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1214 ⏐⏐⏐ APPENDIXES
(b) 50(1 � e �t/(10�10�3 ) )
(c) 10 � 10 �3 e �t/(10�10�3 )
(d) v C � 50 V, i C � 0 A
(e) v C � 50e �t/(4�10�3 )
i C ��25 � 10 �3 e �t/(4�10�3 )
23. (a) 80(1 � e �t/(1�10�6 ) )
(b) 0.8 � 10 �3 e �t/(1�10�6 )
(c) v C � 80e �t/(4.9�10�6 )
i C � 0.163 � 10 �3 e �t/(4.9�10�6 )
25. (a) 10 ms (b) 3kA (c) yes
27. (a) v C � 52 V � 40 V e �t/123.8ms
i C � 2.198 mA e �t/123.8ms
29. 1.386 ms
31. R � 54.567 k�
33. (a) v C � 60(1 � e �t/0.2s ),
0.5 s: 55.07 V, 1 s: 59.596 V
i C � 60 � 10 �3 e �t/0.2s
0.5 s: 4.93 mA,
1 s: 0.404 mA
v R1 � 60 e �t/0.2s
0.5 s: 4.93 V, 1 s: 0.404 V
(b) t � 0.405 s, 1.387 s longer
35. (a) 19.634 V
(b) 2.31 s
(c) 1.155 s
37. (a) v C � 3.275(1 � e �t/52.68ms )
i C � 1.216 � 10 �3 e �t/52.68ms
39. (a) v C � 27.2 � 25.2 e �t/18.26ms
i C � 3.04 mA e �t/18.26ms
41. 0–4 ms: 0.3 mA,
4–6 ms: 0.9 mA,
6–7 ms: 3 mA,
7–10 ms: 0 mA,
10–13 ms: �3.2 mA,
13–15 ms: 1.8 mA
43. 0–4 ms: 0 V,
4–6 ms: �8 V,
6–16 ms: 20 V,
16–18 ms: 0 V,
18–20 ms: �12 V,
20–25 ms: 0 V
45. V 1 � 10 V, Q 1 � 60 mC,
V 2 � 6.67 V, Q 2 � 40 mC,
V 3 � 3.33 V, Q 3 � 40 mC
47. (a) 56.54 V
(b) 42.405 V
(c) 14.135 V
(d) 43.46 V
(e) 433.44 ms
49. 8640 pJ
51. (a) 5 J
(b) 0.1 C
(c) 200 A
(d) 10 kW
(e) 10 s
Chapter 11
1. �: 5 � 10 4 maxwells,
5 � 10 4 lines. B: 8 gauss,
51.616 lines
3. (a) 0.04 T
5. 952.4 � 10 3 At/Wb
7. 2624.67 At/m
9. 2.133 A
11. (a) N 1 � 60 t
(b) 13.34 � 10 �4 Wb/Am
13. 2.687 A
15. 1.35 N
17. (a) 2.028 A (b) �2 N
19. 6.1 � 10 �3 Wb
21. (a) B � 1.5(1 � e �H/700At/m )
(c) H ��700 log e(1 � B/1.5 T)
(e) Eq: 40.1 mA
Chapter 12
1. 4.25 V
3. 14 turns
5. 15.65 mH
7. (a) 2.5 V (b) 0.3 V
(c) 200 V
9. 0�3 ms: 0 V. 3�8 ms: 1.6 V.
8�13 ms: �1.6 V.
13�14 ms: 0 V.
14�15 ms: 8 V.
15�16 ms: –8 V.
16�17 ms: 0 V.
11. 0�5 ms: 4 mA. 10 ms: �8 mA.
12 ms: 4 mA. 12�16 ms: 4 mA.
24 ms: 0 mA.
13. (a) 2.27 ms
(b) 5.45 � 10 �3 (1 � e �t/2.27ms )
(c) v L � 12e �t/2.27ms
v R � 12(1 � e �t/2.27ms )
(d) i L: 1t � 3.45 mA,
3t � 5.179 mA,
5t � 5.413 mA.
v L: 1t � 4.415 V,
3t � 0.598 V,
5t � 0.081 V.
15. (a) i L � 4.186 mA �
3.814 mA e �t/13.95ms )
v L ��32.8 V e �t/13.95ms
17. (a) v L � 20 V e �t/1ms
i L � 2 mA(1 � e �t/1ms )
(b) i L � 2 mA e �t/0.5ms
v L ��40 V e �t/0.5ms
19. (a) i L � 6 mA(1 � e �t/0.5ms )
v L � 12 V e �t/0.5ms
(b) i L � 5.188 mA e �t/83.3ns
v L ��62.256 V e �t/83.3ns
21. 25.68 ms
23. (a) i L � 3.638 �
10 �3 (1 � e �t/6.676ms )
v L � 5.45 e �t/6.676ms
(b) 2.825 mA, 1.2186 V
(c) i L � 2.825 �
10 �3 e �t/2.128ms
v L ��13.27 e �t/2.128ms
25. (a) 0.243 V
(b) 29.47 V
(c) 18.96 V
(d) 2.025 ms
27. (a) 20 V
(b) 12 mA
(c) 5.376 ms
(d) 0.366 V
29. i L ��3.478 mA �
7.432 mA e �t/173.9ms
v L � 51.28 V e �t/173.9ms
31. (a) 8 H
(b) 4 H
33. L: 4 H, 2 H
R: 5.7 k�, 9.1 k�
35. V 1 � 16 V, V 2 � 0 V,
I 1 � 4 mA
37. V 1 � 10 V
I 1 � 2 A
I 2 � 1.33 A
39. W C � 360 mJ
W L � 12 J
Chapter 13
1. (a) 10 ms (b) 2 (c) 100 Hz
(d) amplitude � 5 V,
V p-p � 6.67 V
3. 10 ms, 100 Hz
5. (a) 60 Hz (b) 100 Hz
(c) 29.41 Hz (d) 40 kHz
7. 0.25 s
9. T � 50 ms
11. (a) p/4 (b) p/3 (c) ��p
(d) �� p (e) 0.989p (f) 1.228p
13. (a) 3.14 rad/s
(b) 20.94 � 10 3 rad/s
(c) 1.57 � 10 6 rad/s
(d) 157.1 rad/s
15. (a) 120 Hz, 8.33 ms
(b) 1.34 Hz, 746.27 ms
(c) 954.93 Hz, 1.05 ms
(d) 9.95 � 10 �3 Hz, 100.5 s
17. 104.7 rad/s
23. 0.4755 A
25. 11.537°, 168.463°
29. (a) v leads i by 10°
(b) i leads v by 70°
(c) i leads v by 80°
(d) i leads v by 150°
31. (a) v � 25 sin(qt � 30°)
(b)
i � 3 � 10 �3 sin(6.28 � 10 3 t � 60°)
33. �� ms
35. 0.388 ms
37. (a) 0.4 ms