Complete Solution Manual: Electrical Engineering Principles and
Applications. 7th Edition. By Allan R. Hambley
APPENDIX A
Exercises
EA.1 Given Z1 2 j 3 and Z2 8 j 6, we have:
Z1 Z2 10 j 3
Z1 Z2 6 j 9
Z1 Z2 16 j 24 j 12 j 218 34 j 12
Z / Z 2 j 3 8 j 6 16 j 12 j 24 j 18 0.02 j 0.36
2
1 2
8 j6 8 j6 100
EA.2 Z1 1545∘ 15 cos(45∘ ) j 15 sin(45∘ ) 10.6 j 10.6
Z2 10 150∘ 10 cos(150∘ ) j 10 sin(150∘ ) 8.66 j 5
Z3 590∘ 5cos(90∘ ) j 5 sin(90∘ ) j 5
EA.3 Notice that Z1 lies in the first quadrant of the complex plane.
Z1 3 j 4 32 42 arctan(4 /3) 553.13∘
Notice that Z2 lies on the negative imaginary axis.
Z2 j 10 10 90∘
Notice that Z3 lies in the third quadrant of the complex plane.
Z3 5 j 5 52 52 (180∘ arctan(5 / 5)) 7.07225∘ 7.07 135∘
EA.4 Notice that Z1 lies in the first quadrant of the complex plane.
Z1 10 j 10 102 102 arctan(10 /10) 14.1445∘ 14.14 exp( j 45∘ )
Notice that Z2 lies in the second quadrant of the complex plane.
Z2 10 j 10
1
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,102 102 (180 ∘ arctan(10 /10))
14.14135∘ 14.14 exp( j 135∘ )
2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
,EA.5 Z1Z2 (1030∘ )(20135∘ ) (10 20)(30∘ 135∘ ) 200(165∘ )
Z1 / Z2 (1030∘ ) /(20135∘ ) (10 /20)(30∘ 135∘ ) 0.5(105∘ )
Z1 Z2 (1030∘ ) (20135∘ ) (8.66 j 5) (14.14 j 14.14)
22.8 j 9.14 24.6 21.8∘
Z1 Z2 (1030∘ ) (20135∘ ) (8.66 j 5) (14.14 j 14.14)
5.48 j 19.14 19.9106 ∘
Problems
PA.1 Given Z1 2 j 3 and Z2 4 j 3, we have:
Z1 Z2 6 j 0
Z1 Z2 2 j 6
Z1 Z2 8 j 6 j12 j 2 9 17 j 6
Z / Z 2 j 3 4 j 3 1 j 18 0.04 j 0.72
1 2
4 j3 4 j3 25
PA.2 Given that Z1 1 j 2 and Z2 2 j 3, we have:
Z1 Z2 3 j1
Z1 Z2 1 j 5
Z1 Z2 2 j 3 j 4 j 2 6 8 j1
1 j2 2 j3 4 j7
Z /Z 0.3077 j 0.5385
1 2
2 j3 2 j3 13
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
, PA.3 Given that Z1 10 j 5 and Z2 20 j 20, we have:
Z1 Z2 30 j 15
Z1 Z2 10 j 25
Z1 Z2 200 j 200 j100 j 2100 300 j100
Z / Z 10 j 5 20 j 20 100 j 300 0.125 j 0.375
1 2
20 j 20 20 j 20 800
PA.4 (a) Za 5 j 5 7.071 45∘ 7.071 exp j 45∘
(b) Zb 10 j 5 11.18153.43∘ 11.18 expj153.43∘
(c) Zc 3 j 4 5 126.87∘ 5exp j126.87∘
(d) Zd j12 12 90∘ 12 exp j 90∘
PA.5 (a) Za 545∘ 5 expj 45∘ 3.536 j 3.536
(b) Zb 10120∘ 10 expj120∘ 5 j 8.660
(c) Zc 15 90∘ 15 exp j 90∘ j15
(d) Zd 1060∘ 10 exp j120∘ 5 j 8.660
PA.6 (a) Za 5e j30 530∘ 4.330 j 2.5
∘
∘
(b) Z b 10e j 45 10 45∘ 7.071 j 7.071
∘
(c) Zc 100e j135 100135∘ 70.71 j 70.71
4
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Applications. 7th Edition. By Allan R. Hambley
APPENDIX A
Exercises
EA.1 Given Z1 2 j 3 and Z2 8 j 6, we have:
Z1 Z2 10 j 3
Z1 Z2 6 j 9
Z1 Z2 16 j 24 j 12 j 218 34 j 12
Z / Z 2 j 3 8 j 6 16 j 12 j 24 j 18 0.02 j 0.36
2
1 2
8 j6 8 j6 100
EA.2 Z1 1545∘ 15 cos(45∘ ) j 15 sin(45∘ ) 10.6 j 10.6
Z2 10 150∘ 10 cos(150∘ ) j 10 sin(150∘ ) 8.66 j 5
Z3 590∘ 5cos(90∘ ) j 5 sin(90∘ ) j 5
EA.3 Notice that Z1 lies in the first quadrant of the complex plane.
Z1 3 j 4 32 42 arctan(4 /3) 553.13∘
Notice that Z2 lies on the negative imaginary axis.
Z2 j 10 10 90∘
Notice that Z3 lies in the third quadrant of the complex plane.
Z3 5 j 5 52 52 (180∘ arctan(5 / 5)) 7.07225∘ 7.07 135∘
EA.4 Notice that Z1 lies in the first quadrant of the complex plane.
Z1 10 j 10 102 102 arctan(10 /10) 14.1445∘ 14.14 exp( j 45∘ )
Notice that Z2 lies in the second quadrant of the complex plane.
Z2 10 j 10
1
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
,102 102 (180 ∘ arctan(10 /10))
14.14135∘ 14.14 exp( j 135∘ )
2
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
,EA.5 Z1Z2 (1030∘ )(20135∘ ) (10 20)(30∘ 135∘ ) 200(165∘ )
Z1 / Z2 (1030∘ ) /(20135∘ ) (10 /20)(30∘ 135∘ ) 0.5(105∘ )
Z1 Z2 (1030∘ ) (20135∘ ) (8.66 j 5) (14.14 j 14.14)
22.8 j 9.14 24.6 21.8∘
Z1 Z2 (1030∘ ) (20135∘ ) (8.66 j 5) (14.14 j 14.14)
5.48 j 19.14 19.9106 ∘
Problems
PA.1 Given Z1 2 j 3 and Z2 4 j 3, we have:
Z1 Z2 6 j 0
Z1 Z2 2 j 6
Z1 Z2 8 j 6 j12 j 2 9 17 j 6
Z / Z 2 j 3 4 j 3 1 j 18 0.04 j 0.72
1 2
4 j3 4 j3 25
PA.2 Given that Z1 1 j 2 and Z2 2 j 3, we have:
Z1 Z2 3 j1
Z1 Z2 1 j 5
Z1 Z2 2 j 3 j 4 j 2 6 8 j1
1 j2 2 j3 4 j7
Z /Z 0.3077 j 0.5385
1 2
2 j3 2 j3 13
3
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
, PA.3 Given that Z1 10 j 5 and Z2 20 j 20, we have:
Z1 Z2 30 j 15
Z1 Z2 10 j 25
Z1 Z2 200 j 200 j100 j 2100 300 j100
Z / Z 10 j 5 20 j 20 100 j 300 0.125 j 0.375
1 2
20 j 20 20 j 20 800
PA.4 (a) Za 5 j 5 7.071 45∘ 7.071 exp j 45∘
(b) Zb 10 j 5 11.18153.43∘ 11.18 expj153.43∘
(c) Zc 3 j 4 5 126.87∘ 5exp j126.87∘
(d) Zd j12 12 90∘ 12 exp j 90∘
PA.5 (a) Za 545∘ 5 expj 45∘ 3.536 j 3.536
(b) Zb 10120∘ 10 expj120∘ 5 j 8.660
(c) Zc 15 90∘ 15 exp j 90∘ j15
(d) Zd 1060∘ 10 exp j120∘ 5 j 8.660
PA.6 (a) Za 5e j30 530∘ 4.330 j 2.5
∘
∘
(b) Z b 10e j 45 10 45∘ 7.071 j 7.071
∘
(c) Zc 100e j135 100135∘ 70.71 j 70.71
4
© 2018 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.