5 5.1 35

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C: PC H19 A5 3.BUN 19 8 6 5 35 5.1............................ 35 5.2 1...................... 38 5.3 2...................... 39 5.4............................. 41 5.5 Thevenin................. 46 5.6..................... 47 5.6.1 I.................. 47 5.6.2 II................. 50 5.7........... 53 5.8............................. 55 5.8.1........................ 57 5.9.................... 61

5 5.1 35

liner x 1 y 1 x 2 y 2 x 1 + x 2 y 1 + y 2 y 1 y 1 + y 2 10 y = f(x) y 2 y 1 = fx 1 y 2 = fx 2 y 1 + y 2 = fx 1 + x 2 f(x) 10 1 1 2 2 10 10 100 36

37

5.2 1 1 2 0 n I i = 0 (35) i=1 I 1 C I 2 I 3 C 30. + 0 30 C I 1 I 2 + I 3 + I 4 = 0 12. c 1 I 4 R 1 c R 2 d I 1 I 2 E 1 R 3 I 3 E 2 31. I 1 I 2 + I 3 = 0 I 1 + I 2 I 3 = 0 (I 1 I 2 I 3 38

5.3 2 0 n V i = 0 (36) i=1 0 closed loop E 1 c I 1 I 2 R 1 R 2 d R 3 c d 0 I 3 e E 2 e 32. 33. c d e R 1 I 1 + E 1 R 2 I 1 E 2 R 1 I 3 = 0 39

I I 13. R 1 c R 3 d R 2 I 2 I 1 I 3 R 2 I 2 E 1 E 3 I 1 I 2 E 2 I 3 34. c 1 I 1 + I 3 I 2 = 0 c 2 E 1 + R 1 I 1 + R 2 I 1 + I 3 E 2 = 0 dc E 3 + R 3 I 2 + R 2 I 1 + I 3 E 2 = 0 R 1 + R 2 I 1 + R 2 I 3 = E 2 E 1 R 2 I 1 +R 2 + R 3 I 3 = E 2 E 3 I 1 = 1 I 3 = 3 40

1 3 E 2 E 1 R 2 E 2 E 3 R 2 + R 3 R 1 + R 2 E 2 E 1 R 2 E 2 E 3 R 1 + R 2 R 2 R 2 R 2 + R 3 =R 2 + R 3 E 2 E 1 + RE 2 3 E 2 =R 1 + R 2 E 2 E 3 + RE 2 1 E 2 =R 1 + R 2 R 2 + R 3 R 2 2 = R 1 R 2 + R 3 R 2 + R 3 R 1 R 2 I 2 = I 1 + I 3 = 1 + 3 I 2 = 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 (37) 5.4 I i I i I = n I i i=1 (38) 41

14. I R I E 1 E 2 E 1 () 35 () E 2 I 1 I 1 = E 1 R R R E 1 E 2 (c) E 1 () (c) I 2 I 2 = E 2 R I = I 1 + I 2 = E 1 R E 2 R = E 1 E 2 R I 2 I 1 I 2 35. I I 2 R R E 1 E 2 E 2 42

I = E 1 E 2 R 15. R 1 R 3 R 2 I 2 I 1 I 3 E 1 E 3 E 2 R 2 I 2 36. 36 I 2 3 E 1 E 2 E 3 1 ()()(c) i 2 + i 2 + i 3 R 1 R 3 R 1 R 3 i 1 i 3 i 1 i R 2 i 2 R i 3 i 1 i 2 R 2 i 3 2 2 E 1 E 2 R 2 R 1 R 3 E 3 E 1 i 2 E 2 i 2 E 3 i 2 c i 2 i 2 i 2 37. i 1 R 1 R 2 R 3 i 1 = E 1 R 1 + R 2 //R 3 = E 1 R 1 + R 2R 3 R 2 + R 3 = R 2 + R 3 E 1 R 1 R 2 + R 2 R 3 + R 3 R 1 43

i 2 i 1 i 2 i 3 i 2 = = R 3 R 2 + R 3 i 1 R 3 E 1 R 1 R 2 + R 2 R 3 + R 3 R 1 R 1 R 3 R 2 i 1 E 2 i 2 = R 2 + R 1 //R 3 = c E 2 R 2 + R 1R 3 R 1 + R 3 R 1 + R 3 E 2 = R 1 R 2 + R 2 R 3 + R 3 R 1 E 1 E 3 R 1 R 3 i 2 = R 1 E 3 R 1 R 2 + R 2 R 3 + R 3 R 1 I 2 = i 2 + i 2 + i 2 = 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 16. 20 6 20 I 3 6V 40 4V 38. 4V 39 20 44

i 1 6V 40 20 i 2 I i 1 i 2 6 6V 40 20 i 1 6 40 20 39. 40. i 2 4V i 1 = 6 6 + 40//20 40 60 = 6 6 + 4020 40 + 20 2 3 = 360 360 + 800 = 36 116 2 3 = 6 29 i 2 = 4 20 + 40//6 = 4 20 + 406 40 + 6 = 446 2046 + 240 I = i 1 i 2 = 45

5.5 Thevenin 11 III 2 I 2 1 1 R s E I 41. 1 1 E R s 11 Blck ox 46

II 2 1 1 I R p II 42. 1 1 I 2 R p 5.6 5.6.1 I I R s E V A I 47

I E R s I E E 12 R s R s 0 Ω 13 14 E 0 I R s = E I (39) z R s = E I ( z I = ) E R s + z (40) 12 1000 G = 10 12 14 0 Ω 0 Ω 14 48

17. 43() () E R s 200 c 300 R s 6V 200 E d () () 43. E () V V 6V 200 200 cd 3V c 300 c V () E E = 3V 43() 44 R s 2 200 300 R s = 200//200 + 300 = 400 45 200 c 300 R s =400 200 E =3V 44. 45. 49

5.6.2 II II V A I R p II II I R p II I 0 I II R p 0 R p R p R p 0 Ω 15 16 I E R p 15 0 Ω 0 Ω 16 50

R p = E I (41) z R p = E I ( z I = R p R p + z 18. c V I 1 R 1 R 2 I 2 R V I E R s ) R I 0 (42) R p R 46. c R 1 +R 2 //R I 1 I 1 = I 1 V R 1 + R 2 //R I 2 R I I = = R 2 R 2 + R I 1 R 2 R 2 + R V R 1 + R 2 //R = R 2 R 2 + R R 2 V = R 2 + RR 1 + R 2 R = V R 1 + R 2R R 2 + R R 2 V R 1 R 2 +R 1 + R 2 R 51

I = R 2 R 1 + R 2 V R 1 R 2 R 1 + R 2 + R (43) E R 2 V R s R 1R 2 = R 1 //R 2 R 1 + R 2 R 1 + R 2 I = E R s + R R c 43 I = R 2 V R 1 + R 2 = R 1 R 2 + R R 1 + R 2 R 1 R 2 R 1 + R 2 R 1 R 2 R 1 + R 2 V R 1 + R = R 1 //R 2 V R 1 R 1 //R 2 + R I 0 V R p R 1 //R 2 R 1 I = R p R p + R I 0 c R c 52

5.7 19. R 5 I V R 1 R 3 R 5 d I R 2 R 4 c c d R 5 d d V R 1 R 2 c R 5 R 3 d R 4 V R 1 R 2 c V c 47. R 5 I d R 5 c 1 1 e V d R 3 d R 4 53

e E r R 5 I I = E r + R 5 (44) E R 5 d c E = V V d = R 2 R 1 + R 2 V R 4 R 2 R 3 R 1 R 4 V = R 3 + R 4 R 1 + R 2 R 3 + R 4 V r R 5 V d r = R 1 //R 2 + R 3 //R 4 = R 1R 2 R 1 + R 2 + R 3R 4 R 3 + R 4 = R 1R 2 R 3 + R 4 + R 3 R 4 R 1 + R 2 R 1 + R 2 R 3 + R 4 17 R 5 I = E r + R 5 = R 2 R 3 R 1 R 4 R 1 + R 2 R 3 + R 4 V ( ) R1 RR 2 3 + R 4 + R 3 RR 4 1 + R 2 + R 5 ) R 1 + R 2 R 3 + R 4 17 R 5 1 E r R 5 54

I = R 2 R 3 R 1 R 4 V (45) R 1 RR 2 3 + R 4 + R 3 RR 4 1 + R 2 +R 1 + R 2 R 3 + R 4 R 5 R 1 R 3 R s V R 5 d E R 5 R 2 c R 4 d I 45 I = 0 R 2 R 3 R 1 R 4 = 0 (46) R 5 R 1 R 2 R 3 R 4 0 51 R 1 5.8 IV 55

20. R 3 I 3 R 1 c R 2 d I 1 I 2 E 1 R 3 I 3 E 2 i 1 i2 48. 2 1 1. I 1 I 2 I 3 c 1 i I i = 0 I 1 + I 2 I 3 = 0 (47) c dc 2 i V i = 0 V 1 R 1 I 1 R 3 I 3 = 0 V 2 R 2 I 2 R 3 I 3 = 0 3 I 1 I 2 2 I 3 2. i 1 i 2 c dc 2 i V i = 0 V 1 R 1 i 1 R 3 i 1 + i 2 = 0 (48) V 2 R 2 i 2 R 3 i 1 + i 2 = 0 (49) 56

2 i 1 i 2 I 3 = i 1 + i 2 1 5.8.1 1 1 2 1 C + N 2 18 + 2 19 1 0 1 3 4 2 1 2 3 4 18 3 19 C B N N + C B = 2 (50) 57

21. 2 R 5 I 5 V R 1 R 3 R 5 R 2 R 4 c c d R 1 V R 3 I 1 I 2 R 2 R 5 I 3 R 4 d 49. 49,,c,d I 1 I 2 I 3 2 3 3 + c RI 1 2 I 1 + RI 2 3 I 1 + V = 0 d R 3 I 2 + RI 5 3 I 2 + RI 1 1 I 2 = 0 cdc RI 2 1 I 3 + RI 5 2 I 3 R 4 I 3 = 0 58

I 1 I 2 R 1 + R 2 I 1 R 1 I 2 R 2 I 3 = V R 1 I 1 R 1 + R 3 + R 5 I 2 + R 5 I 3 = 0 R 2 I 1 + R 5 I 2 R 2 + R 4 + R 5 I 3 = 0 I 3 I 5 I 5 = I 3 + I 2 R 1 R 4 R 2 R 3 I 5 = R 1 RR 2 3 + R 4 + R 3 RR 4 1 + R 2 + RR 5 1 + R 2 R 3 + R 4 V I = 0 R 1 R 4 R 2 R 3 = 0 R 1 R 4 = R 2 R 3 (51) 49 I 5 = 0 R 5 51 59

I 1 I 2 I 3 R 1 + R 2 R 1 R 2 R 1 R 1 + R 3 + R 5 R 5 R 2 +R 5 R 2 + R 4 + R 5 =R 1 + R 2 R 1 + R 3 + R 5 R 2 + R 4 + R 5 + = R 1 R 2 R 3 + R 4 + R 3 R 4 R 1 + R 2 + R 5 R 1 + R 2 R 3 + R 4 1 V R 1 R 2 0 R 1 + R 3 + R 5 R 5 0 R 5 R 2 + R 4 + R 5 = R 1 + R 3 + R 5 R 2 + R 4 + R 5 V + R5 2 V 2 R 1 + R 2 V R 2 R 1 0 R 5 R 2 0 R 2 + R 4 + R 5 = R 2 R 5 V + R 1 R 2 + R 4 + R 5 V 3 R 1 + R 2 R 1 V R 1 R 1 + R 3 + R 5 0 R 2 R 5 0 = R 1 R 5 V R 2 R 1 + R 3 + R 5 V I 1 = 1 = R 1 + R 3 + R 5 R 2 + R 4 + R 5 + R5 2 R 1 R 2 R 3 + R 4 + R 3 R 4 R 1 + R 2 + R 5 R 1 + R 2 R 3 + R 4 V I 2 = 2 = R 2 R 5 + R 1 R 2 + R 4 + R 5 R 1 R 2 R 3 + R 4 + R 3 R 4 R 1 + R 2 + R 5 R 1 + R 2 R 3 + R 4 V I 3 = 3 = R 1 R 5 R 2 R 1 + R 3 + R 5 R 1 R 2 R 3 + R 4 + R 3 R 4 R 1 + R 2 + R 5 R 1 + R 2 R 3 + R 4 V 60

5.9 x + y + cz = A dx + ey + fz = B gx + hy + iz = C c x d e f y g h i z = A B C c = d e f = ei + fg + cdh di fh ceg g h i x dg ABC x y y z z x = A c B e f C h i y = A c d B f g C i z = A d e B g h C x = Aei + fc + cbh Afh Bi cec y z = Bi + Afg + cdc fc Adi cbg = ec + Bg + Adh Bh dc Aeg x = x y = y z = z 61

c c d e f g h i = e f h i d f g i + c d e g h dg = e f h i d c h i + g c e f 62