Chapter 5 Solutions

# Chapter 5 Solutions - 1 2 2 j 3 j 4 8 20 10-5 j12"...

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Unformatted text preview: 1 2 ( 2 + j )( 3 - j 4 ) . , 8 - 20 + 10 -5 + j12 ! # ! " \$ ! * + ' ' , " 1545 ., 3 - j4 1545 ., 5 - 53.13 + ., *,* ., ( ! , , . .* + . . * ., " * , , * ## \$ % & ' (' \$" " # ' ' ) " \$ & " 8 - 20 10 (2 + j)(3 - j4) - 5 + j12 8 - 20 (-5 - j12)(10) 11.18 - 26.57 25 + 144 . ,+ * , , ' ++ - , -. . - , -. - , \$( + * ( \$ * -" & ( " * , , -" & ( &( " , % & " ' , ) , , % * " ' , ( * ,* ) " ' -" & ( ' " , * , . , , , , , * * + * * % & " ' ( * * * * #& " ## \$ % # & , / ( 2 + j 3) + ( 7 - j8 ) 1 - j6 -5 + j11 ( 510 )(10 - 40 ) ( 4 - 80 )( -650 ) 2 + j3 - j 2 - j 2 8 - j5 # &# " # & ' ) & &# %&# / 1545 = j2 3 - j4 (-0.4324 + j 0.4054)+ (-0.8425 - j 0.2534) = - 1.2749 + j 0.1520 3 4 - -" * -" ( 1 % a , -" ( ( * * a- ( + - , * .* , 50 - 30 o = - 2.0833 24150 o , . . * . * * . , * + . , , * * , ., , (# ( ! " , , ., , , , .+ , +* * \$ # " 0 #) " ## \$ % / ., ( 5 - j 6 ) - ( 2 + j8 ) ( -3 + j 4 )( 5 - j ) + ( 4 - j 6 ) * . ++ .* + + .+ +* ** ** + * , # " ( 24075 + 160 - 30 ) ( 60 - j80 ) ( 67 + j84 ) ( 2032 ) ! ' ( %# & ' ' % " " " / 10 + j 20 3 + j4 2 (10 + j5)(16 - j 20 ) 3 - j14 = - 0.5751 + j 0.5116 - 15 + j11 (62.116 + j 231.82 + 138.56 - j80)(60 - j80) 24186 - 6944.9 = = - 1.922 - j11.55 (67 + j84)(16.96 + j10.5983) 246.06 + j 2134.7 V = 40 - 60 V = -3010 + 5060 I = j 6e- j10 2 + 10 - 45 j I= ( w # \$ " + * * . + + \$ # w ! \$ " . .+ + \$ # w ! " . (- 2 + j 4)2 (260 - j120) = - 256.4 - j 200.89 + 1 , * , * * , * % " ( '/ 2 j * # + * , ( 2 " * " + ., w ( \$" . , + & , 34 # % , ! \$" " & " &%" 5 ( ( ( . , 6 ( w , Z= V = IZ = (4 25)(0.5 - 90) = 2 - 65 -" ( \$ 1 1 = = - j 0.5 jC j (10 6 )(2 10 -6 ) Z= 8 -" V 18010 = = 1540 = 11.49 + j 9.642 I 12 - 30 # " # \$ " - \$ " 6 W '& \$ " w9 +*, 9 ( / 3 & # + ) # #& & 3 , 5 2 " # ' %# # " 4 # ' -" # &# &# % # % " 3 " & '& ' 5 & 7 " # % " 5( ' " # % -" & ( . + -" & ( w , + + + + w , w -+ w + w - w -+ 2 2 110 = v R + v L 2 v L = 110 2 - v R v L = 110 2 - 85 2 = \$ ( - Z= 0 ' . " ( " # \$ " 6 \$ W V 65 - 60 = = 6.5 I 10 - 60 7 , 5 " & ! % *,( ' ( -\$ 7 , 3( # # , ' ' " " \$ #& ! % * ! %& ! %& * *, 7 : ( # 8 V = 4I = (4)(4.472 - 18.43) = 17.89 - 18.43 Vs = 50 jL = j (2)(1) = j2 1 1 = = - j2 jC j (2)(0.25) j2 j2 Vo = V = 50 = (190)(50) = 2 - j2 + j2 s 2 v o (t ) = , + ("- " - 1 F 12 3H 1 1 = = - j3 jC j (4)(1 / 12) jL = j (4)(3) = j12 I= : V 50 0 = = 1036.87 Z 4 - j3 ( # -" & ( ! \$ " 0 j12 V= (50 0) = 41.6 33.69 8 + j12 : ! ' ' " " & ! % * ( \$# ! \$ " - 7 " & ! % '< '< '< * ( ' ; \$" / ! %& * ! %& * 1 F 6 1 1 = = - j2 jC j (3)(1 / 6) - j2 I= (1045) = 4.472 - 18.43 4 - j2 : ( (# " 0 ! = 1( 1H jL = j (1)(1) = j 1 1 0.05 F = = - j20 jC j (1)(0.05) - j40 = 1.98 + j0.802 2 - j20 Z = j + 2 || (- j20) = j + : ! = 5( 1H jL = j (5)(1) = j5 1 1 0.05 F = = - j4 jC j (5)(0.05) - j4 = 1.6 + j4.2 1 - j2 V 4 0 4 0 Io = = = = 1.872 - 22.05 Z 1.98 + j0.802 2.13622.05 i o (t ) = (# (( " 0 ( 9 10 i s = 5 cos(10t + 40) I s = 540 0.1 F 0.2 H 9 1 1 = = -j jC j (10)(0.1) jL = j (10)(0.2) = j2 Z1 = 4 || j2 = Z = j5 + 2 || (- j4) = j5 + j8 = 0.8 + j1.6 ( 4 + j2 Io = Io = -" & ( Z2 = 3 - j : ! = 10 ( 1H jL = j (10)(1) = j10 1 1 0.05 F = = - j2 jC j (10)(0.05) - j4 = 1 + j9 2 - j2 4 0 4 0 V = = 0.89 - 69.14 Io = = Z 1.6 + j4 4.49469.14 i o (t ) = # \$ " 0 ( Z1 0.8 + j1.6 I = (540) Z1 + Z 2 s 3.8 + j0.6 (1.78963.43)(540) = 2.32594.46 3.847 8.97 i o (t ) = ( ( # ! \$" 0 Z = j10 + 2 || (- j2) = j10 + ( 7 5 " & ! % : V 40 4 0 Io = = = = 0.4417 - 83.66 Z 1 + j9 9.05583.66 i o (t ) = # \$\$" 0 ( ( ' . \$ 7 " & ! % ( * 3 ' ! %& ( 5 || j5 = j25 j5 = = 2.5 + j2.5 5 + j5 1 + j Z1 = 10 ( Z 2 = - j5 + 2.5 + j2.5 = 2.5 - j2.5 ! %& I2 IS \$ Z1 Z2 11 I2 = Vo = I 2 (2.5 + j2.5) 830 = 10 (1 + j) 4 I (2.5)(1 + j) = I 5- j s 5- j s +(\$ 0 Z1 10 4 I = I = I Z1 + Z 2 s 12.5 - j2.5 s 5 - j s 1 - j2 Z in = j0.5 + 2 - j2 Z in = j0.5 + 0.25 (3 - j) Z in = ! , ( W 0.4 H 12 jL = j (50)(0.4) = j20 Is = (830)(5 - j) =( 10 (1 + j) 1 mF 0.2 H jL = j (50)(0.2) = j10 1 1 = = - j20 jC j (50)(1 10 -3 ) ! " ## # # ( 1 1 1 1 = + + Z p 20 j10 - j20 Z p = 10 + j10 3 '< (' 1 " " & ! % + -" ( Z in = ., Zp ( ! , W \$ ! " & " \$ ! % ( ' " #& 1- ! %& ! %& + \$ ! ( # " \$) ' " , " ( " ( ' . " ' \$ " " ' % ' # 10 mF 10 mH 1 1 = = - j2 jC j (50)(10 10 -3 ) jL = j (50)(10 10 -3 ) = j0.5 z2 = 200 + j150 + j300 = 20 + j45 z1 = 10 200 + j450 200 + j450 = 30 - j13.333, z3 = = 10 + j22.5 j15 20 Z in = j0.5 + 1 || (1 - j2) j12 j16 z2 10 13 I= 14 V 6090 = = 4.2594.76 Z T 14.118 - 4.76 I2 20 W = \$ ## \$ ' ' ' j10 W z 2 (10 - j16) = z3 (10 - j16) = 21.70 - j3.821 ZT = 8 - j12 + z1 (8.721 - j8.938 + 21.7 - j3.821) = 34.69 - j6.93 (30 - j13.333)(10 - j16) = 8.721 - j8.938 40 - j29.33 40 + j10 8 + j2 I= I 60 + j5 12 + j I1 = I2 = + Vab - 20 - j5 4- j I= I 60 + j5 12 + j Vab = -20 I 1 + j10 I 2 \$\$ ! 1 " & ! % ( # &# ' - Vab = Vab = - (160 + j40) 10 + j40 I+ I 12 + j 12 + j - 150 (-12 + j)(150) I= I 12 + j 145 Vab = (12.457 175.24)(4.2597.76) Vab = ( ( - ! %& \$\$ Z T = (20 - j5) || (40 + j10) = ZT = \$ , (W * (20 - j5)(40 + j10) 170 = (12 - j) 60 + j5 145 * + 6 " # &# ! ' " & " @& " ) \$" ! % " " ,> : ? " " * 15 16 ! %& + ! %& 3 " ' ( 120 - 15o - V V V = 630 o + + 40 + j20 - j30 50 Vo = \$" V 1 j 1 + + 40 + j20 30 50 V= 115.91 - j31.058 - 5.196 - j3 = 40 + j20 - jX c V R - jX c i Xc = 1 1 = = 3.979 C (2 )(2 10 6 )(20 10 -9 ) - 3.1885 - j4.7805 = 124.08 - 154 o V 0.04 + j0.0233 Vo - j3.979 = = Vi 5 - j3.979 3.979 5 2 + 3.979 2 (-90 - 38.51) (-90 + tan -1 (3.979 5)) Vo = Vi 3.979 25 + 15.83 Vo = 0.6227 - 51.49 Vi -" 2 ( " " " 22 1 " #) ' & . " & ! % # \$ = -45 = -90 + tan -1 (X c R ) R = X c = 45 = tan -1 (X c R ) 1 = 2 f = RC 1 1 = = 2RC (2)(5)(20 10 -9 ) f= 1 C ! %& 3 /4 ' " \$ A " \$ # \$ 80 W Io ' " & ! % + j60 W 20 W 1 ' # #) 100120 V + - I1 -j40 W I2 -j40 W I3 + - 60-30 V 17 ! # ( - 10020 + (80 - j40) I1 + j40 I 2 = 0 1020 = 4 (2 - j) I 1 + j4 I 2 j40 I 1 + ( j60 - j80) I 2 + j40 I 3 = 0 0 = 2 I1 - I 2 + 2 I 3 , ! # ,( ! # ( 60 - 30 + (20 - j40) I 3 + j40 I 2 = 0 - 6 - 30 = j4 I 2 + 2 (1 - j2) I 3 ! ,( 2 I 3 = I 2 - 2 I1 0& & % " @& ( - 6 - 30 = -2 (1 - j2) I 1 + (1 + j2) I 2 * ! ' *( I1 10120 4 (2 - j) j4 = - 6 - 30 - 2 (1 - j2) 1 + j2 I 2 = 8 - j4 10120 = -4.928 + j82.11 = 82.2593.44 - 2 + j4 - 6 - 30 2 =( \$ 0 8 - j4 - j4 = 32 + j20 = 37.7432 - 2 + j4 1 + j2 2 = Io = I2 = ...
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