89251 26 apph 4/5/07 2:22 pm page 821...

821

Answers to Selected Problems

AppendixHChapter 11.1 110 giga-watt hours

1.3 a) 111.6 seconds

b) 2480 bytes

1.6 0.10 mm

1.9

1.12 a) from A to B

b) from B to A

c) from B to A

d) from A to B

1.17 a)

b)

c)

1.24 a)

b) (delivered)

c)

d) (extracted)

e) , , ,

1.26

Chapter 22.2

2.3 Not valid, due to and current sources inthe rightmost branch

2.6 Not valid, since the voltage drop between the topand bottom nodes is different due to different volt-age sources in the left and right branches

2.8 Not valid, since the voltage drop between the topand bottom nodes is different due to different volt-ages in the left and right branches

2.10 resistor

2.11 resistor4 kÆ

8 kÆ

5 A4 A

1700 W

770 mW

0 mJ4 mJ4 mJ0 mJ

5.196 mW

t = 2.366 s

5.196 mW

t = 0.634 s

21.67 mJ

1.24 mJ

3.1 mW

4800 W

2400 W

2000 W

600 W

6 sin 4000t mC

2.14 a) A current source in parallel with a resistor

b)

2.17 a)

80 W

20 Æ5 A

10

80

40506070

3020

00 75 150 225 300 400 500

iS (mA)

vS (V)

b) A source in series with a resistor

c)

d)

e)

f) A linear model cannot predict non-linearbehavior

2.18 a)

b)

c)

d) , ,

e)

2.19 a) ,

b)

c) Power developed and dissipated is

2.24 a) , , , ,

b)

c) Power developed and dissipated is

2.28 a)

b) Power developed and dissipated is 741 mW

4.5 V

83.33 W

83.33 W

0 W16.67 W11.11 W33.33 W22.22 W

768 W

192 V

1.6 A2.4 A

125 W

20 W80 W25 W

40 V

0.5 A

2 A

500 mA

375 mA

125 mA

200 Æ75 V

89251_26_AppH 4/5/07 2:22 PM Page 821

Electric Circuits, Eighth Edition, by James A. Nilsson and Susan A. Riedel.ISBN-13: 978-0-13-198922-1. © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

2.34 , so a warning sign should be postedand precautions taken

2.35

2.36 a) ; ;

b) ; ;

c) All values are much greater than a few minutes

2.37 a)

b) No, will cause a shock

2.38

Chapter 33.1 a) and , and ; simplified

circuit is

b) and , and ; simplifiedcircuit is

240 �

340 �

480 �

10 V�

�

200 Æ140 Æ300 Æ180 Æ

6 k�10 k� 12 k�

11 k�

2 mA

7 kÆ5 kÆ8 kÆ3 kÆ

3000 V

12 V>800 Æ = 15 mA

40 V

ttrunk = 70,422.54 s

tleg = 7071.13 starm = 1414.23 s

Ptrunk = 7.40 W

Pleg = 29.59 WParm = 59.17 W

RA

RA

RT

RLRL

V�

�

i = 385 mA c) , and , and ; simplifiedcircuit is

3.2 a) and , and ; simplifiedcircuit is

b) and , and ; simplified circuit is

c) and , , and ;simplified circuit is

3.5 a)

b)

c)

3.6 a)

b)

c)

3.13 a)

b) ,

c) ,

3.15 a) ,

b)

3.21 , , , 41.2 kÆ8240 Æ1030 Æ257.5 Æ

1>8 W

15 kÆ60 kÆ

12,408 Æ17,672 Æ

1.32 W1.88 W

66 V

125 kÆ

14 Æ

6 Æ

50 Æ

500 Æ

6 kÆ

25 k�

75 k�

25 k�

0.5 V�

�

150 kÆ50 kÆ75 kÆ300 kÆ100 kÆ

4.2857 �

8 V

20 � 6 �

40 � 4 ��

18 Æ9 Æ5 Æ30 Æ

18 �7.5 �

12 �

200 mA

21 Æ28 Æ20 Æ12 Æ

50 V�

�75 �150 �

30 Æ45 Æ60 Æ50 Æ40 Æ

822 Answers to Selected Problems

89251_26_AppH 4/5/07 2:23 PM Page 822



Answers to Selected Problems 823

3.22 a)

b)

c)

d)

3.23 a)

b)

c)

3.30 a)

b)

c) Yes

3.33 a)

b)

c)

3.48 a)

b)

c) ,

d) ,

3.52 ,

3.53 a) -connected — — become Y-connected— — ; equivalent resistance is

b) Y-connected — — become -connected— — ; equivalent resistance

is

c) Convert the delta connection — — to its equivalent wye. Convert the wye connection

— — to its equivalent delta.

3.54

3.71 , , ,

, , ,

, ,

3.72

3.73 a) , , ,

, , ,

, ,

b) , or ;

, or ;

, or ;

= PdissPdel = 997.5 W

150 W>mib2Rb = 7.5 Wib = 33.75 A

150 W>mi22R2 = 187.5 Wi2 = 16.23 A

150 W>mi12R1 = 187.5 Wi1 = 17.52 A

Rd = 0.0244 ÆRc = 0.0066 ÆRb = 0.0066 Æ

Ra = 0.0244 ÆR5 = 0.6106 ÆR4 = 0.7122 Æ

R3 = 0.768 ÆR2 = 0.7122 ÆR1 = 0.6106 Æ

= PdelPdiss = 624 W

Rd = 0.0259 ÆRc = 0.0068 ÆRb = 0.0068 Æ

Ra = 0.0259 ÆR5 = 1.0372 ÆR4 = 1.1435 Æ

R3 = 1.2 ÆR2 = 1.1435 ÆR1 = 1.0372 Æ

99 Æ

R6R4R3

R6R5R4

50 Æ45 Æ270 Æ90 Æ

¢R5R4R2

50 Æ6 Æ18 Æ3 ÆR4R3R2¢

24 V48 V

90 mW900 Æ

180 mW800 Æ

25 mA

900 Æ

50 Æ

4950 Æ

99,950 Æ

1>2500

im =

(25>12)

50 + (25>12) (imeas) = 1

25 imeas

20 mA

13.33 mA

3.2 V

1.33 V

3.2 V

12 V

1.2 mA Chapter 4

4.1 a) 5

b) 3

c) , ,

d) 2

e) ,

4.2 a) 11

b) 10

c) 11

d) 10

e) 5

f) 5

g) 7

4.3 a) 2

b) 5

c) 7

d) 1, 4, 7

4.4 a) 10

b) 4

c) 4

d) Avoid the three meshes with current sources

4.6

4.9 ,

4.10 a) , , , ,

b)

4.19

4.20 a)

b)

4.21

4.26 ,

4.27

4.31 a)

b)

4.32 a)

b) 1140 W, absorbed

1140 W, developed

-1.72 A, 1.08 A, 2.8 A

9.8 A, -0.2 A, -10 A

26 V

1.2 W200 V

3.2 V

165 W

165 W

375 W

582 W

-1 A3 A2 A2 A4 A

90 V25 V

10 V

R3i3 + R5i5 - R4i4 = 0

R1i1 + R3i3 - R2i2 = 0

i5 - i2 - i3 = 0

- i1 + i4 + i3 = 0- ig + i1 + i2 = 0

89251_26_AppH 4/5/07 2:23 PM Page 823




4.37

4.38

4.41 a)

b)

c) checks

4.42 a)

b)

c)

4.47

4.50 a)

b)

4.54 a) Mesh current method requires fewer equations

b)

c) No—you can solve for the voltage from themesh currents

d)

4.56 a) The constraint equations are easier to formu-late if the node voltage method is used

b)

4.59 a)

b)

4.62 a)

b)

4.63 ,

4.66 (down), 10

4.67 a)

b) %

4.71 , 43.2

4.77 ,

4.79 ,

4.80 a)

b)

4.91 a)

b)

4.92

4.105 ,

4.106 ,

4.107 , v2 = 117.5 Vv1 = 52.083 V

v2 = 105 Vv1 = 37.5 V

v2 = 102.5 Vv1 = 39.583 V

30 V

72.2 W

38 V

48 W

12 Æ

150 Æ16.67 Æ

8 Æ0 V

kÆ-86.40 V

-5.67

45.28 V

kÆ8 mA

16 Æ48 V

1 A

1 A

3 mA

3 mA

180 W

200 mW

4 mW

1319.685 W

5.7 A, 4.6 A, 0.97 A, -1.1 A, 3.63 A

99 W

2.912 mW

200 mW

-5.2 mA

6847.36 W

2643.36 W

2700 W

98 W Chapter 55.1 a)

b) The input resistance;

c) The open-loop voltage gain;

d)

5.2 a)

b) (saturates)

c)

d)

e) (saturates)

f)

5.3

5.8 a) Non-inverting amplifier

b)

5.9 a) Many possible designs; one uses a single input resistor and four series-connected resistors in the feedback path

b)

5.12 a) Inverting summing amplifier

b)

c)

5.13 a)

b)

5.15

20 k�

Vcc

Vo�Vcc

Va

12 k�Vb

15 k�Vc

30 k�

60 k�

Vd �

��

�

8.4 V … vb … 13.2 V

-6 V

-7.5 V … vc … 1.5 V

-6 V

;10 V

10 kÆ

10 kÆ

4.5 V

-3.1 mA

2.8125 V … va … 7.3125 V

18 V

-14 V

10 V

-18 V

-12 V

vo = -4 V

(vp - vn) = 0

in = 0

Positivepower supply

Negativepower supply

Output

Non-invertinginput

Invertinginput �

�

89251_26_AppH 4/5/07 2:24 PM Page 824




5.17 a) Non-inverting amplifier

b)

c)

5.18 a)

b)

c)

5.24

5.25 a)

b)

5.26 a)

b)

c)

5.32 a) 19.975

b)

c) 399.5

5.33

5.42 a)

b)

c)

d) , ,

5.43 a) 30.98

b) ,

c)

d)

e) 31, , ,

5.48 a)

b)

Chapter 66.1 a)

50 ms 6 ti = 0

25 … t … 50 msi = 0.8 - 16t A

0 … t … 25 msi = 16t A

t 6 0i = 0

12 mÆ

2 kÆ

0 A0 V1 V

836.22 pA

367.94 mV

999.87 mV999.5 mV

5000 Æ0 V-20

5003.68 Æ

736.1 mV

-19.9844

32.89 kÆ … Rx … 33.11 kÆ

-0.05

80 kÆ

114.3 kÆ

56.25 mV

-638 mV … vb … 962 mV

-15.95 V

20 kÆ

35 kÆ

-3.97 V … vg … 3.97 V

7.56 V

-2.4 V … vs … 4 V

3.75vs

6.14

t(s)0.5 1 21.5

60

40

20

00

�20

�40

�60

ic(�A)

t(s)

5

4

3

2

1

0.1 0.2 0.30

0 0.4 0.5 10.6 0.7 0.8 0.9

iL(A)

t(s)

30

25

20

15

10

5

0.20

0 0.4 10.6 0.8

vL(mV)

b)

6.3

50 ms 6 tw = 0

25 6 t 6 50 msw = 48t 2

- 4.8t + 0.12 J

0 6 t 6 25 msw = 48t 2 J

t 6 0w = 0

50 ms 6 tp = 0

25 6 t 6 50 msp = 96t - 4.8 W

0 6 t 6 25 msp = 96t W

t 6 0p = 0

50 ms 6 tv = 0

25 6 t 6 50 msv = -6 V

0 6 t 6 25 msv = 6 V

t 6 0v = 0

89251_26_AppH 4/5/07 2:24 PM Page 825




6.15 a)

b)

c)

d)

100 V

4 * 105t - 20 V

-200 * 103t + 40 V 6.43 ,

6.47 a)

b)

c)

d)

6.48 a)

b) No

6.49

6.51 a)

b)

Chapter 77.1 a) 5 A

b) 40 ms

c) A, V,

d)

7.2 a) 0.2 mA, 0.2 mA

b) 0.2 mA,

c)

d)

e) The current in a resistor can changeinstantaneously

7.3 a) 0 A

b) 62.5 mA

c) 87.5 mA

d) 62.5 mA

e) 150 mA

f) 0 A

g)

h) 0 V

i)

j) 0 V

k)

l)

7.21 a) , ,

b)

c) , 4500 mJ1125 mJ

5625 mJ

-15e-125t+ 15 V60e-125t

+ 15 V15e-125tmA

150 - 62.5e-4000t mA

-12.5e-4000t V

-12.5 V

62.5e-4000t mA

-0.2e-106t mA

0.2e-106t mA

-0.2 mA

9.02%

-500e-25t V-400e-25t5e-25t

3C dv

dt= 0

2C dv

dt= 0

v =

13

vs(t) + v(0)

-5 A

6.5 J

6.5 J

18.5 J

18.5 J

3.6 nWb>A2.8 nWb>A

t(�s)5004003002001000�100

120

100

80

60

40

20

0

v(V)

6.21 20 H

6.22 a)

b)

c)

d) 540 J

e) 3920 J

f) 3380 J

g) (checks)

6.26 5 nF, initial voltage is

6.27 a)

b)

c)

d)

e)

f)

g)

6.34 a)

b)

c)

d) , which is consistent with the circuit’sbehavior

6.42 a) , 1.25

b) , 0.25 * 10-6 Wb>A0.25 * 10-6 Wb>A160 mH

-48.75 V

-105e-t+ 56.26e-2.25t V

50e-t

40[-e-t+ 11.25e-2.25t] + 90[e-t

- 5e-2.25t] =

40di2

dt+ 90i2 = -5

dig

dt

18.225 mJ

12

(20 * 10-9 )(27)2

+

12

(30 * 10-9 )(27)2

=

18.225 m J

23.625 m J

5.4 m J

12e-2500t- 27 V

18e-2500t+ 27 V

30e-2500t V

-10 V

12

(10)(13)2+

12

(30)(13)2= 3380 J

-3e-20t- 13 A

-9e-20t+ 13 A

-12e-20t A

89251_26_AppH 4/5/07 2:25 PM Page 826




7.24 a)

b)

7.33 mA,

7.34 a) A,

b) V, 0 V

7.35 a)

b)

7.50 a)

b)

c)

d)

e) 6 mA

7.51

7.53 a) 120 V

b)

c) 2 ms

d)

e)

f)

7.54 a)

b) 25 V

c) 2.5 ms

d) 1.97 ms

7.65 a)

b)

c)

d)

e) Yes

7.67 a)

b)

c)

d)

e) Yes

7.72

7.76 V, ms;

V, ms

7.86 a) 2

b) s

7.87 s173.23 m

529.83 m

… t 6 q250vo = 100e-1000(t - 0.25)

0 … t … 250vo = 100

-559.12 mV

24 - 24e-5000t mA

16 - 16e-5000t mA

10e-5000t V

40 - 40e-5000t mA

-50 + 50e-10,000t mA

0.25 - 0.25e-10,000t A

15e-10,000t V

0.2 - 0.2e-10,000t A

-30 V

5.4e-500t mA

-150 + 270e-500t V

-5.4 mA

-150 V

15 - 105e-4000t V

8 - 4e-5000t mA

2 + 4e-5000t mA

2 - e-5000t mA

40 - 40e-5000t V

15 + 285e-2000t V

3 - 19e-2000t A

-40

16 - 16e-4000t V4 + 2e-4000t

-60e-80,000t V9 + 3e-80,000t

14.05%

39.6e-2000t mA 7.92 25 ms

7.93 mV, mV,

7.103 a) 1.091 M

b) 0.29 s

7.104 a)

b) 559.3

7.105 a)

b) 99.06 mA

c) per year

Chapter 88.1 a) ,

b) overdamped

c)

d) ,

e)

8.2 a) , 200 mH, ,

b) ,,

8.3 a) 800 mH

b)

c) 125 V

d) 12.5 mA

e)

8.4 a) , 12.5 nF, , 25 V

b)

8.5 a) , , 6.25 H, F, 20 mA,

b)

c)

d)

8.19

8.20

8.21

8.25

8.26

8.27

8.45 40 - 40e-5000t cos 5000t - 40e-5000t sin 5000t V

15 - 1500te-100t- 45e-100t mA

15 - 45e-80t cos 60t - 10e-80t sin 60t mA

15 - 40e-50t- 5e-200t mA

(60 - 132 * 104t)e-10,000t V

60e-4000t cos 3000t - 320e4000t sin 3000t V

-140e-2000t+ 200e-8000t V

5e-160t- 20e-40t mA

-25e-160t+ 25e-40t mA

-5e-160t+ 5e-40t V

-5 mA25 m80 rad>s100 rad>s

(25,000t - 7.5)e-4000t mA

-5 * 105 V>s10 kÆ

e-4000t(12.5 cos 3000t + 68.75 sin 3000t) mA

2500 Æ

1.25e-5000t- 20e-20,000t mA

5e-5000t- 5e-20,000t mA

-6.25e-5000t+ 25e-20,000t mA

10,000 rad>s12,500 rad>s800 Æ

6250 Æ

-8000 - j6000 rad>s-8000 + j6000 rad>s7812.5 Æ

-20,000 rad>s-5000 rad>s

$43.39

24.3 flashes>min

kÆ

8.55 flashes>min

Æ

30,000t - 40 - 5e-2000t mV10 + 5e-2000t30,000t - 30

89251_26_AppH 4/5/07 2:26 PM Page 827




8.46

8.47

8.58 a) s: V, V; 0.2 s :,

b) 2.844 s

8.59 : , ;s: ,

8.64 a) s

b) 262.42 V

c) s,

8.65 a) 40 mJ

b)

c) 568.15 V

Chapter 99.1 a) 120 Hz

b) 8.33 ms

c) 100 V

d) 70.71 V

e) , 0.7854 rad

f) 1.042 ms

g) 3.125 ms

9.5 a) 170 V

b) 60 Hz

c)

d) rad

e)

f) 16.67 ms

g) 2.78 ms

h)

i)

j)

9.8

9.9 a)

b) A,

c) 133.61 mA

d) 2 A, ,

e) 36.87°

23.13°400 rad>s

2 cos(400t + 23.13°) A-1.84e-533.33t

-1.84e-533.33t+ 2 cos(400t + 23.13°) A

Vm

2

25>9 ms

25>18 ms

-170 sin 120pt V

-60°

-1.05

377 rad>s

45°

-27,808.04 V

v(tmax) = 262.15 Vtmax = 53.63 m

55.23 m

0.5 - 1.66e-2(t - 0.2) V-6.25 + 22.38e-(t - 0.2)

- 15.31e-2(t - 0.2) Vt Ú 0.2-2 + 2e-2t V25 - 50e-t

+ 25e-2t V0 … t … 0.2 s

t - 1 V-6.25t 2

+ 12.5t - 1.25 V… t … tsat-4t25t

20 … t … 0.2

40 - 53.33e-2000t+ 13.33e-8000t V

40 - 200,000te-5000t- 40e-5000t V 9.12 a) 50 Hz

b)

c)

d) 127.32 mH

e)

9.13 a)

b)

c)

d) F

e)

9.14 a)

b) s

9.15 a)

b)

c)

9.16 a)

b)

c)

9.21 a)

b) 200 mS

c) 100 mS

d) 2.24 A

9.26

9.27

9.28

9.34

9.40 ,

9.41 , 50 - j25 Æ8l -36.87° A

8.64 + j11.52 Æ60l -36.87° V

2>3 Æ

32 cos (8000t + 90°) V

33.94 cos (5000t + 45°) V

5000 rad>s

223.6l26.57° mS

1 cos(8000t + 23.13°) A

1l23.13° A

60� V500 �j400 �

400 � j700 �

I

�

�

46.4 cos(5 * 104t + 34.46°) V

46.4l34.46° V

�20� A20 j2 ��j20 �

1 �

20 �

50 m

5l72° Æ

-j19.89 Æ

0.2 m

-19.89 Æ

90°

251,327.41 rad>sj40 Æ

40 Æ

-90°

89251_26_AppH 4/5/07 2:27 PM 28




9.47 20 A,

9.51

9.56

9.58

9.61

9.72 a) A,

b) 0.5

c) 112.5 mJ, 37.5 mJ

9.73 a) 0.5657

b) 1.5 A

9.77

9.81 a)

b) ,

c)

9.82

9.85 a) , ,, ,

,

b)

9.86 a) 0 A

b) 0.436 A

c) When the two loads are equal, more current isdrawn from the primary

Chapter 1010.2 a) 2404.16 W (abs), 2404.16 VAR (abs)

b) 155.29 W (abs), VAR (del)

c) W (del), VAR (del)

d) W (del), 845.72 VAR (abs)

10.3 a) Yes

b) Yes

10.13 a) 60 V(rms)

b) 300 W

-307.82

-1174.62-427.53

-579.56

0.42l0° A

I6 = 2.55l0° AI5 = 4.6l0° AI4 = 19.40l0° AI3 = 21.96l0° A

I2 = 2.04l0° AI1 = 24l0° A

Rx� ��Vm/2

Vo � (Vm/2) � IRx

Vo�IRx

IRx

I

Rx� 0

Vm/2 Vm

-j26.90 Æ

241 + j8 = 241.13l1.90° V-j32 Æ

247 + j7.25 = 247.11l1.68° V

800 + j600 Æ

5 cos (10,000t - 180°) A18.03 cos(10,000t - 56.31°)

11.31 cos(5000t - 45°) V

12 cos 5000t V

72 + j96 = 120l53.13° V

15.81l18.43° V

0.4 - j1.2 Æ 10.17 a)

b) Balances (80 W)

c) Balances (80 VAR)

10.21 a) 0.9 lagging, 0.43; 0.43 leading, ;0.57 leading,

b) 0.94 lagging, 0.343

10.22 a)

b) 0.9487 leading

10.41 a)

b) 16.875 mW

10.44 a)

b) 280 W

c)

10.45 a) 3240 W

b) 6480 W

10.49 a) 9 W

b) , 8 mH

c) 17.31 W, yes

d) 18.75 W

e) , 9 mH

f) Yes

10.50 a) 8 mH, , 18.26 W

b) Yes

c) Yes

10.58 160 W

10.59 a) 8

b) 250 W

10.66 a)

b)

c) Yes

10.67 a)

b) 1125 W

10.68 , 24 Æ36 Æ

= PM

2

PM - PL

PH =

V2(R1 + R2)R1R2

=

V2V2

PL

¢V2

PL-

V2

PM≤ ¢ V2

PM≤

PL =

V2

R1 + R2 PM =

V2

R2

28.8 Æ

28.8 Æ

31.62 Æ

30 Æ

20 Æ

9.72%

140l0° V(rms)

30 + j10 kÆ

72 - j24 = 75.89l -18.43° Æ

-0.82-0.9

-80 W(del), 60 VAR, 100 VAR

89251_26_AppH 4/5/07 2:28 PM Page 829




Chapter 1111.1 a) abc

b) acb

11.2 a) Balanced, positive phase sequence

b) Balanced, negative phase sequence

c) Balanced, positive phase sequence

d) Balanced, negative phase sequence

e) Unbalanced, due to unequal amplitudes

f) Unbalanced, due to unequal phase angleseparation

11.8 ,,

11.9 a) 32.84 A(rms)

b) V(rms)

11.10 a) , ,

b) , ,

c) ,,

d) ,,

11.14 a)

b)

c)

11.15

11.16

11.24

11.25 a)

b) 519.62 V(rms)

11.41 197.29 W, 476.63 W

1833.46l22° VA

6120l36.61° VA

10.82l71.34° A(rms)

159.5l29.34° V(rms)

35.3l116.63° V(rms)

0.23l156.87° A(rms)

�

�39 � j33 �

1 � j3 �

�

�

VAN150�20

V (rms)

IaA

VCA = 8071.28l -154.37° VVBC = 8071.28l85.63° VVAB = 8071.28l -34.37° V

VCN = 4659.96l -124.37° VVBN = 4659.96l115.63° VVAN = 4659.96l -4.37° V

Vca = 8313.84l -150° VVbc = 8313.84l90° VVab = 8313.84l -30° V

IcC = 24l -136.26° AIbB = 24l103.74° AIaA = 24l -16.26° A

12,845.94

vCA = 13,799.25 cos (vt - 150°) VvBC = 13,799.25 cos (vt + 90°) VvAB = 13,799.25 cos (vt - 30°) V

11.42 a)

Thus,

b)

11.52 a)

b)

11.53 a)

b)

11.54 , so the voltage is below theacceptable level of 13 kV. Thus, when the load atthe substation drops to zero, the capacitor bankmust be switched off.

11.55 kW, kW

Chapter 1212.1 a)

b)

c)

12.2 a)

b)

12.5 a) 1.0

b) 0

c)

12.6 a) 52

b) 6.25

q

6)u(t - 6) - 5(t - 9)u(t - 9)3)u(t + 3) + 5(t - 3)u(t - 3) + 5(t -5(t + 9)u(t + 9) - 5(t + 6)u(t + 6) - 5(t +

(5t - 50)u(t - 10)(2.5t + 50)u(t + 20) - 2.5tu(t) +

(30 - 3t)t[u(t) - u(t - 10)]

a50 sin p

2 tbu(t) - a50 sin

p

2 tbu(t - 4)

8) - u(t - 12)]30t)[u(t) - u(t - 8)] + (-360 + 30t)[u(t -(120 + 30t)[(u(t + 4) - u(t)] + (120 -

PL(after) = 40.83PL(before) = 81.66

ƒ Vab ƒ = 12,548.8 V

50.14 mF

16.71 mF

1.2MW

1.2 MW

1.2 MVAR

1.70 MVA

45�

(a)

-4172.79 VAR

13(W2 - W1) = 13VLIL sin u = QT

30°)] = 2VLIL sin u sin 30° = VLIL sin u

W2 - W1 = VLIL[ cos (u - 30°) - cos (u +

89251_26_AppH 4/5/07 2:29 PM Page 830




12.7

12.13 a)

b)

c)

d)

e)

12.17 a)

b)

c) check

12.18 a)

b)

c) 2

d) check

12.24 a)

b)

c)

l5e-tt cosh t6 =

s 2

+ 2s + 2

s 2(s + 2)2

l5t sin bt6 =

2bs

(s 2

+ b2)2

l5t 56 =

120

s 6

= (-1)nl5t nf(t)6

So d

nF(s)ds

n = (-1)n

L

q

0-

t nf(t)e-st

dt

d 3F(s)

ds 3 =

L

q

0-

- t3f(t)e-st dt

d 2F(s)

ds 2 =

L

q

0-

t2f(t)e-st dt

So l5tf(t)6 = -

dF(s)ds

= -L

q

0-

tf(t)e-st dt

dF(s)ds

=

d

ds BL

q

0-

f(t)e-st dtR

-v2

s 2

+ v2

sv

s 2

+ v2

1

s 3

1s(s + a)

sinh u + s[cosh u]

(s 2

- 1)

1

s 2

v cos u + s sin u

s 2

+ v2

v

s 2

+ v2

1

(s + a)2

3>812.25 a)

b)

12.26

12.40 a)

b)

c)

d)

12.41 a)

b)

c)

d)

e)

12.42 c)

12.47 a)

b)

c)

d)

Chapter 13

13.4 a)

b) Zeros at and

; pole at 0- 1000 - j3000 rad>s-1000 + j3000 rad>s

5[s 2

+ 2000s + 107]s

f(0+) = 56, f(q) = 8

f(0+) = 11, f(q) = 0

f(0+) = 8, f(q) = 10

f(0+) = 18, f(q) = 0

d¿(t) + 5d(t) + 50e- 20tu(t)

36.87)]u(t)[50te- t cos(2t - 16.26°) + 20e- t cos(2t +

[(2t - 1.5t 2

+ 1)e- 2t ]u(t)

[10t - 5 + 10e- 2t cos (t + 53.13°)]u(t)

[10 - 40te- 2t+ 20e- 2t]u(t)

[40t - 8 + 16e- 10t]u(t)

[8 + 50e- 7t cos (24t + 16.26°)]u(t)

[5e- 2t+ 10e- 6t cos (8t - 53.13°)]u(t)

[10 + 5e- 2t- 8e- 3t

+ e- 5t]u(t)

[3e- t+ 6e- 2t

+ 9e- 3t]u(t)

200s 2

(s 2

+ 40s + 64)(s 2

+ 100)

l5t sin bt6 =

b

s 2

+ b2

= lb f(t)tr

=

L

q

0-

f(t)B -e-st

- tR dt

=

L

q

0-

f(t)B e-tu

- t2 qsR dt

=

L

q

0-

f(t)L

q

se-ut

du dt

=

L

q

0-

BL

q

sf(t)e-ut

duR dt

L

q

sF(u)du =

L

q

sBL

q

0-

f(t)e-

ut dtR du

89251_26_AppH 4/5/07 2:30 PM Page 831




13.5 a)

b) Zero at 0; poles at and

13.9 a)

b)

c)

13.10 a)

b)

c)

d)

e)

13.15 a)

b) Compare solution at and tocircuit at and t = qt = 0

t = qt = 0

[5 - 6e- 5t+ 4e- 20t]u(t) V

- [25,000t + 10]e- 5000tu(t) mA

[5 * 105te- 5000t+ 100e- 5000t]u(t) V

-0.01(s + 7500)

(s + 5000)2

100(s + 104)

s 2

+ 104s + 25 * 106

10 k� 108/s � 0.01/s A106 A 4s � Vo

IL

�

�

(-8e- 500t+ 8e- 2000t)u(t) V

-12,000

s 2

+ 2500s + 106

2000 �

15 10�3

s0.8 106

s0.8s �

�

�

Vo

2000 �

0.8 106

s12 10�3 V

0.8s �

�

�

�

�Vo

�

�

A

-4000 rad>s -1000 rad>s25 * 106s

s 2

+ 5000s + 4 * 106

13.16 a)

b)

c)

13.26 a)

b)

c) Compare solutions at and tocircuit at and

13.27 a)

b) Initial values: 15 A, 12 A; final values: 4 A, 4 A

c)

13.35

13.36 a)

b) Initial value is 0, final value is 650 mA

c)

13.37 a)

b)

13.42 a)

b)

13.49 a) , no zeros, pole at

b) , zero at 0, pole at

c) , zero at 0, pole at -3 * 106 rad>ss

s + 3 * 106

-50 rad>ss

s + 50

-50 rad>s50s + 50

(56 - 108e- 2000t+ 52e- 3000t)u(t) V

6 * 104(s + 4000) + 96 * 106

s(s + 2000)(s + 3000)

(-51e- 200t+ 51e- 850t)u(t) mA

(51e- 200t- 51e- 850t)u(t) mA

(650 - 425e- 200t- 225e- 850t

)u(t) mA

276.25(s + 400)s(s + 200)(s + 850)

[5 - 5000te- 1000t- 5e- 1000t]u(t) mA

(4 + 27e- 2t- 19e- 3t)u(t) A

(4 - 27e- 2t+ 38e- 3t)u(t) A,

12s 2

+ 63s + 24s(s + 2)(s + 3)

15s 2

+ 15s + 24s(s + 2)(s + 3)

,

t = qt = 0t = qt = 0

(75 + 5e- 10,000t- 80e- 40,000t)u(t) mA

(256e- 40,000t- 4e- 10,000t)u(t) V

3.35e- 1000t cos (3000t - 26.57°)u(t) A

3(s + 2500)

s 2

+ 2000s + 107

0.02s �

40 �

0.06 V

Io

120/s V

270/s V�

��

�

� �

106

5s�

89251_26_AppH 4/5/07 2:31 PM Page 832




d)

t(ms)

500

400

300

200

100

�200

�1002.5

00 5 12.5 15 17.5 207.5 10

vo(V)

c) Voltage spikes in Problem 13.89 but not here

Chapter 1414.1 a)

b)

c) V,V,

14.2 a)

b)

14.12 a)

b)

14.13 a)

b)

14.21 a)

b)

c) 7.5

159.15 kHz

1 Mrad>s60 kÆ

4 kÆ

917.03 Hz

9.95 kÆ

1640.85 Hz

392.70 Æ

vo(3vc) = 15.81 cos(18,000t - 71.57°) Vvo(0.3vc) = 47.89 cos(1800t - 16.70°)vo(vc) = 35.36 cos(6000t - 45°)

0.3162l -71.57°0.9578l -16.70°, H( j3vc) =

H( jvc) = 0.7071l -45°, H( j0.3vc) =

954.93 Hz

13.90 a)

b)

-20.58e-1475pt+ 172.62 cos(120pt - 83.15°) V

t(ms)

200

100150

�150

50

�50

�200

�100

2.50

0 5 12.5 15 17.5 207.5 10

vo(V)

d) , no zeros, pole at

e) , no zeros, pole at

13.57

13.58

13.74

13.75 a)

b)

13.76 a)

b)

c)

13.83 a)

b)

c)

d)

e)

f)

g)

13.84 a)

b)

c)

d)

e)

f)

g)

13.89 a) ;

b)

c) V0 = 122.06l6.85° V(rms)

v0(0+) = 424.26 V

6.85°) V

v0 = 252.89e- 1475pt+ 172.62 cos (120pt +

+

30012s + 1475p

V0 =

1440p(122.9212s - 3000p12

(s + 1475p)(s 2

+ 14,400p2)

iL(0-) = iL(0+) = 35.36 A

i2(0-) = i2(0+) = 0 A

[-1.6 * 10- 3d(t)] - [7200e-2 * 106tu(t)] V

-0.6 e-2 * 106tu(t) A

0.6e-2 * 106tu(t) A

-0.6 A

0.2 A

0.6 A

0.8 A

20 V

4 V

16 V

32d(t) mA

0 V

20 V

80 V

11.68 cos(2000t + 30.96°) V

(35e- 2000t- 25e- 4000t)u(t) V

s(s + 9000)(s + 2000)(s + 4000)

4 cos(8000t - 161.57°) V

-16 * 104s

(s + 8000)(s + 16,000)

50 cos(8000t + 36.87°) V

(1 - e)e- t V

(e - 1)e- t V

-125 rad>s100s + 125

- 3 * 106 rad>s3 * 106

s + 3 * 106

89251_26_AppH 4/5/07 2:32 PM Page 833




d)

e)

f)

g)

h)

14.22 a) ,

b) ,

c)

14.33 a)

b)

c) 16

d)

e)

f)

g)

h)

14.34 a) ,

b) ,

c)

14.43 a) ,

b) ,

c)

14.44 H, F,

14.45 63.7 times as large as the DTMF tones

Chapter 1515.4 a) ,

b)

�

� �

�

vo

�

�

vi

3.18 k�

5 nF

0.57 k�

kÆR2 = 3.18kÆR1 = 0.57

0.344|Vpeak|C = 0.057 mL = 0.225

|V1209Hz| = 0.344|Vpeak|

|V770Hz| = |V852Hz| = 0.948|Vpeak|

|V697Hz| = |V941Hz| = 0.707|Vpeak|

0.10 mF0.39 H

6.25 kHz

53.22 kHz46.97 kHz

101.32 mH254.65 Æ

79.58 kHz

1.31 Mrad>s8.25 Mrad>s1.234 MHz

7.75 Mrad>s

1.27 MHz

8 Mrad>s795.77 Hz

8.37 kHz7.57 kHz

16 mH8 kÆ

21.22 kHz

170.12 kHz

1068.89 krad>s148.90 kHz

935.55 krad>s 15.7 a) ,

b)

15.13 a) 1 H, 1 F,

b) 0.9 H, 0.11 nF, 3.6

c)

15.14 a)

b)

c) 5 k , 2 H, 0.2 nF

d)

e)

15.30 Hz, Hz,,

15.31 , ; if then

15.33 a) 4

b) dB-48.16

kÆRf = 4kÆRi = 1RH = 20.7 ÆRL = 784.6 Æ

RH = 821.64 ÆRL = 21.64 ÆfC2 = 49,037.85fC1 = 1291.4

2500s

s 2

+ 2500s + 25 * 108

2 H �

�

vo

�

�

vi

0.2 nF

5 k�

Æ

(1>Q)s

s 2

+ (1>Q)s + 1

1>L = 1>Q F

0.9 H

�

�

vo

�

�

vi

0.11 nF

3.6 k�

kÆ

0.04 Æ

vo

�

�

vi

�

�

�

�

23.29 k�

5.85 k�680 pF

kÆR2 = 23.29kÆR1 = 5.85

89251_26_AppH 4/5/07 2:33 PM Page 834




15.36 a) First stage: 208.05 nF, 30.44 nF; second stage:86.12 nF, 73.53 nF

b)

15.37 a) ,

b)

15.58 a),

b)

c)

15.59 Choose , . Then,, dB,

dB

15.60 Choose k , then ,nFC1 = 7.96

kÆR2 = 400ÆR1 = 100

|H( j>R2C1)| = 17.04|H( jv)|max = 20.01C = 39 nF

R2 = 100 kÆR1 = 11.1 kÆ

s 2

+ 64 * 106p2

s 2

+ 533.33ps + 64 * 106p2

�

��

��

�

265 �132.5 �

265 �

261 �

4.4 �

150 nF 150 nF

300 nF

vi

�

�

va

2C = 300 nF4.4 Æ, C = 150 nFR = 265 Æ, sR = 261 Æ, (1 - s)R =

��

�

900 �

1.81 k�vi

�

�va

25 nF 25 nF

1800.63 Æ900.32 Æ

��

��

�

�

�

2 k�2 �2 k�

208 nF

2 k�

v1

va

86 nF

30 nF 74 nF

Chapter 1616.1 a) ,

b) Hz, kHz

c) ,

d) for all k; for k even;

for k odd

V for all k;

for all k

e)

16.2 a)

b)

c)

16.3

16.10 a) 100 Hz

b) no

c) yes

d) yes

e) yes

f) , for all k, for k even,

for k oddbk =

80

p2k2 sin kp

4

bk = 0ak = 0av = 0

600p

aq

n = 2,4,6 cos(np>2) cos(nvot)

(n2- 1)

V

300p

+ 50 cos vot -

2Vm

p aq

n = 2,4,6,Á

1

1 - n2 cos nvot V

Vm

p+

Vm

2 sin vot +

2Vm

p B1 + 2 a

q

n = 1

1

1 - 4n2 cos nvotR V

4Vm

p a

q

n = 1,3,5,Á 1n

sin nvot V

50p

aq

n = 1 1n

¢sin np

4+ sin

np

2≤ cos nvot V

vb(t) = 18.75 +

200p

aq

n = 1,3,5,Á 1n

¢2 - cos np

3≤ sin nvot V

va(t) =

bkb = 0

akb =

50kpb sin

kp

4+ sin

kp

2r

bka =

200pkB2 - cos

pk

3R V

bka = 0aka = 0

avb = 18.75 Vava = 0

fob = 125foa = 11,111.11

vob = 785,398.16 rad>svoa = 69,813.17 rad>s

89251_26_AppH 4/5/07 2:34 PM Page 835




16.11 a)

b) no

c) yes

d) no

16.18 a) where

b) 888.92 mV

16.27

16.28 a)

b) The 5th harmonic at is eliminated bythe bandreject filter whose center frequency is

16.32 a) 287.06 W

b) 300 W

c)

16.33 41.52 mW

16.36 a) 74.5356 V(rms)

b) 74.5306 V(rms)

16.37 a) 77.9578 V(rms)

b)

c) 46.1880 V(rms),

16.44 ,

,

16.45 a) 4000 W

b) 7.72 A

c) -10.57%

n = ;1, ;2, Á

Cn =

Im

n2p2 [2 cos(np>2) + np sin(np>2) - 2]

C0 =

Im

4

-0.0156%

-2.55%

-4.31%

50 krad>s50 krad>s

118.74 cos(70,000t - 171.70°) V

278.78 cos(30,000t + 174.64°) +

839.82 cos(10,000t - 1.19°) +

123.69°) + 17.83 cos(10,000t - 68.20°) V

214.66 cos (2000t - 26.57°) + 44.38 cos (6000t +

Akl -uk =

0.756k

¢ 2pk

- j1≤ mV, for odd k

aq

n = 1,3,5An cos(nvot - un )

p

6 rad>s 16.48 a)

b)

16.49 a)

00

100

200

300

400424

270

13590 67.5 54 45

500

4vo 5vo 6vo1vo 2vo 3vo

Ak

00

90

4vo 5vo 6vo1vo 2vo 3vo

�uk(deg)

�1

�1

�3�5�7

2

4

6

8

10�Cn�

n7531

�3�5�7

�135

135

�90

9045

�45

1 3 5 7n

uk�

00

1 2 3k

Ak (V)

4 5 6 7 8

2468

101214161820

0 1 2 3k4 5 6 7 8

0

45

90

135uk�

89251_26_AppH 4/5/07 2:34 PM Page 836




b)

Chapter 17

17.2 a)

b)

c)

�15

0.20.10.0

0.30.40.5

1.00.90.80.70.6

�10 0v (rad/s)

�5 5 10 15

�F(v)�

At

2

2A

v2t b2 cos

vt

2+ vt sin

vt

2- 2 r

00

100

200

300

400

500

2 4�2�4�6

00

90

�90

21 43 5�1�3�5 �2�4�6

Cn

�un(deg)

17.3 a)

b) 0

c)

17.4 a)

b)

c)

d)

e)

17.19 a)

b)

17.22 a)

b) Yes, check the initial conditions and final values

17.28 a)

b) 5 V

c) 5 V

d)

e) Yes

17.32 166.67 cos(2500t + 90°) mA

(12.5e-t- 7.5e-5t)u(t) V

5e5tu(- t) + (12.5e-t- 7.5e-5t)u(t) V

20sgn(t) - 40e-50tu(t) V

F(v) : p[d(v - vo) + d(v + vo)]

t

2• sin[(v + vo)t>2]

(v + vo)(t>2)+

t

2• sin[(v - vo)t>2]

(v - vo)(t>2)

e-jvto

v - vo

a2+ (v - vo)2 +

v + vo

a2+ (v + vo)2

a

a2+ (v - vo)2 +

a

a2+ (v + vo)2

j48av(a2

- v2)

(a2+ v2)4

2(a2- v2)

(a2+ v2)2

t (s)

f(t)

10

�1.0

�0.4�0.2

0.00.2

0.60.81.0

50�5�10

�0.6�0.8

0.4

A

pvot 2[vot cos(vot>2) - 2 sin(vot>2)]

89251_26_AppH 4/5/07 2:35 PM Page 837




17.39 a)

b)

c)

d) 720 J

e) 28 J

v

00

1

2

3

4

5

2 4 6 8 10�2�4�6�8�10

Vo(v)

v

00

5

10

15

20

25

2 4 6 8 10�2�4�6�8�10

Vg(v)

15e-5t- 5e-25t

]u(t) + 10e5tu(- t) V f)

g)

Chapter1818.2 ; ; ;

18.4 ; ; ;

18.5 ; ; ;

18.11 ; ; ;

18.12 a) ; ;;

b) ; ;;

18.30 15.625

18.32 a)

b) 11.20 mW

c)

18.37 7.5 W

18.38 3.88 V

2.88 mW

28l180° V(rms)

a22 = -0.025a21 = -5 * 10-7 Sa12 = -25 Æa11 = -4 * 10-4

a22 = -0.025a21 = -5 * 10-7 Sa12 = -25 Æa11 = -4 * 10-4

h22 = 20 * 10-6 S

h21 = 40h12 = 1 * 10-4h11 = 1000 Æ

b22 = 50b21 = 20 mSb12 = 2 MÆb11 = 500

z22 = 22 Æz21 = 18 Æz12 = 18 Æz11 = 20 Æ

z22 = 80 Æz21 = 20 Æz12 = 20 Æz11 = 25 Æ

96.93%

95.95%

89251_26_AppH 4/5/07 2:35 PM Page 838



89251 26 apph 4/5/07 2:22 pm page 821...

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