = 2 2 7π 12 ( 2 2 π 4 5π ) 6 = 1 2 11π 12 (3.24) (3.25) 3.12 z 1 z 6 (1) z 1 = 1 + j (2) z 2 = 1 + j 3 (3) z 3 = j (4) z 4 = 1 π 4 (5) z 5 = 3 π 6 (6) z 6 = 2 7π 4 3.13 (1) 3 + j (2) 1 j (3) 2 ( 3 exp j π ) 3 (4) ( 2 exp j 3π ) ( 4 (5) exp j π ) 2 (6) 2 e jπ 3.14 3.5 1 1 (1) z 1 (2) z 2

3.2 c 2009 59 3.5 3.14 (3) z 3 (4) z 4 3.15 (1) (5 + j2) (3 j4) (2) (4 + j2) (3 j) (3) 3 2π 5 2 3π ( 5 (4) 6 exp j 4π 7 ) 2 exp ( j 3π ) 7 3.16 z 1 = 3 + j 2 z 2 = 6 j2 (1) z 1 + z 2 (2) z 1z 2 (3) z 1 z 2 (4) z 1 z 2 3.17 z 1 = 2 π ( 4 z 2 = 2 π ) 6 (1) z 1z 2 (2) z 1z 2 (3) z 1 /z 2 (4) z 1 + z 2 3.18 z = 1 + j 3 2 (1) z 2 (2) z 3 (3) z + z 2 + z 3 (4) z 1

60 c 2009 3 (5) z z 3.3 3.4 i(t) v(t) (1) i(t) = 2 sin ωt [A] (2) i(t) = 2 2 sin ( ) ωt π 2 (3) v(t) = 5 sin ωt [V] (4) v(t) = 6 sin ( ) ωt + π 6 [A] [V] 3.4 (1) i (t) = 2 sin ωt I = 1 e 0 = 1 0 = 1 (3.26) (2) (3) (4) i (t) = 2 ( 2 sin ωt π ) ( I = 2 e π 2 = 2 π ) = j2 (3.27) 2 2 v (t) = 5 sin ωt = 5 sin (ωt + π) V = 5 2 e π = 5 2 π = 5 2 (3.28) v(t) = ( 6 sin ωt + π ) = ( 6 sin ωt 5π ) 6 6 V = 3 e 5π 6 = 3 ( 5π 6 ) = 3 2 j 3 2 (3.29) 3.19 t ω

3.3 c 2009 61 ( (1) i(t) = 12 sin ωt + π ) ( 3 (2) v(t) = 10 sin ωt π ) ( 12 (3) I = 3 π ) A 4 [A] [V] (4) V = 8 π 2 V 3.20 (1) 3 π ( 3 (2) 5 π ) 6 (3) 2 π 2 (4) 1 + j 3 (5) 6 + j 1 6 1 6 (6) j 2 2 3.21 (1) i 1 = 2 sin ( ωt [A] I 1 (2) i 2 = 2 sin ωt + π ) [A] I 2 2 (3) i 3 = ( 6 sin ωt π ) [A] I 3 3 (4) i 4 = 2 ( 2 sin ωt + π ) [A] I 4 4 (5) I 1 I 4 3.22 ( (1) 100 sin ωt 4π ) [A] ( 3 (2) 200 sin ωt + π ) [A] 2 (3) ( 2 cos ωt π ) [V] 4 (4) ( 2 sin ωt + π ) + ( 2 sin ωt π ) 3 3 [V] 3.5 3.6 V 50 V I 10 A f 50.0 Hz (1) V I (2) I (3) v(t)

62 c 2009 3 3.6 3.5 (4) i(t) (5) L 3.5 (1) I V π 2 3.7 V I 3.7 3.5 (2) I = I e j π 2 = j I = j10 A (3.30) (3) V m V m = 2 V = 7/0 1./7 V = 71 V (3.31) ω ω = 2πf = 314./1 rad/s = 314 rad/s (3.32) v(t) = 71 sin 314t (3.33) (4) I m I m = 2 I = 14./1 A = 14 A (3.34)

3.3 c 2009 63 90.0 i(t) = 14 sin (314t 90.0 ) (3.35) (5) V = ωl I L = V ω I = 50 V 314 rad/s 10 A = 0.01/56 /9 H = 16 mh (3.36) 3.23 3.8 L 96 mh f 50 Hz 3.8 3.23 (1) 1.5 ( 30 ) A I V (2) (1) I V (3) 90 0 V I (4) (3) V I 3.24 3.9 C 5.0 µf 1.0 A 100 krad/s 60 i v C 3.9 3.24 (1) i(t)

64 c 2009 3 (2) I (3) X C (4) V (5) I V (6) v(t) 3.25 C 100 µf v(t) v(t) = 71 sin (100t 30 ) [V] (3.37) (1) I m (2) i(t) (3) V I (4) V I (5) 2 I m (6) 2 i (t) 3.26 50 mh 21 V 200 rad/s 30 v(t) (1) v(t) (2) V (3) I (4) V I (5) i(t) (6) 3.0

c 2009 65 4 4.1 4.1 (1) (3.0 + j2.0) V V (4.0 j3.0) A I Z (2) (3.0 j4.0) V V (2.0 j2.0) A I Y (3) Z (3.0 + j4.0) Ω (5.0 + j6.0) V V I (4) Y (12 + j5.0) S (1.0 + j2.0) A I V 4.1 (1) Z = V (3.0 + j2.0) V (3.0 + j2.0)(4.0 + j3.0) = = I (4.0 j3.0) A 4.0 2 + 3.0 2 Ω 6.0 + j17 = Ω = (0.24 + j0.68) Ω (4.1) 25

66 c 2009 4 (2) (3) (4) Y = I (2.0 j2.0) A (2.0 j2.0)(3.0 + j4.0) = = V (3.0 j4.0) V 3.0 2 + ( 4.0) 2 S 14 + j2.0 = S = (0.56 + j0.080) S (4.2) 25 I = V (5.0 + j6.0) V (5.0 + j6.0)(3.0 j4.0) = = Z (3.0 + j4.0) Ω 3.0 2 + 4.0 2 A 39 j2.0 = A = (1./5 6 /6 j0.080) A = (1.6 j0.080) A (4.3) 25 V = I (1.0 + j2.0) A (1.0 + j2.0)(12 + j5.0) = = Y (12 + j5.0) S 12 2 + 5.0 2 V 22 + j19 = V = (0.13/0 + j0.11/2 ) V = (0.13 + j0.11) V (4.4) 169 4.1 4.1 Z Y V I 4.1 4.1 (1) I (5.0 + j2.0) A Z (2.0 + j3.0) Ω V (2) V (2.0 + j1.0) V I (4.0 j3.0) A Z (3) V (3.0 + j1.0) V Z (3.0 + j4.0) Ω I (4) V (3.0 + j4.0) V I (2.0 + j4.0) A Y (5) I ( 3.0 + j4.0) A Y (3.0 j2.0) S V 4.2 (1) Z (4.0 + j2.0) Ω Y

4.1 c 2009 67 (2) Y (6.0 j8.0) S Z (3) Z (16 j12) Ω Z (4) Y (20 + j15) Ω Y 4.2 (1) (2) Y = 1 Z = 1 = (0.20 j0.10) S (4.5) (4.0 + j2.0) Ω Z = 1 Y = 1 = (60 + j80) mω (4.6) (6.0 j8.0) S (3) Z = 16 2 + ( 12) 2 = 20 Ω (4.7) (4) Y = 20 2 + 15 2 = 25 S (4.8) 4.2 (1) 15 mh 1.0 khz (2) 4.0 µf 3.9 khz (3) 40 µh 8.0 khz (4) 1000 pf 1.0 MHz 4.3 4.2 5.0 Ω (7.0 + j5.0) V V I 4.4 4.3 X C 3.0 Ω (4.5 j9.0) V V Z I

68 c 2009 4 4.2 4.3 4.3 4.4 4.4 4.5 4.5 4.4 X L 1.3 Ω ( 0.39 + j2.6) V V Z I 4.6 Z (30 + j40) Ω 100 V V I 4.3 v i v(t) = 100 ( 2 sin 120πt + π ) [V] (4.9) 4 i(t) = 5 2 sin 120πt [A] (4.10) Z 4.3

4.2 c 2009 69 I V I = 5 e j0 A = 5 A (4.11) V = 100 e j π 4 V = (50 2 + j50 2) V (4.12) Z Z = V I = (50 2 + j50 2) V 5 A = (10 2 + j10 2) Ω (4.13) 4.7 Z ( 3 + j) Ω v(t) v(t) = 100 sin 200t (4.14) i(t) 4.2 4.4 4.5 L 449 mh e(t) e(t) = 141 sin(100πt + π ) [V] (4.15) 4 3 i(t) e(t) L 4.5 4.4 (1) E e (2) E

70 c 2009 4 (3) Z (4) I 4.4 (1) E m 141 V E e = E m 2 = 99.7 V (4.16) (2) E = V e e j π 4 = (70.5 + j70.5) V (4.17) (3) Z = jωl = j 100π 449 mh = j141 Ω (4.18) (4) V = ZI I = V Z = (70.5 + j70.5) V j141 Ω = (0.500 + j0.500) A (4.19) 4.8 4.6 v(t) v(t) = 212 sin (785t 30.0 ) [V] (4.20) 1 12.5 A i(t) e(t) C 4.6 4.8 (1) V e 1

4.3 c 2009 71 (2) V (3) X C (4) C 4.9 e 1 = ( 2 sin ωt + π ) e 2 = ( 2 sin ωt + π ) 2 3 6 4.7 4.7 4.9 (1) e 1, e 2 E 1, E 2 (2) E 1, E 2 e E (3) E e 4.10 4.8 E, ω R C L I R I C I L ω R C L 4.8 4.10 4.3 4.5

72 c 2009 4 R C L 4.9 (a) (d) ω 4.9 (a) (d) 4.9 4.5 4.5 (a) (b) (c) (d) 1 1 R + 1 jωl = jωlr R + jωl 1 R = 1 R + jωc 1 + jωcr 1 R + jωl = 1 R + jωl + jωc 1 ω 2 LC + jωcr 1 1 R + 1 jωc + 1 jωl = ω2 LCR + jωl 1 ω 2 LC + jωcr (4.21) (4.22) (4.23) (4.24) 4.11 4.10 Z 1 = 2 j4, Z 2 = 4 + j2, Z 3 = 2 + j (a) (d)

4.3 c 2009 73 4.10 4.11 4.11 4.12 4.12 4.11 π 3.14 (1) R 15 Ω, f 50 Hz 4.11(a) (2) C 0.16 µf, f 1.0 MHz 4.11(b) (3) L 32 mh, f 5.0 khz 4.11(c) (4) R 20 Ω, C 2.1 µf, f 1.5 khz 4.11(d) (5) R 3.0 Ω, L 8.0 mh, f 50 Hz 4.11(e)

74 c 2009 4 4.13 4.12 R 4.0 Ω X L 3.0 Ω 4.12 4.13 (1) 4.12(a) (2) 4.12(a) (3) 4.12(b) (4) 4.12(b) 4.14 4.13 ω 4.13 4.14 (1) 4.13 (a) Z a (2) 4.13 (b) Z b (3) ωc 2 R 2 = 1 Z a = Z b R 1 C 1 R 2 C 2 4.15 4.14 Z ω 4.14 4.15

4.3 c 2009 75 4.16 4.15 RLC G B ω 4.15 4.16 4.17 4.16 ω 4.16 4.17 4.18 4.17 ω ( 0) (1) Z (2) Z = 0 ω 1 (3) Y (4) Y = 0 ω 2

76 c 2009 4 4.17 4.18 4.19 4.18 0 ω 1 0 ω 2 0 4.18 4.19 4.20 4.19 A B R 1 0.70 Ω R 2 3.0 Ω X L1 0.10 Ω X L2 1.0 Ω 4.19 4.20 4.21 4.20 A B R 1 0.40 Ω R 2 2.0 Ω X C1 0.50 Ω X C2 1.0 Ω

4.3 c 2009 77 4.20 4.21 4.22 4.21 R 1 5.0 Ω R 2 2.0 Ω X L1 10 Ω X L2 1.0 Ω 4.21 4.22 (1) a b (2) a b 4.23 4.22 R 1 2.0 Ω R 2 1.0 Ω X C1 2.0 Ω X C2 3.0 Ω (1) a b (2) a b 4.24 4.23 Z Z 1 Z 1, Z 2, Z 3 4.25 4.24 Z 1

78 c 2009 4 4.22 4.23 4.23 4.24 4.24 4.25 4.26 ω 4.25 R 0 L 0 R L ω 4.25 4.26 4.27 4.26 R 1 R 2

4.4 c 2009 79 4.26 4.27 (1) Z (2) 0 4.4 4.6 4.27 (1) Z 1 (3.5 + j2.0) Ω Z 2 (1.5 j2.0) Ω V (4.0 + j1.0) V V 1 (2) Z 1 j7.0 Ω Z 2 6.0 Ω V 1 14 V V 4.27 4.6 4.6

80 c 2009 4 (1) (2) Z 1 (3.5 + j2.0) Ω V 1 = V = (4.0 + j1.0) V Z 1 + Z 2 (3.5 + j2.0) Ω + (1.5 j2.0) Ω (3.5 + j2.0) (4.0 + j1.0) = V = (2.4 + j2.3) V (4.25) 5.0 V = Z 1 + Z 2 6.0 Ω + j7.0 Ω V 1 = 14 V Z 1 j7.0 Ω = (6.0 + j7.0) ( j2.0 V) = (14 j12) V (4.26) 4.28 4.28 4.28 4.28 (1) 4.28 R 4.0 Ω X L 3.0 Ω V (15 j20) V I (2) 4.28 R 1.2 Ω X L 1.4 Ω V L 4.2 V V 4.29 4.29 4.29 4.29

4.4 c 2009 81 (1) 4.29 V R 24 V V C 10 V V (2) 4.29 R 4.0 Ω X C 2.0 Ω V 30 V V R 4.30 4.30 R 6.0 Ω X L 13 Ω X C 5.0 Ω V (30 + j20) Ω 4.30 4.30 (1) Z (2) I (3) V C 4.7 4.31 E 100 V, R 3.0 Ω, X C 4.0 Ω 4.31 4.7 (1) Z (2) I (3) V R (4) V C

82 c 2009 4 4.7 (1) Z = R jx C = (3.0 j4.0) Ω (4.27) (2) (3) I = E Z = 100 V = (12 + j16) A (4.28) (3.0 j4.0) Ω V R = RI = 3.0 Ω (12 + j16) A = (36 + j48) V (4.29) (4) V C = jx C I = j4.0 Ω (12 + j16) A = (64 j48) V (4.30) 4.31 4.32 X L 1.0 Ω R 2.0 Ω E 20 V 4.32 4.31 (1) Z (2) Y (3) I (4) E I (5) I (6) E I θ 4.32 4.33 E 100 V, I 10 A, θ 60

4.4 c 2009 83 4.33 4.32 (1) E I (2) I (3) Z (4) Z (5) R (6) X L 4.33 4.34 LR E (= E 0 + je 1 ) E 0, E 1 I I 4.34 4.33 4.34 4.35 E R L ω 4.35 4.34

84 c 2009 4 (1) Z (2) I (3) I (4) V R (5) V L (6) E, V R, V L I V R (7) E I θ 4.35 4.36 ω 10 krad/s R 3.0 Ω C 25 µf V (20 j10) V 4.36 4.35 (1) Z C (2) Z (3) I (4) V R 4.36 4.37 I 10 A R 4.0 Ω X C 3.0 Ω 4.37 4.36 (1) Z (2) E (3) V R V C E I (4) E I θ

4.4 c 2009 85 (5) Z (6) E I θ 4.37 4.38 ω 4.38 4.37 (1) (a) Z a (b) Z b (2) (a) Z a (b) Z b (3) R = 3 r L = 2r/ω Z a = Z b L C r 4.38 4.39 1.5 V 0.10 A 50 Hz 100 V 4.0 A 2 4.39 4.38 (1) R 0 Ω (2) Z (3) X L (4) L 4.39 4.40 (1) 4.40(a) 100 V V 20.0 A I 1 Z 3

86 c 2009 4 4.40 4.39 (2) Z R + jx Z R, X (3) 4.40(a) R 0 = 6.00 Ω (b) 100 V V 10.0 A I 2 Z + R 0 3 (4) Z + R 0 R, R 0, X (5) (2) (4) R X 3 4.40 4.41 E = E 0 + je 1, E 0, E 1 ω E 0, E 1, C, R, ω 4.41 4.40 (1) Z (2) I (3) ωcr = 1 I E 0, E 1, R (4) (3) θ E θ I tan θ E tan θ I (5) (4) (3) θ I = θ E + π ( 4 tan θ I = tan θ E + π ) 4 4.41 4.42 E 13 V V R 12 V V L 8.0 V (1) V R E, V R, V L, V C (2) E, V R, V L, V C (3) V C

4.4 c 2009 87 4.42 4.41 4.42 4.43 X L 25.0 Ω X C 17.0 Ω I 600 ma E 6.00 V 4.43 4.42 (1) V L (2) V C (3) E, V L, V C, V R, I (4) V R 4.43 4.44 E 50 V X L 9.0 Ω X C 1.0 Ω I 5.0 A (1) Z (2) X (3) R (4) V R (5) 0.50 Z

88 c 2009 4 4.44 4.43 4.5 4.8 4.45 4.45 4.8 (1) Z 1 (1.8 + j1.6) Ω Z 2 (1.2 j1.6) Ω I 6.0 A I 1 (2) Z 1 (1.0 j2.0) Ω Z 2 (2.0 + j4.0) Ω I 1 (6.0 + j5.0) A I 4.8

4.5 c 2009 89 (1) (2) Z 2 (1.2 j1.6) Ω I 1 = I = Z 1 + Z 2 (1.8 + j1.6) Ω + (1.2 j1.6) Ω 6.0 A (1.2 j1.6) 6.0 = A = (2.4 j3.2) A (4.31) 3.0 I = Z 1 + Z 2 I 1 = = Z 2 (1.0 j2.0) Ω + (2.0 + j4.0) Ω (2.0 + j4.0) Ω (6.0 + j5.0) A 8.0 + j27 124 + j22 A = A = (6.2 + j1.1) A (4.32) 2.0 + j4.0 20.0 4.44 4.46 4.46 4.44 (1) 4.46(a) R 2.0 Ω X L 4.0 Ω I 40 A I L (2) 4.46(a) R 13 Ω X L 7.0 Ω V 91 V I (3) 4.46(b) R 10 Ω X C 5.0 Ω I (2.0 + j4.0) A V (4) 4.46(b) R 5.0 Ω I R (6.0 j9.0) A I (9.0 j7.0) A X C 4.9 4.47 E 120 V I L 3.0 A, R 40 Ω

90 c 2009 4 4.47 4.9 (1) I R (2) I (3) Y (4) X L (5) Y 4.9 (1) I R = E R = 120 V 40 Ω = 3.0 A (4.33) (2) I = I R 2 + I L 2 = (3.0 A) 2 + (3.0 A) 2 = 2 3.0 A = 4.2 A (4.34) (3) Y = I 2 3.0 A E = = 35 ms (4.35) 120 V (4) X L = E I L = 120 V = 40 Ω (4.36) 3.0 A (5) Y = 1 R + 1 = 1 jx L 40 Ω + 1 = (25 j25) ms (4.37) j40 Ω

4.5 c 2009 91 4.48 4.45 4.45 4.48 (1) 4.48(a) ωl = 2R I I R (2) 4.48(b) V 24 V I 10 A R 3.0 Ω C I C 4.46 4.49 ω 4.49 4.46 (1) I R (2) I C (3) E I R I C I (4) E I θ 4.47 4.50 (12 + j28) V V R 5.0 Ω C 2.0 µf f 20 khz

92 c 2009 4 4.50 4.47 (1) R I R (2) C I C (3) I (4) I, I R, I C, V (5) Y 4.48 4.60 E 20 V C I C 1.0 A R 10 Ω 4.51 4.48 (1) R I R (2) I (3) Y (4) X C 4.49 4.52 E 120 V R 20 Ω X L 15 Ω (1) Z (2) I R (3) I L

4.5 c 2009 93 4.52 4.49 (4) E, I, I R, I L (5) I (6) E I θ 4.50 4.53 R 4.0 Ω L X L 3.0 Ω I R 12 A 4.53 4.50 (1) V (2) I R V (3) I L (4) I L V (5) I (6) I (7) 4 I 4.51 4.54 E 10 V I 5.0 A I R 3.0 A (1) I C (2) Y (3) R (4) X C (5) Y

94 c 2009 4 4.54 4.51 4.52 4.55 f 50 Hz, V 33 V R I R 5.5 A V I θ θ = 60 4.55 4.52 (1) I, I R, I L, V (2) L I L (3) I (4) I (5) R (6) L 4.10 4.56 R 3.0 Ω X C 4.0 Ω X L 6.0Ω E 12 V (1) I R (2) I C (3) I L (4) I (5) E I R I C I L I

4.5 c 2009 95 4.56 4.10 4.10 (1) (2) (3) (4) I C = I L = I R = E R = 12 V = 4.0 A (4.38) 3.0 Ω E = 12 V = j3.0 A (4.39) jx C j4.0 Ω E = 12 V = j2.0 A (4.40) jx L j6.0 Ω I = I R + I C + I L = (4.0 + j1.0) A (4.41) (5) 4.57 4.57 4.10 4.53 4.58 I R 5.0 A I L 19.0 A I C 7.0 A

96 c 2009 4 4.58 4.53 (1) I R I L I C I E (2) I (3) I 4.54 4.59 E 85 V I 13 A L I L 17.0 A C I C 5.0 A 4.59 4.54 (1) R I R I, I R, I L, I C, E (2) I R (3) I (4) R (5) X L (6) X C 4.55 R X 4.60 (a) (b) (1) (a) Z a R X (2) (a) V V R V X (3) (a) V R X I (4) (b) Y b R X

4.6 c 2009 97 4.60 4.55 (5) (b) Z b R X (6) (b) I I R I X 4.6 4.11 4.61 R 15 Ω X C 20 Ω E 60 V I X 3.0 A I E 4.61 4.11 (1) I R (2) I, I R, I X, E (3) I (4) X C X L Z X

98 c 2009 4 (5) X L 4.11 (1) I R = E R = 60 V = 4.0 A (4.42) 15 Ω (2) I E I R E 4.62 IR E I IX 4.62 4.11 (3) 4.62 I X = j I X = j3.0 A (4) I = I R + I X = (4.0 j3.0) A (4.43) (5) Z X = E I X = 60 V = j20 Ω (4.44) j3.0 A Z X = jx L jx C = j20 Ω (4.45) X C = 20 Ω (4.46) X L = 40 Ω (4.47) 4.56 4.63 R I R 4.0 A X C 10 Ω X L 10 Ω R 5.0 Ω

4.6 c 2009 99 4.63 4.56 (1) V 1 (2) V 1 I R I L (3) I L (4) I (5) V 2 (6) V 4.57 4.64 X C 5.0 Ω X L 8.0 Ω R 4.0 Ω I c 4.0 A 4.64 4.57 (1) V 1 (2) I R (3) I (4) V 1, I R, I C I (5) V 2 (6) V 4.58 4.65 (6.0 j9.0) V V (3.0 j2.0) A I

100 c 2009 4 X C 3.0 Ω R 4.0 Ω L 4.0 mh 4.65 4.58 (1) V 1 (2) V 2 (3) I R (4) L I L (5) X L (6) ω 4.59 4.66 X C 5.0 Ω X L 1.0 Ω R 2.0 Ω V 5.0 A I C 4.66 4.59 (1) V I C V (2) I L I L V (3) I I C, I L I 4.60 4.67 X L 5.0 Ω I L j2.0 A I (2.0 j1.0) A

4.6 c 2009 101 4.67 4.60 (1) V (2) I C (3) R X C Z (4) R (5) X C 4.61 4.68 r 0.20 Ω R 1.0 Ω X C 0.40 Ω X L 2.0 Ω V 10 V 4.68 4.61 (1) Z (2) I (3) V 1 (4) V 2 (5) I R (6) I L 4.62 4.69 r 0.10 Ω R 3.0 Ω X L 0.60 Ω X C

102 c 2009 4 1.0 Ω V 25 V 4.69 4.62 (1) Z (2) I (3) V 1 (4) V 2 (5) I R (6) I C 4.63 4.70 R 20 Ω r 5.0 Ω X L 10 Ω X C 10 Ω V I R 6.0 A 4.70 4.63 (1) V 2 (2) I C (3) I (4) I R, I C, I (5) V 1 (6) V

4.6 c 2009 103 4.64 4.71 I C 1.0 A R 15 Ω r 6.0 Ω X C 30 Ω X L 8.0 Ω 4.71 4.64 (1) V C (2) I L (3) I (4) R V R (5) V 4.65 4.72 R 1 1.0 Ω R 2 3.0 Ω X C 3.0 Ω X L 6.0 Ω V (30 + j60) V 4.72 4.65 (1) I 1 (2) I 2 (3) I 2 (4) Z (5) V I 1 I 2 I

104 c 2009 4 (6) V I 2 θ V 4.66 4.73 R C E ω R C E ω 4.73 4.66 (1) c a V ac (2) c b V bc (3) b a V ab 4.67 4.74 ω V R L C ω V L CR 2 4.74 4.67 (1) a V a (2) b V b (3) a b V ab (4) V V ab (5) (4) V ab

4.7 c 2009 105 4.68 4.75 4.75 4.68 (1) I L (2) I C (3) I L = I C ω (4) ω V R R C L E (5) ω V C R C L E (6) ω V R = V C (7) (3) (6) I 4.7 4.12 4.76 Maxwell R 1 L 1 0 A R 1 L 1 R 2 R 3 R 4 C 4 E ω 4.12 ( ) 1 (R 1 + jωl 1 ) 1 = R 2 R 3 (4.48) R 4 + jωc 4 R 1 + jωl 1 = R 2 R 3 ( 1 R 4 + jωc 4 ) (4.49)

106 c 2009 4 4.76 4.12 R 1 = R 2R 3 R 4 (4.50) L 1 = R 2 R 3 C 4 (4.51) 4.69 4.77 Wien ω R 1 R 5 ω, R 1 R 2, R 3, R 4, C 3, C 4 4.77 4.69 4.70 4.78 Hay ω

4.7 c 2009 107 4.78 4.70 4.71 4.79 Owen ω 4.79 4.71 4.72 4.80 ω 4.80 4.72

108 c 2009 4 4.73 4.81 ω 4.81 4.73

c 2009 109 5 5.1 λ 96.0% 250 V V 2.00 A I (1) P a (2) P (3) P r 5.1 (1) P a = V I = 250 V 2.00 A = 500 VA (5.1) (2) P = P a λ = 500 VA 0.960 = 480 W (5.2) (3) P 2 a = P 2 + P 2 r P r = ± P 2 a P 2 = ± 500 2 480 2 var = ±140 var (5.3) 5.1 (1) 2.0 kva 90%

110 c 2009 5 (2) 300 VA 100 V (3) 4.0 kw 3.0 kvar (4) 1.5 kva 900 var (5) 2.4 kw 96% 5.2 (1) Z (3.0 + j4.0) Ω I 2.0 A P (2) V 10 V I 2.0 A θ 30 P (3) V 25 V I 3.0 A θ 60 P a 5.3 100 V (3.0 + j4.0) A Z Y P 5.4 E (40 + j30) V Z (3.0 + j4.0) A I (1) Z (2) Z (3) (1) 2 λ (4) P a (5) P (6) P r 5.5 200 V V P 3.2 kw 0.80 2 I V (1) P a (2) P r (3) I (4) Z (5) Z 5.6 200 V 25.0 A 2.50 kw

c 2009 111 (1) P a (2) λ (3) θ (4) I 5.7 100 V 50 6 V 5.2 5.1 E 10 V R 24 Ω X L 7.0 Ω 5.1 5.2 (1) Z (2) I (3) P a (4) λ (5) P 5.2 (1) Z = R + jx L = R 2 + X L 2 = 24 2 + 7.0 2 Ω = 25 Ω (5.4) (2) I = E Z = 10 V = 0.40 A (5.5) 25 Ω

112 c 2009 5 (3) P a = E I = 10 V 0.40 A = 4.0 VA (5.6) (4) (5) λ = R Z = 24 Ω = 0.96 (5.7) 25 Ω P = P a λ = 4.0 VA 0.96 = 3.8/4 W = 3.8 W (5.8) P = R I 2 = 24 Ω (0.40 A) 2 = 3.8/4 W = 3.8 W (5.9) 5.8 5.2 R 48 Ω X L 14 Ω P 12 W 5.2 5.8 (1) I (2) Z (3) λ (4) V 5.9 5.3 R 4.0 Ω X C 3.0 Ω V I 10 A (1) Z (2) V (3) λ (4) P

c 2009 113 5.3 5.9 5.10 5.4 E 125 V P 600 W R 24 Ω 5.4 5.10 (1) I (2) Z (3) X L 5.3 5.5 R 2.0 Ω X L 2.0 Ω X C 4.0 Ω 2.0 V V 5.5 5.10

114 c 2009 5 (1) Z (2) I (3) Z I P (4) V 1 (5) V 2 (6) R P R V 2 P 5.3 (1) (2) I = V Z = (3) I (4) (5) (6) Z = jx L + R ( jx C) = j2.0 + j8.0 R jx C 2.0 j4.0 = j2.0 + (1.6 j0.80) = (1.6 + j1.2) Ω (5.10) 2.0 V 2.0 (1.6 j1.2) = A = (0.80 j0.60) A (5.11) (1.6 + j1.2) Ω 4.0 Z Re Z 1.6 Ω I = 0.80 2 + ( 0.60) 2 A = 1.0 A (5.12) P = Re Z I 2 = 1.6 Ω (1.0 A) 2 = 1.6 W (5.13) V 1 = jx L I = j2.0 Ω (0.80 j0.60) A = (1.2 + j1.6) V (5.14) V 2 = V V 1 = 2.0 V (1.2 + j1.6) V = (0.80 j1.6) V (5.15) P = V 2 2 R = 0.802 + ( 1.6) 2 2.0 W = 3.2 W = 1.6 W (5.16) 2.0

c 2009 115 5.6 5.11 5.11 5.6 E 84 V R 3.5 Ω X C 32 Ω X L 20 Ω (1) I R (2) I X (3) I (4) E I R I X I (5) E I λ 5.12 5.7 P 150 W R 6.0 Ω X L 8.0 Ω X C 25 Ω 5.7 5.12 (1) I L (2) V (3) I C 5.13 5.8 I 1 2.0 A

116 c 2009 5 R 5.0 Ω X C1 3.0 Ω X C2 8.0 Ω X L1 4.0 Ω X L2 6.0 Ω 5.8 5.13 (1) I 2 (2) I (3) R 5.14 5.9 RLC ω E P λ 5.9 5.14 5.4 (100 + j50.0) V (10.0 + j20.0) A (1) P c (2) P a (3) P (4) P r

c 2009 117 (5) λ 5.4 (1) P c = V I = (100 j50.0) V (10.0 + j20.0) A = (2.00 + j1.50) kva (5.17) (2) P a = P c = 2.00 2 + 1.50 2 kva = 2.50 kva (5.18) (3) P P c P = Re P c = 2.00 kw (5.19) (4) P r P c P r = Im P c = 1.50 kvar (5.20) (5) λ = P P a = 2.00 kw = 0.800 (5.21) 2.50 kva 5.15 (100 j50) V E (3.0 j4.0) A I 5 = 2.24 (1) Z (2) Y (3) P c (4) P a (5) P (6) P r (7) λ 5.16 5.10 E 300 V Z 1 (16 j12) Ω Z 2 j75 Ω (1) SW λ (2) SW I

118 c 2009 5 5.10 5.16 (3) SW P c (4) SW Z 2 I 2 (5) SW I (6) SW P c (7) SW λ 5.17 5.11 E I P a cos θ 0 5.11 5.17 (1) 5.11(a) I (2) 5.11(a) I (3) 5.11(b) I 1 I 2 (4) 5.11(b) I (5) 5.11(b) P c (6) 5.11(b) P a (7) 5.11(b)

c 2009 119 6 6.1 6.1 6.1 6.1 6.1 (1) (2) (3) I 1 I 2 I 3 6.1 (1) I 1 + I 2 I 3 = 0 (6.1)

120 c 2009 6 (2) E 1 = 1 jωc I 1 + RI 3 (6.2) E 2 = jωli 2 + RI 3 (6.3) (3) I 3 ( ) 1 E 1 = jωc + R I 1 + RI 2 (6.4) E 2 = RI 1 + (jωl + R) I 2 (6.5) I 1 = ( ω 2 LC + jωcr ) E 1 jωcre 2 R (1 ω 2 LC) + jωl I 2 = jωcre 1 + (1 + jωcr) E 2 R (1 ω 2 LC) + jωl I 3 = I 1 + I 2 = ω2 LCE 1 + E 2 R (1 ω 2 LC) + jωl (6.6) (6.7) (6.8) 6.1 6.2 6.2 6.1 (1) I 1 I 2 I 3 (2) N V N (3) V N = 0 6.2 6.3 I 1, I 2, I 3 E 1 E 3 Z 1 Z 3 I 4 I 6

6.2 c 2009 121 6.3 6.2 (1) (2) I 4 I 5 I 6 (3) (4) I 1 I 2 I 3 6.2 6.2 6.4 E 1 6.0 V E 2 2.0 V X L 3.0 Ω X C 2.0 Ω R 12.0 Ω 6.4 6.2 (1) (2) I 1 I 2 (3) R I R

122 c 2009 6 6.2 (1) E 1 = (R + jx L ) I 1 + RI 2 (6.9) E 2 = RI 1 + (R jx C ) I 2 (6.10) (2) 6.0 V = (12.0 + j3.0) Ω I 1 + 12.0 Ω I 2 (6.11) 2.0 V = 12.0 Ω I 1 + (12.0 j2.0) Ω (6.12) I 1 = (0.80 j3.6) A (6.13) I 2 = ( 1.2 + j3.4) A (6.14) (3) I R = I 1 + I 2 = (0.80 j3.6) A + ( 1.2 + j3.4) A = ( 0.40 j0.20) A (6.15) 6.3 6.5 V 6.5 6.3 (1) (2) I 1 I 2 (3) V 6.4 6.6

6.2 c 2009 123 6.6 6.4 (1) I 1 I 2 (2) I 1 I 2 (3) ω 1 LC V E R, L, C 6.5 Z 1, Z 2, Z 3 E 1, E 2 6.7 6.7 6.5 (1) I 1 I 2 (2) I 1 I 2 6.6 6.8 ω 6.8 6.6

124 c 2009 6 (1) (2) I 1 I 2 6.7 6.9 I 1, I 3 E 1, E 2, E 3 Z 1, Z 2, Z 3 6.9 6.7 6.8 6.10 ω 6.10 6.8 (1) (2) I 1 I 2 I 3 6.9 6.11 I 1 I 3 (1) (2) E = (8.0 j8.0) V R 4.0 Ω X C1 X C2 2.0 Ω X L1 2.0 Ω X L2 1.0 Ω I 1 I 3 6.10 6.12

6.2 c 2009 125 6.11 6.9 6.12 6.10 (1) (2) L = CR 2 I 2 = I 3 (3) L = CR 2 I 1 I 2 I 3 6.11 6.13 I 1, I 2, I 3 E 1, E 2 Z 6.13 6.11

126 c 2009 6 6.12 6.14 E a j7.0 V E b (12 + j5.0) V R 3.0 Ω X L1 6.0 Ω X L2 1.0 Ω X C 6.0 Ω 6.14 6.12 (1) 6.14 (2) I 1 I 2 I 3 2 (3) R P 6.13 6.15 E 1 (4.0 j4.0) V E 2 j2.0 V E 3 j2.0 V R 4.0 Ω X L 2.0 Ω X C 4.0 Ω 6.15 6.13 (1) (2) I 1 I 2 I 3

6.2 c 2009 127 6.14 6.16 E 1 (8.0 + j8.0) V E 2 j4.0 V E 3 j4.0 V R 2.0 Ω X L 4.0 Ω X C 1.0 Ω 6.16 6.14 (1) (2) I 1 I 2 I 3 6.15 6.17 I a I c I c Z 1 Z 2 Z 3 0 6.17 6.15 (1) (2) I a + I b + I c (3) E 1

128 c 2009 6 (4) E 1 + E 2 + E 3 = 0 Z 1 = Z 2 = Z 3 = Z E 1 E 1 Z (5) I a + I b + I c E 1 E 2 I a + I b + I c 6.16 6.18 6.18 6.16 (1) I 1 I 2 I 3 (2) Z a = Z b = Z c = Z r 1 = r 2 = r 3 = r I 1 E 1 E 2 E 3 Z r (3) (2) Z a I a E 1 E 2 E 3 Z r 6.17 6.19 6.19 6.17 (1) (2) E 1 = E 2 = E I 1 = I 2 I 3 = I 4 I 1 I 3 E Z

6.3 c 2009 129 6.18 6.20 6.20 6.18 (1) I 1 I 4 (2) I 1 = I 2 = I 3 = I 4 E2 E 1, E3 E 1, E4 E 1 6.3 6.3 6.21 V 1 V 2 V 3 J 1 J 2 Y V 0 = 0 6.21 6.3 6.3 J 1 Y (V 1 V 3 ) Y (V 1 V 3 ) = 0 (6.16) J 2 2Y (V 2 V 3 ) Y (V 2 V 1 ) = 0 (6.17) Y (V 3 V 1 ) Y (V 3 V 0 ) 2Y (V 3 V 2 ) = 0 (6.18)

130 c 2009 6 V 0 = 0 J 1 = 2Y V 1 Y V 2 Y V 3 (6.19) J 2 = Y V 1 + 3Y V 2 2Y V 3 (6.20) 0 = Y V 1 2Y V 2 + 4Y V 3 (6.21) V 1 = 8J 1 + 6J 2 5Y V 2 = 6J 1 + 7J 2 5Y V 3 = J 1 + J 2 Y (6.22) (6.23) (6.24) 6.19 J Y 2Y 6.22 V 0 0 6.22 6.19 (1) (2) V 1 V 2 V 3 6.20 6.23 V 0 0 (1) V 1, V 2, V 3 (2) J 1, J 2 Y 6.21 6.24 a b V a V b ω ( 0, ) (C 1 + C 2)/LC 1C 2 (1)

6.3 c 2009 131 6.23 6.20 6.24 6.21 (2) V a V b (3) L 0 6.22 6.25 ω 6.25 6.22 (1) (2) V a V b (3) V b /V a = 1/ 2 6.23 6.26 a b c d V a V b V c V d J 1 3.0 A J 2 2.0 A R 1 2.0 Ω, R 2 3.0 Ω, R 3 4.0 Ω, R 4 6.0 Ω, R 5 6.0 Ω

132 c 2009 6 6.26 6.23 (1) b c d V a = 0 (2) V a 6.24 Y J 1 J 2 6.27 a d V a V d V a = 0 6.27 6.24 (1) (2) V b V d 6.25 6.28 a b c V a V b V c (1) (2) V a V b V c

6.4 c 2009 133 6.28 6.25 6.4 6.4 6.29 ω( 1/ 3LC) 6.29 6.4 (1) (2) a b c d Z (3) I 1 I 2 6.4

134 c 2009 6 (1) ( E 1 = jωl + 1 ) I 1 + jωli 2 (6.25) jωc ( E 2 = jωl + 1 ) I 2 + jωli 1 (6.26) j2ωc (2) [ E1 E 2 ] = [ jωl + 1 jωc jωl jωl jωl + 1 j2ωc ] [ ] I1 I 2 (6.27) Z = [ jωl + 1 ] jωc jωl jωl jωl + 1 j2ωc (6.28) (3) [ I1 ] = I 2 = [ jωl + 1 jωc jωl jωl jωl + 1 1 3ω 2 LC 1 ] 1 [ ] E1 E j2ωc 2 [ ( jωc 2ω 2 LC 1 ) j2ω 3 LC 2 j2ω 3 LC 2 j2ωc ( ω 2 LC 1 ) ] [ ] E1 E 2 (6.29) I 1 = jωc {( 2ω 2 LC 1 ) } E 1 2ω 2 LCE 2 3ω 2 LC 1 I 2 = j2ωc {( ω 2 LC 1 ) } E 2 ω 2 LCE 1 3ω 2 CL 1 (6.30) (6.31) 6.26 6.30 J 1, J 2 Y 1, Y 2, Y 3 (1) V 0 = 0 (2) a b c d (3) V 1, V 2 6.27 6.31 (1) (2) I 3 a b c d

6.5 c 2009 135 6.30 6.26 6.31 6.27 6.5 6.5 6.32 6.32 6.5 (1)

136 c 2009 6 (2) I 1, I 2, I 3 (3) (4) V a V b, V c, V d 6.5 (1) I 1 (2) I 2, I 3 I 1 = J (6.32) 0 = Z 2 I 1 + (Z 1 + Z 2 + Z 3 ) I 2 + Z 3 I 3 (6.33) E = Z 4 I 1 + Z 3 I 2 + (Z 3 + Z 4 ) I 3 (6.34) Z 2 J = (Z 1 + Z 2 + Z 3 ) I 2 + Z 3 I 3 (6.35) E Z 4 J = Z 3 I 2 + (Z 3 + Z 4 ) I 3 (6.36) I 1 = J (6.37) I 2 = Z 3E + (Z 2 Z 3 + Z 3 Z 4 + Z 4 Z 2 ) J (Z 1 + Z 2 ) (Z 3 + Z 4 ) + Z 3 Z 4 (6.38) I 3 = (Z 1 + Z 2 + Z 3 ) E {Z 2 Z 3 + Z 4 (Z 1 + Z 2 + Z 3 )} J (Z 1 + Z 2 ) (Z 3 + Z 4 ) + Z 3 Z 4 (6.39) (3) a d J = 1 Z 1 (V b V a ) + 1 Z 2 (V b V c ) (6.40) 0 = 1 Z 2 (V c V b ) + 1 Z 3 (V c V a ) + 1 Z 4 (V c V d ) (6.41) V d = E + V a (6.42) (4) V a = 0 V d = E + V a = E ( 1 J = + 1 ) V b 1 V c (6.43) Z 1 Z 2 Z 2 E = 1 ( 1 V c + + 1 + 1 ) V c (6.44) Z 4 Z 2 Z 2 Z 3 Z 4

6.5 c 2009 137 V b = Z 1Z 3 E Z 1 (Z 2 Z 3 + Z 3 Z 4 + Z 4 Z 2 ) J (Z 1 + Z 2 ) (Z 3 + Z 4 ) + Z 3 Z 4 (6.45) V c = Z 3 (Z 1 + Z 2 ) E Z 1 Z 3 Z 4 J (Z 1 + Z 2 ) (Z 3 + Z 4 ) + Z 3 Z 4 (6.46) V d = E (6.47) 6.28 6.33 J = βi J Z (= E/I) 6.33 6.28 6.29 6.34 I 1, I 2, I 3 Z 1, Z 2, Z 3, Z 4, Z 5 E J 6.34 6.29 6.30 6.35 a b c d V a V b V c V d ω

138 c 2009 6 6.35 6.30 (1) a b V c = E 1, V d = E 2 (2) V a V b (3) a b V ab V ab 6.31 6.36 E 1, E 3 Z 1, Z 2, Z 3 6.36 6.31 (1) I 1, I 3 (2) V 1 V 0 = 0

c 2009 139 7 7.1 7.1 7.1 ω 7.1 7.1 (1) V V (2) lim V ω 0 (3) lim V ω (4) V = E ω 0 2 (5) ω = ω 0 V E 7.1 (1) V = R R + 1 E = jωcr 1 + jωcr E (7.1) jωc

140 c 2009 7 V = ωcr E (7.2) 1 + (ωcr) 2 (2) ω 0 1 + (ωcr) 2 1 (3) ω 1 + (ωcr) 2 (ωcr) 2 = ωcr lim V = lim ωcr E = 0 (7.3) ω 0 ω 0 (4) ωcr lim V = lim E = E (7.4) ω ω ωcr V = E 2 (7.5) (5) (7.1) ω 0 CR = 1 7.1 V = ω 0 CR 1 + (ω0 CR) = 1 (7.6) 2 2 2(ω 0 CR) 2 = 1 + (ω 0 CR) 2 (7.7) ω 0 CR = 1 (7.8) ω 0 = 1 CR V E π 4 (7.9) j 1 + j E = 1 + j 2 E = 1 exp(j π 2 4 ) E (7.10) 7.2 Z a, Z b, Z c, Z d ω ω 0 ω 7.2 RL kr (k > 1) 7.3 RC π 6 R 7.4 7.3 ω

7.1 c 2009 141 7.2 7.1 7.3 7.4 (1) A B Z (2) lim ω Z = R 1 + R 2 7.5 7.4 A B Z K R, L, C K 7.4 7.5 7.6 7.5 ω (1) lim ω 0 V o V i (2) lim Vo ω V i

142 c 2009 7 7.5 7.6 7.7 7.6 a b V ab 7.6 7.7 7.8 7.7 A B (1) V 1 V 2 V1 V 2 V 1 (2) lim ω 0 (3) lim ω V 2 V 1 V 2 7.7 7.8 7.2 7.8 V i V o V i V o k ω

7.1 c 2009 143 V i V o 7.8 7.2 7.2 C 1 R 1 C 2 R 2 R 2 1 R 1 j ωc 1 R 1 R 1 + 1 = (7.11) 1 + j ωc 1 R 1 j ωc 1 1 R 2 j ωc 2 R 2 R 2 + 1 = (7.12) 1 + j ωc 2 R 2 j ωc 2 V o 1 + j ωc = 2 R 2 R 2 (1 + j ωc 1 R 1 ) = V i R 1 R 2 R + 1 (1 + j ωc 2 R 2 ) + R 2 (1 + j ωc 1 R 1 ) 1 + j ωc 1 R 1 1 + j ωc 2 R 2 R 2 + j ωc 1 C 2 R 2 = (7.13) R 1 + R 2 + j ω (C 1 + C 2 ) R 1 R 2 (7.13) ω R 2 R 1 + R 2 = jc 1 R 2 R 2 j (C 1 + C 2 ) R 1 R 2 = C 1 C 1 + C 2 (7.14) C 1 R 1 = C 2 R 2 (7.15) (7.13) (7.15) V o R 2 = (7.16) V i R 1 + R 2

144 c 2009 7 7.9 7.9 7.9 7.9 (1) E a b V ab V ab E (2) V ab E ω (3) (2) ω 0 E V ab (4) (2) ω E V ab (5) (2) E V ab π/2 7.10 7.10 V 7.10 7.10 (1) V 1 (2) V 1 (3) V 2 (4) V 2 (5) V 1 2 + V 2 2 ω

7.2 c 2009 145 7.11 7.11 E 7.11 7.11 (1) V C 2 + V L 2 ω (2) (1) P 7.12 7.12 E ω I L 2 + I C 2 ω 7.12 7.12 7.2 7.3 V = 1.5 V V 0 = 0.30 V V 7.3 V 0

146 c 2009 7 20 log V = 20 log 1.5 V 0.30 V = 20 log 5.0 = 13.9 db 14 db (7.17) V 0 7.13 I = 3.2 ma I 0 = 1.0 A I I 0 7.14 3.5 db 7.15 1.0 W [dbm] 7.16 18.45 dbm 7.4 7.13 V 0 V A(ω) Θ(ω) 7.13 7.4 7.4 V R = V 0 R + jωl (7.18) A(ω) = V = V V 0 = R R + jωl = R (7.19) R2 + (ωl) 2 V 0 Θ(ω) = arg V V 0 = arg V arg V 0 = tan 1 0 R tan 1 ωl R = tan 1 ωl R (7.20)

7.3 c 2009 147 7.17 7.14 V/V 0 A(ω) Θ(ω) 7.14 7.17 7.3 7.5 7.15 R = 1.0 Ω, L = 5.0 mh, C = 2.0 µf ω 0 f 0 Q 7.15 7.5 7.5 ω 0 ω 0 = 1 1 = = 1.0 10 4 rad/s = 10 krad/s (7.21) LC 5.0 mh 2.0 µf f 0 Q f 0 = ω 0 2π = 1.0 104 rad/s = 1./5 6 /9 10 3 Hz = 1.6 10 3 Hz = 1.6 khz (7.22) 2π Q = ω 0L R = 1 ω 0 CR = 1 L = 50 (7.23) R C

148 c 2009 7 7.18 7.16 (a) 7.16 (b) f 0 Q 7.16(a) R 1 5.0 Ω C 1 0.25 µf L 1 10 mh 7.16(b) R 2 300 kω C 2 100 pf L 2 10 mh 7.16 7.18 7.19 7.17 R 10 Ω L 5.0 mh E 150 V f 1.0 khz 7.17 7.19 (1) C I C (2) (1) I max 7.20 100 V R = 50 Ω L C 7.18 (a) I 1 2.0 A 7.18 (b) I 2

7.3 c 2009 149 7.18 7.20 7.21 7.19 C 40 pf 800 pf C 1.0 MHz 3.0 MHz C 0 L L C0 C 7.19 7.21 7.22 7.20 ω 0 C0 L0 C1 7.20 7.22 (1) C 0 L 0 Y 0 (2) Z (3) Z = 0 ω 0 (4) Z = ω

150 c 2009 7 (5) ω 0 ω (6) ω 0 Z 0 (7) ω Z (8) Z ω 7.6 7.21 ω 7.21 7.6 (1) Z (2) Z 0 ω 1 (3) ω = ω 1 Z 1 (4) CR Q C Q C = ωcr ω = ω 0 = 1 LC Q C Q 0 ω 1 ω 0 Q 0 (5) R ω 1 ω 0 7.6 (1) Z = j ωl + = R 1 j ωc R + 1 j ωc R 1 + (ωcr) 2 + j ω = j ωl + R R (1 j ωcr) = j ωl + 1 + j ωcr 1 + (ωcr) 2 [ ] CR 2 L 1 + (ωcr) 2 (7.24)

7.3 c 2009 151 (2) (3) (4) CR 2 L 1 + (ω 1 CR) 2 = 0 (7.25) L + ω 2 1 LC 2 R 2 = CR 2 (7.26) ω 2 1 = CR2 L LC 2 R 2 = 1 [ LC 1 L ] CR 2 (7.27) [ 1 ω 1 = LC 1 L ] CR 2 (7.28) R Z 1 = 1 + (ω 1 CR) 2 = R 1 + 1 [ 1 L ] = LC CR 2 C 2 R 2 LCR = LC + (C 2 R 2 LC) = L CR R 1 + 1 LC (C2 R 2 LC) (7.29) C Q 0 = ω 0 CR = R L (7.30) ω 1 = 1 LC [ 1 L ] CR 2 = 1 1 L LC CR 2 = ω 0 1 1 2 (7.31) Q 0 (5) lim Q 0 = (7.32) R lim ω 1 = lim ω 0 R R 1 1 Q 0 2 = ω 0 (7.33) R LC 7.23 7.22 (1) Y

152 c 2009 7 7.22 7.23 (2) B 0 ω 0 (3) Y 0 (4) I 0 7.24 7.23 ω 7.23 7.24 (1) Y (2) Y 0 ω 1 (3) ω = ω 1 Y 1 (4) LR Q L Q L = ωl/r ω = ω 0 = 1/ LC Q L Q 0 ω 1 ω 0 Q 0 (5) R 0 ω 1 ω 0 7.25 7.24 ω 0 Z 0 CR 2 L 7.26 7.25 R 1 200 Ω R 2 100 Ω C 1 2.0 µf C 2 0.10 F (1) C 1 L 500 rad/s L

7.3 c 2009 153 7.24 7.25 7.25 7.26 (2) (1) 500 rad/s V 20 A I V (3) (1) (2) A

154 c 2009 8 8.1 8.1 8.1 I 8.1 8.1 8.1 8.1 8.2 (a) 8.2 (b) 8.2 I, I I E 2E = = 3R 2 + R 5R I R 3R = J 11R 4 + R 3R + R = J 5 I = I + I = 2E 5R + J 5 (8.1) (8.2) (8.3)

8.1 c 2009 155 8.2 8.0 8.1 8.3 I 1 I 2 I 3 8.3 8.1 8.2 8.4 I 8.3 8.5 (1) 8.5 (2) (1) A B V AB (3) 8.5 (4) (3) A B V AB (5) 8.5 A B V AB

156 c 2009 8 8.4 8.2 8.5 8.3 8.4 8.6 a V a 8.6 8.4 8.5 8.7 V 8.7 8.5

8.2 c 2009 157 8.6 8.8 V 8.8 8.6 8.7 8.9 A B V 0 8.9 8.7 8.2 8.2 8.10 J 3.0 A R 1 2.0 Ω R 2 3.0 Ω B (1) E 0 (2) R 0 (3) J 0 (4) G 0

158 c 2009 8 8.10 8.2 8.2 (1) E 0 = R 1 J = 2.0 Ω 3.0 A = 6.0 V (8.4) (2) R 0 = R 1 + R 2 = 2.0 Ω + 3.0 Ω = 5.0 Ω (8.5) (3) (4) J 0 = J R 1 2.0 Ω = 3.0 A = 1.2 A (8.6) R 1 + R 2 2.0 Ω + 3.0 Ω G 0 = 1 = 1 = 0.20 S (8.7) R 1 + R 2 5.0 Ω 8.8 8.11 E 0 Z 0 J 0 Y 0 B 8.11 8.8

8.2 c 2009 159 8.9 8.12 E 0 Z 0 B 8.12 8.9 8.10 8.13 I 8.13 8.10 8.11 8.14 8.14 8.11 (1) A B E 0 Z 0 B

160 c 2009 8 (2) A B A B 8.12 8.15 8.15 8.12 (1) 8.15 (a) E 0 Z 0 (2) 8.15 (b) E 0 Z 0 8.13 8.16 E 0 Z 0 8.16 8.13 8.14 8.17 R 1 = 4.0 Ω, R 2 = 1.0 Ω, J = 1.0 A, E = 6.0 V (1) 8.17 R 0 (2) 8.17 E 0 8.15 8.18 R 1 2.0 Ω R 2 4.0 Ω, J 9.0 A E 12.0 V (1) A B R 0

8.2 c 2009 161 8.17 8.14 8.18 8.15 (2) A B E 0 B (3) A B J 0 A B 8.16 8.19 8.19 8.16 (1) R 1 I 1 (2) R 1 R 1 + R R 1 I 1 (3) R 1 R 1 + R A I (4) (2) R 4 (5) R R 1 I R, I 1, R 1, R 2, R 3

162 c 2009 8 8.3 8.3 8.20 ω R L, C L 8.20 8.3 (1) E 0 Z 0 (2) R L R L C L R S, L S, ω 8.3 (1) (2) Z E 0 = jωl se R s + jωl s (8.8) Z 0 = jωl sr s R s + jωl s (8.9) Z = R L + 1 jωc L (8.10)

8.3 c 2009 163 Z 0 = Z R L jωl s R s = R L 1 R s + jωl s jωc (8.11) (ωl s ) 2 2 R s + jωl s R s 1 R 2 s + (ωl s ) 2 = R L + j (8.12) ωc L R L = (ωl s) 2 R s R s 2 + (ωl s ) 2 (8.13) C L = 1 ω 2 L s + L s R s 2 (8.14) 8.17 E 0 R 0 R 8.21 8.21 8.17 (1) R P max (2) R P P max R R 0 8.18 8.22 8.22 8.18

164 c 2009 8 (1) E 0 R 0 (2) r 8.19 R 1, R 2 L R 3 C 8.23 E ω 8.23 8.19 (1) E 0 Z 0 (2) R 3 C 8.20 8.24 R C R ω 8.24 8.20 8.21 8.25 E 0 Z 0 Z Z 100%

8.4 c 2009 165 8.25 8.21 8.4 8.4 8.26 8.26 8.4 (1) I 2 (2) I 1 (3) 8.4 (1) (2) I 2 = E 1 R 1 + R 2R 3 R 2 + R 3 R 3 R 2 + R 3 = R 3 E 1 R 1 R 2 + R 2 R 3 + R 3 R 1 (8.15) I 1 = E 2 R 2 + R 1R 3 R 1 + R 3 R 3 R 1 + R 3 = R 3 E 2 R 1 R 2 + R 2 R 3 + R 3 R 1 (8.16)

166 c 2009 8 (3) E 1 = E ( 2 = R 1 + R 2 + R ) 1R 2 I 2 I 1 R 3 (8.17) 8.22 8.27 2 Z a (2.0 + j1.0) V E 1 Z b (1.0 j3.0) A I b1 Z b E 2 Z a (1.0 + j2.0) A I a2 E 2 8.27 8.22

c 2009 167 9 9.1 9.1 9.1 I1 M I2 M I1 M I2 V1 L1 L2 V2 V1 L1 L2 V2 L1 L2 (a) (b) (c) 9.1 9.1 (1) 9.1 (a) V 1, V 2, I 1, I 2 (2) 9.1 (b) V 1 V 2 (3) 9.1 (c) I 1 I 2 9.1 (1) V 1 = jωl 1 I 1 + jωmi 2 (9.1) V 2 = jωmi 1 + jωl 2 I 2 (9.2)

168 c 2009 9 (2) I 2 = 0 (9.1) (9.2) V 1 = jωl 1 I 1 (9.3) V 2 = jωmi 1 (9.4) (9.4) (9.3) V 1 : V 2 = jωl 1 I 1 : jωmi 1 = L 1 : M (9.5) (3) V 2 = 0 (9.2) 0 = jωmi 1 + jωl 2 I 2 (9.6) MI 1 = L 2 I 2 (9.7) I 1 : I 2 = L 2 : M (9.8) 9.1 9.2 M = M I1 M I2 I1 M' I2 V1 V2 V1 V2 9.2 9.1 9.2 9.3 (1) (a) (2) (b) (3) (a) (b) (c) (1) (2) I 1, I 2, I 4 (4) (c) (d) L 1, L 4, M L 1 L 4 M m 9.3 9.4 Z (= V/I) ω

9.1 c 2009 169 I1 M I2 I3 m I4 V1 L1 L2 V2 V3 L3 L4 V4 (a) (b) I1 M I2 m I4 I1 M' I4 V1 L1 L2 L3 L4 V4 V2 V1 L1' L4' V4 (c) (d) 9.3 9.2 I2 M L2 I I1 L1 V 9.4 9.3 (1) I, I 1, I 2 (2) V, I 1, I 2 (3) (2) I 1 : I 2 (4) (1) (3) I 1, I 2 I, L 1, L 2, M (5) (2) (4) Z 9.4 9.5 (a) (a) (b) (c) L 3 L 4 L 5 L L 1 L 2 M 9.5 9.6 (1) L 3, L 4, L 5 L 1, L 2, M (2) 9.6 9.7 ω (1) V 1, V 2, I 1, I 2

170 c 2009 9 M L3 L4 L1 L2 L5 L' (a) (b) (c) 9.5 9.4 9.6 9.5 9.7 9.6 (2) I, I 1, I 2 (3) V R I (4) V, V 1, V 2, V R (5) Z 9.7 9.8 (a) 1 V 1, V 2 I 1, I 2 9.8 (b) A B L 1 A A L 2 L 1 L 2

9.2 c 2009 171 M I2 A' I2 A' I2 ' A' A I1 V2 A I1 L2 M V2 A V2 ' L2 M V1 V1 L1 V1 ' I1' L1 B (a) B' B (b) B' B (c) B' 9.8 9.7 (1) 9.8 (c) V 1, V 2, I 1, I 2 (2) 9.8 (b) (c) I 1, I 2 I 1, I 2 (3) 9.8 (b) (c) V 1, V 2 V 1, V 2 (4) 9.8 (b) V 1, V 2, I 1, I 2 9.2 9.2 9.9 9.9 9.2 (1) (2) I 1 I 2 (3) Z 9.2

172 c 2009 9 (1) (2) V 2 = RI 2 (9.10) V 1 = jωl 1 I 1 + jωmi 2 (9.9) V 2 = jωmi 1 + jωl 2 I 2 (9.10) I 2 = jωm I 1 (9.11) R + jωl 2 (3) (9.9) (9.11) ( ) jωm V 1 = jωl 1 I 1 + jωmi 2 = jωl 1 I 1 + jωm I 1 R + jωl 2 = ω2 ( M 2 L 1 L 2 ) + jωl1 R R + jωl 2 I 1 (9.12) Z = V ( ) 1 = ω2 M 2 L 1 L 2 + jωl1 R (9.13) I 1 R + jωl 2 9.8 9.10 M E I1 I2 L1 L2 9.10 9.8 (1) I 1, I 2 (2) I 1, I 2 9.9 9.11 I 1, I 2, I 3 jω s s (1) (2)

9.2 c 2009 173 9.11 9.9 (3) E 2, E 3 (4) (1) (2) (3) I 1, I 2, I 3 9.10 9.12 Z ω 0 M L2 L1 C 9.12 9.10 9.11 9.13 L 1 L 2 M 2 I1 M I2 V1 C1 L1 L2 V2 9.13 9.11 (1) V 1 V 2 I 1 I 2 (2) V 1 /I 1 (3) V 1 /I 1 = ω

174 c 2009 9 9.12 9.14 9.14 9.12 9.13 9.15 Campbell M I1 L1 L2 I2 E A C 9.15 9.13 (1) I 1 I 2 (2) 9.14 9.16 ω ( 0) (1) (2) Z (= E/I 1 ) (3) Z = ω (4) Z = 0 ω 0 (5) ω 0 ω k

9.2 c 2009 175 M E I1 L1 L2 I2 C 9.16 9.14 9.15 9.17 L 1L 2 M 2 I1 M I2 V1 L1 L2 V2 C2 9.17 9.15 (1) V 1 V 2 I 1 I 2 (2) V 2 V 1 1 (3) ω 1 = V 2 L2 C 2 V 1 (4) V 2 V 1 = ω 0 ω 1 k 9.16 9.18 ω ( 0) 9.18 9.16 (1) (2) I 1 I 2

176 c 2009 9 (3) E I 1 E I E = ai (a ) 9.17 9.19 V 0 E ω 0 9.19 9.17 9.18 9.20 9.20 9.18 (1) V I (2) Z (3) V I ω 0 9.19 9.21 (1) Z (2) ω 0 (3) Q

9.3 c 2009 177 9.21 9.19 9.20 9.22 jω = s 9.22 9.20 9.3 9.3 9.23 9.23 9.3

178 c 2009 9 (1) M L 1 = n L 2 = n 2 L 1 (2) V 2 V 1 = n (3) 9.23 (b) Z 2 L 1 Z 2 n 2 (4) 9.23 (b) Z 2 Z 2 n 2 (5) 9.23 (b) Z 2 I 2 = 1 n I 1 9.3 (1) k ±1 k 2 = M 2 L 1 L 2 = 1 (9.14) L 2 M = M L 1 = n (9.15) L 2 = nm = n(nl 1 ) = n 2 L 1 (9.16) (2) (9.15) (3) V 2 V 1 = jωmi 1 + jωl 2 I 2 jωl 1 I 1 + jωmi 2 = jωnl 1I 1 + jωnmi 2 jωl 1 I 1 + jωmi 2 = n (9.17) V 2 = Z 2 I 2 (9.18) (9.20) V 2 = jωmi 1 + jωl 2 I 2 = Z 2 I 2 (9.19) I 2 = jωm jωl 2 + Z 2 I 1 (9.20) V 1 = jωl 1 I 1 + jωmi 2 (9.21)

9.4 c 2009 179 L 1 L 2 = M 2 (1) L 2 = n 2 L 1 V 1 = jωl 1Z 2 jωl 2 + Z 2 I 1 (9.22) V 1 I 1 = jωl 1Z 2 jωn 2 L 1 + Z 2 = jωl 1 Z 2 n 2 jωl 1 + Z 2 n 2 (9.23) L 1 Z 2 n 2 (4) Z 2 (5) (9.20) jωl 1 + Z 2 n 2 jωl 1 (9.24) Z 2 V jωl 1 1 n 2 = Z 2 I 1 jωl 1 n 2 (9.25) jωl 2 + Z 2 jωl 2 (9.26) I 2 = jωm jωm I 1 jωl 2 + Z 2 jωl 2 = M L 2 = 1 n (9.27) 9.4 9.4 9.24 (1) n 1 : n 2 V 1, V 2, I 1, I 2 (2) Z 2, I 2, V 2 (3) E 1, Z 1, I 1, V 1

180 c 2009 9 9.24 9.4 (4) V 1, V 2 I 1, I 2 9.4 (1) V 1 : V 2 = n 1 : n 2 (9.28) n 1 I 1 + n 2 I 2 = 0 (9.29) (2) V 2 = Z 2 I 2 (9.30) (3) E 1 = Z 1 I 1 + V 1 (9.31) (4) (9.28) (9.30) (9.29) (9.32) (9.33) V 1 = n 1 n 2 V 2 = n 1 n 2 Z 2 I 2 (9.32) I 2 = n 1 n 2 I 1 (9.33) V 1 = (9.31) ( n1 n 2 ) 2 Z 2 I 1 (9.34) E 1 = Z 1 I 1 + ( n1 n 2 ) 2 Z 2 I 1 (9.35)

9.4 c 2009 181 (9.33) I 1 = Z 1 + E 1 ( n1 n 2 ) 2 Z 2 = n 2 2 E 1 n 22 Z 1 + n 12 Z 2 (9.36) I 2 = n 1 n 1 n 2 E 1 I 1 = (9.37) n 2 n 22 Z 1 + n 12 Z 2 9.21 9.25 Z = E/I 1 n 1 : n 2 : n 3 n 2 n 3 9.25 9.21 (1) V 1, V 2, V 3 (2) I 1, I 2, I 3 (3) I 2 I 3 (2) I 3 (4) (5) (4) (1) (3) I 2, V 2, V 3 Z 9.22 9.26 L 1, L 2, M ω (1) V 1 V 2 I 2 I 3 (2) I 1, I 3, I 4 (3) V 1 I 4 L (4) (1) (3) I 1, I 2, V 1 (5) (1) (3) I 1, I 2, V 2 (6) I 1, I 2, V 1, V 2 (7) L 1, L 2, M (8) k