+ - + - ++ o 12 mA || 12 mA 12mA - - 12mA ^ O ''''~Io 11'210>| !>~n ~ | ---1------ 11> - 4.5m A -
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12 mA
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12mA
-
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2 kW
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20V
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10kW
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2.88 Given I"
=
2 mA in the network in Fig. P2.88,
find V.I'
VA 3
v.. ..•.
1 kn
Iq
+ VJ1 kfl
-'t 1 kfl
~
-
+
2kf!
.,. _I
KC,.L""
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3
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c
s
=
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-
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Is
>
R1 12V
Ix
R2
R3
R4
R5
R6 The correct answer is d. Req = { [[( R5 + R6 )
R4 ] + R3 ]
Req = { [[(8 + 2) 10] + 1]
R2 } + R1
3} + 1
Req = (6 3) + 1 = 3Ω Is =
12 12 = = 4A Req 3
R ' = [( R5 + R6 )
R4 ] + R3 = 6Ω
24 8 ⎛ 6 ⎞ = A Ix = ⎜ ⎟(4) = 9 3 ⎝3+ 6⎠
Chapter 2: Resistive Circuits
Pr oblem 2.FE-10
3k W
| -
1 O
2 kW
Vo
6 kW
4 kW
l
2
3
o
3
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+
Vo -
>
> '
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+ \/
o
+ -
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-
+
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-o +
o
\/ x
1
\/
'
'''
>
\/
6Vx
'
"
'''
\/
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^ \/
\/ 2
o\/
2
-O
-O
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c. ⎛ − R2 ⎞ ⎛ R ⎞ Vo = ⎜ ⎟(4) − ⎜ 2 ⎟(−2) ⎝ 4k ⎠ ⎝ 12k ⎠ Vo = −3V 1 − 3 = −1m( R2 ) + m( R2 ) 6 5 − m ( R 2 ) = −3 6 R2 = 3.6kΩ
Chapter 4: Operational Amplifiers
Problem 4.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: 36kΩ 18kΩ
-
V1
+ 6kΩ
+ 6kΩ
12 kΩ
12kΩ
2V
3V 1V
The correct answer is b.
⎛ 18k ⎞ ⎛ 18k ⎞ V1 = −2⎜ ⎟(4) + 1⎜ ⎟ = −4.5V ⎝ 6k ⎠ ⎝ 12k ⎠ ⎛ 36k ⎞ ⎛ 36k ⎞ V0 = −V1 ⎜ ⎟ ⎟ − 3⎜ ⎝ 6k ⎠ ⎝ 12k ⎠ ⎛ 36k ⎞ ⎛ 36k ⎞ V0 = 4.5⎜ ⎟ ⎟ − 3⎜ ⎝ 6k ⎠ ⎝ 12k ⎠ V0 = 18V
Chapter 4: Operational Amplifiers
Problem 4.FE-2
Vo
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: if 2Ω
i=0 -
Vo
+
3Ω 4Ω
6V
2V
The correct answer is a. V1 V2 6 2 + = + = 2 .5 A R1 R2 3 4 V0 = −i f R f = −(2.5)(2) if =
V0 = −5V
Chapter 4: Operational Amplifiers
Problem 4.FE-3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is d. The op-amp is a noninverting op-amp. Rf A = 1+ R1 R f = ( A − 1) R1
R f = (50 − 1)5k = 245kΩ
Chapter 4: Operational Amplifiers
Problem 4.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: R1 = 6kΩ + -
+
R2 = 2kΩ
5V R3 = 1kΩ
8kΩ
Vo
2 kΩ
−
The correct answer is c. The 8kΩ and 2kΩ resistors make up a noninverting op-amp. ⎛ 8k ⎞ V1 = ⎜1 + ⎟5 = 25V ⎝ 2k ⎠ Use nodal analysis at node A: Vo Vo − Vi Vo − 25 + + =0 R3 R1 2k
Chapter 4: Operational Amplifiers
Problem 4.FE-5
2
Irwin, Basic Engineering Circuit Analysis, 9/E
Vo Vo − 5 Vo − 25 + + =0 1k 6k 2k 6Vo + Vo − 5 + 3Vo − 75 = 0
10Vo = 80 Vo = 8V
Problem 4.FE-5
Chapter 4: Operational Amplifiers
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Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Chapter 5: Additional Analysis Techniques
Problem 5.113
2
Problem 5.113
Irwin, Basic Engineering Circuit Analysis, 9/E
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Chapter 5: Additional Analysis Techniques
Problem 5.114
2
Problem 5.114
Irwin, Basic Engineering Circuit Analysis, 9/E
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Chapter 5: Additional Analysis Techniques
Problem 5.115
2
Problem 5.115
Irwin, Basic Engineering Circuit Analysis, 9/E
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Chapter 5: Additional Analysis Techniques
Problem 5.116
2
Problem 5.116
Irwin, Basic Engineering Circuit Analysis, 9/E
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
I' R1
R2
R4
Voc'
4mA
R3
The correct answer is d. Use superposition. R1 (4m) I ' R1 R2 R3 1k I' (4m) 1mA 1 k 1 k 2 k ' Voc I ' R3 (1m)(2k )
Voc' 2V
Chapter 5: Additional Analysis Techniques
Problem 5.FE-1
2
Irwin, Basic Engineering Circuit Analysis, 9/E
R2
R1
R4
12V
Voc"
R3
R3 (12) Voc" R1 R2 R3 2k Voc" (12) 1k 1k 2k Voc" 6V Voc Voc' Voc" 2 6 8V
R1
R2
R4
R3
RTH
RTH R1 R2 R3 R4 RTH
2k (2k ) 1k 2k 2k 2k
Problem 5.FE-1
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
3
RTH 2k
Voc 8V
RL
PLmax I L2 RL
R L RTH for maximum power. V PLmax oc 2 RTH PLmax
2
RTH V2 82 oc 8mW 4 RTH 4(2k )
Chapter 5: Additional Analysis Techniques
Problem 5.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Vx
2k
1k
I
12V
Voc
+ -
2V x
The correct answer is c. 12 2kI 1kI 2V x V x I ( 2k ) 12 2kI 1kI 2(2kI ) 12 I mA 7 12 2kI Voc 12 12 2k m Voc 7 Voc 8.57V
Chapter 5: Additional Analysis Techniques
Problem 5.FE-2
2
Irwin, Basic Engineering Circuit Analysis, 9/E
Vx
2k
I1
12V
1k
I sc
I2
+ -
2V x
12 I 1 6mA 2k
1kI 2 2V x 0
1kI 2 2(2kI1 ) 0 I 2 24mA I 1 I 2 I sc I sc 6m (24m) 30mA Voc 8.57 285.7 I sc 30m RL RTH for maximum power.
RTH
RTH 285 .7
Voc 8.57V
PLmax
Problem 5.FE-2
RL
Voc2 (8.57) 2 64.3mW 4 RTH 4(285.7)
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Ix
R1
12V
I R2
2I x
text
Voc
The correct answer is a. I I x 2I x I 3I x 12 3I x 12 I 12 3I x 12(3I x ) 4 Ix A 13
4 Voc 12 I 12(3I x ) 12(3) 11.08V 13
Chapter 5: Additional Analysis Techniques
Problem 5.FE-3
2
Irwin, Basic Engineering Circuit Analysis, 9/E
Ix R1
I2 12V
R2
2I x
I sc
text
I sc I x I 2 2 I x 3I x I 2 I2 0A I sc 3I x 12 3I x
I x 4A I sc 3(4) 12 A V 11.08 0.92 RTH oc 12 I sc
RTH 0.92
12
Voc 11.08V
RL
RL 0.92 12 12.92 R L 12.92 for maximum power transfer.
Problem 5.FE-3
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
2
I' 3
10 A
2
4
The correct answer is c. Use superposition. 2 I' (10) 4 A 2 3
I" 3
Chapter 5: Additional Analysis Techniques
2
4
20V
2
Problem 5.FE-4
2
Irwin, Basic Engineering Circuit Analysis, 9/E
20 4A 5 I I' I" I 4 4 I 0A I"
Problem 5.FE-4
Chapter 5: Additional Analysis Techniques
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Use superposition.
4
a I
2
3
'
12 A
Voc'
b The correct answer is b.
4 I' (12) 8 A 2 4 Voc' I ' (2) 8(2) 16V
Chapter 5: Additional Analysis Techniques
Problem 5.FE-5
2
Irwin, Basic Engineering Circuit Analysis, 9/E
a 3
4 12V
2
Voc"
b 2 Voc" (12) 4V 2 4 Voc 16 4 12V
Problem 5.FE-5
Chapter 5: Additional Analysis Techniques
-
S S
s s
S S
t
2.24
/
c
3
t
t
t
3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a. Yes. The capacitors should be connected as shown.
6 F 2 F
4 F
C eq
6 (6 ) 3 F 6 6
Chapter 6: Capacitance and Inductance
Ceq
Problem 6.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c. q (t ) i (t ) dt
0 C , t 0 q (t ) 6t C , 0 t 1 s 6 C , t 1 s q (t ) C 0 V , t 0 v(t ) 6 x10 6 t V , 0 t 1 s 6 V , t 1 s v(t )
1 C v 2 (t ) 2 0 J , t 0 w(t ) 18 x10 6 t 2 J , 0 t 1 s 18 J , t 1 s
w(t )
Chapter 6: Capacitance and Inductance
Problem 6.FE-2
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is b. The voltage across the unknown capacitor Cx is (using KVL): 24 8 V x V x 16V q Cv The capacitors are connected in series and the charge is the same. q 60 (8) 480 C q 480 30 F Cx v 16
Chapter 6: Capacitance and Inductance
Problem 6.FE-3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: 2 mH
Leq
3mH
3mH
6mH
12mH
9mH
The correct answer is d. Leq [ [(3m 9m) 12m] 6m 3m] 2m Leq [ [(12m) 12m] 6m 3m] 2m
Leq [ 6m 6m 3m] 2m Leq [ 3m 3m] 2m Leq 1.5m 2m Leq 3.5mH
Chapter 6: Capacitance and Inductance
Problem 6.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a. di(t ) v(t ) L dt di(t ) 20te 2t (2) 20e 2t 20e 2t 40te 2t dt
v(t ) 10m 20e 2t 40te 2t 0 V , t 0 v(t ) 2t 2t 0.2e 0.4te V , t 0
Chapter 6: Capacitance and Inductance
Problem 6.FE-5
2
3
c
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i(t)
i(t)
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t
____
____
.
(
-
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-
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C
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3
-
-
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-
-
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-
.
.
.
.
.
.
.
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^ i L (0+)
-
=
2
R2
-
-
-
-
- -
-
> i(t)
-
Note: Please go to next page to see the graph on Output Voltage vs Time
-
12V
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
8k
6 k
vc (0)
6k
12V
6 k
The correct answer is b.
R'
12k (6k ) 4k 12k 6k
8k 12V
R ' 4 k
Chapter 7: First- and Second- Order Transient Circuits
v c ( 0 )
Problem 7.FE-1
2
Irwin, Basic Engineering Circuit Analysis, 9/E
4k v c ( 0 ) (12) 4V 4 k 8k
The t 0 circuit:
6k vc (t )
6k
vc (t) 12k x i c (t) 0 dv (t ) ic (t ) C c dt dv (t ) vc (t ) 12k (100 ) c 0 dt dvc (t ) 1 vc (t ) 0 dt 1.2 1 r 0 1.2 1 r 1.2 vc (t ) Ae
t 1.2
vc (0) 4V A4 vc (t ) 4e
t 1. 2
V, t 0
vc (2) 0.756V
Problem 7.FE-1
Chapter 7: First- and Second- Order Transient Circuits
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Find the initial condition:
12k
4k
12 k
12V
v0 (0)
The correct answer is d. vo (0) 0V
The t 0 circuit:
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-2
2
Irwin, Basic Engineering Circuit Analysis, 9/E
R3 4k
R1 12k
R 2 12 k
v0 (t )
12V
R 3 4 k
R1 12k
R 2 12 k
voc
12V
voc
R2 12k (12) (12) 6V R1 R2 12k 12k
R1 12k R 2 12 k
R3 4k
RTH
RTH ( R1 R2 ) R3 RTH
Problem 7.FE-2
12k (12k ) 4k 10k 12k 12k
Chapter 7: First- and Second- Order Transient Circuits
Irwin, Basic Engineering Circuit Analysis, 9/E
3
RTH 10k
100 F
voc 6V
v0 (t )
10k x i(t) o v (t) 6 dv (t ) ic (t ) C o dt dv (t ) RTH C c v o (t ) voc dt v dv o (t ) 1 v o (t ) oc RTH C dt RTH C 1 0 r RTH C 1 r RTH C The natural solution is: t
von (t ) Ae RTH C t
von (t ) Ae 10 k (100 ) Ae t The forced solution is: vo f (t ) k
dv o f (t ) dt
0
1
0
k
RTH C k voc vo f (t ) 6V
voc RTH C
vo (t ) 6 Ae t vo (0) 0V 0 6 A A 6
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-2
4
Irwin, Basic Engineering Circuit Analysis, 9/E
vo (t ) 6 6e t V , t 0 vo (1) 6 6e 1
vo (1) 3.79V
Problem 7.FE-2
Chapter 7: First- and Second- Order Transient Circuits
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Find the initial condition: 12 k
v c (0 )
12V
6k
The correct answer is a.
6k v c ( 0) (12) 4V 6k 12k The t 0 circuit:
vc (t )
6k
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-3
2
Irwin, Basic Engineering Circuit Analysis, 9/E
vc (t ) 6kic (t ) 0 dv (t ) ic (t ) C c dt dv (t ) vc (t ) 6k (100 ) c 0 dt dvc (t ) 1 vc (t ) 0 dt 0.6 1 r 0 0.6 1 r 0.6 t
vc (t ) Ae 0.6
vc (0) 4V A4 t
vc (t ) 4e 0.6 V , t 0 t
0.5(4) 4e 0.6 t
1 e 0.6 2 1 t ln 2 0.6 t 0.6 ln t 0.416 s
Problem 7.FE-3
1 2
Chapter 7: First- and Second- Order Transient Circuits
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Find the initial condition:
i L (0)
2
2
10V
The correct answer is c.
i L ( 0 )
10 5A 2
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-4
2
Irwin, Basic Engineering Circuit Analysis, 9/E
1
5A
voc
2
1A
1 2
2 3
2 3
6A
voc
2 voc 6 4V 3
2
2
Problem 7.FE-4
RTH
2
Chapter 7: First- and Second- Order Transient Circuits
Irwin, Basic Engineering Circuit Analysis, 9/E
RTH 2 2 2 1 2
2 3
RTH
2 3
voc 4V
3
iL (t )
4H
di L (t ) 2 i L (t ) 4 dt 3 di L (t ) 1 i L (t ) 1 dt 6 1 r 0 6 1 r 6 4
t
i Ln (t ) Ae 6 i L f (t ) k
di L f (t )
0 dt 1 0 k 1 6 k 6 i L f (t ) 6
i L ( 0 ) 5 A t
i L (t ) 6 Ae 6 56 A A 1 t
i L (t ) 6 e 6 A, t 0
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: Find the initial condition: i L (0)
3 1
12V
The correct answer is d. i L ( 0 )
12 3A 4
Chapter 7: First- and Second- Order Transient Circuits
Problem 7.FE-5
2
Irwin, Basic Engineering Circuit Analysis, 9/E
L
iL (t )
R1 R2 Vs
di L (t ) R1 R2 i L (t ) Vs dt V di L (t ) R1 R2 i L (t ) s dt L L R1 R2 0 r L R R2 r 1 L L
i Ln (t ) Ae i Ln (t ) Ae
R R 1 2 t L 5 t 3
i L f (t ) k di L f (t )
0 dt 5 0 k 4 3 12 k 5
i L (0 ) 3 A 5
t 12 i L (t ) Ae 3 5 3 2. 4 A A 0. 6
i L (t ) 2.4 0.6e
Problem 7.FE-5
5 t 3
A, t 0
Chapter 7: First- and Second- Order Transient Circuits
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AC ANALYSIS
***************************************************************************************************************************
FREQ
IM(V_PRINT1)
4.000E+02
6.058E+00
IP(V_PRINT1) -1.361E+01
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
2
j1
120V
+ 40 V
j1
1
V0 -
The correct answer is d.
j1
+ 80 A
2
j1
1
V0 -
Chapter 8: AC Steady-State Analysis
Problem 8.FE-1
2
Irwin, Basic Engineering Circuit Analysis, 9/E
Z
2( j1) 0.4 j 0.8 2 j1 I0 j1
80 A
Z
1
0.4 j 0.8 80 1.6 j 4.8 A I 0 0.4 j 0.8 1 j1 V0 1.6 j 4.81 5.06 71.6V
Problem 8.FE-1
Chapter 8: AC Steady-State Analysis
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
text
2I x
1
V1 I1
j1
2
V2
V0
I2
120V
20 A
Ix The correct answer is c.
Chapter 8: AC Steady-State Analysis
Problem 8.FE-2
2
Irwin, Basic Engineering Circuit Analysis, 9/E
V2 120V V Ix 1 j1 2I x I x I1 0 V V V 120 2 1 1 1 0 1 j1 j1 2V1 V1 j1V1 j1(120) 0 j1(120) V1 1.2 j 3.6V 3 j1 KCL at node 0: 2 I x I 2 20 0 V V V0 2 1 2 20 0 2 j1 1.2 j 3.6 120 V0 2 20 0 2 j1 V0 30.88.97V
Problem 8.FE-2
Chapter 8: AC Steady-State Analysis
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
I
2
j 2
j1
I1 120V
2V0
I2 +
4
V0
-
The correct answer is a.
I1 I I 2 I I1 I 2 KVL around the left loop: 120 2 I 1 j 2 I 2V0 V0 4I 2 (2 j 2) I 1 (8 j 2) I 2 120 KVL around the right loop: 2V0 j 2 I j1I 2 4 I 2 j 2 I 1 (4 j1) I 2 0
Chapter 8: AC Steady-State Analysis
Problem 8.FE-3
2
Irwin, Basic Engineering Circuit Analysis, 9/E
Two equations and two unknowns: (2 j 2) I 1 (8 j 2) I 2 120 j 2 I 1 (4 j1) I 2 0 It follows that: I 1 4.2445 A
I 2 2.06 30.96 A V0 4( 2.06 30.96) V0 8.24 30.96V
Problem 8.FE-3
Chapter 8: AC Steady-State Analysis
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is b. Z c is small at midband. Vx 5k 5 Vs 5k 1k 6
V0 6k (12k ) 40 x10 3 160 Vx 6k 12k V0 V x V0 Vs Vs V x
5 160 133.33 6
Chapter 8: AC Steady-State Analysis
Problem 8.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
Is 60V Zeq
The correct answer is c. (1 j1)(1 j3) 3 1.58 18.43 3 4.53 6.34 1 j1 1 j 3 60 Is 1.32456.34 A 4.53 6.34
Z eq
Chapter 8: AC Steady-State Analysis
Problem 8.FE-5
2
Irwin, Basic Engineering Circuit Analysis, 9/E
3
j 1
Io j 3
1
60 V
1
KVL around the outer loop: 60 3(1.32456.34) I 0 (1 j1) I 0 1.4832.92 A
Problem 8.FE-5
Chapter 8: AC Steady-State Analysis
-
c
>
I2
>I
4
-
>
-I
I
1
>
3
-
supplied
W
>I
-
-
O |
39
2 x
1 2
\/
|
2
2
2
2
Unknown element
.
.
.
.
-
.
.
.
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c. From the power triangle: Qold Pold tan old
Qold 120k tan 45 120k var S old (120k j120k ) VA 17045 kVA S new Pold jQnew
new cos 1 (0.95) 18.19 Qnew Pold tan new Qnew 120k tan 18.19 39.43k var S new 120k j 39.43k VA S new 126.3118.19 kVA S cap S new S old j80.57 kVA Qcap CV 2 80.57 k 2 60(C )(480 2 ) C 928 F
Chapter 9: Steady – State Power Analysis
Problem 9.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is d. T
Vrms
1 2 v (t ) dt T 0
Vrms
2 3 1 4 1 2 2 2 2 1 dt 2 dt 1 dt 0 dt 4 0 1 2 3
Vrms Vrms
1 1 2 3 t 0 4t 1 t 2 0 4 1 1 (8 4) (3 2) 1.22V 4
Chapter 9: Steady – State Power Analysis
Problem 9.FE-2
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: 2
j1 j 2
ZTH
The correct answer is b. Z TH 2 j1 j 2 0.4 j1.2 * Z L Z TH 0.4 j1.2
Chapter 9: Steady – State Power Analysis
Problem 9.FE-3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a. 36k Vs 12k 1.414 Vs 10 V rms 2 36k 10 30 V rms V0 12k V0
The meter will read 3V.
Chapter 9: Steady – State Power Analysis
Problem 9.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is b. T
I rms
1 2 i (t ) dt T 0
I rms
1 2 1 2 2 t dt (2) dt 2 0 1
I rms
1 1 (8 4) 1.47 A 2 3
2 P I rms R (1.47) 2 ( 4) 8.64 W
Chapter 9: Steady – State Power Analysis
Problem 9.FE-5
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Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
M 4
24 0V
I1
j 5 j 8
j 2
I2
5
k=0.5
The correct answer is a.
M k L1 L2 1H 240 I 1 (4 j 2) j 2 I 2 j 2 I 1 (5 j 3) I 2 0 I 1 4.92 19.75 A
I 2 1.6939.29 A 240 Z1 4.8819.75 4.92 19.75
Chapter 10: Magnetically Coupled Networks
Problem 10.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
48 n 2
j 32n 2
j 2
R L 3
V2
The correct answer is b.
Z TH 3 for maximum power transfer. Reflecting the primary into the secondary: Z TH 48n 2 j 32n 2 j 2 3 48n 2 j32n 2 j 2 3 1 if n : 4 Z TH
48 32 j 2 3 16 16
Chapter 10: Magnetically Coupled Networks
Problem 10.FE-2
2
Irwin, Basic Engineering Circuit Analysis, 9/E
3
I RL 3
300V
300 50 A 6 1 1 PL I M2 RL (5) 2 (3) 37.5W 2 2 I
Problem 10.FE-2
Chapter 10: Magnetically Coupled Networks
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
1k
+ +
5k
Vs
4V x 100
Vx
10 k
Voc
-
The correct answer is d. 5 4 Voc Vs x10 4 6 100
1k + Vs
5k
Vx
4V x 100
10 k
I sc
-
5 4 I sc Vs 6 100 Find Rout of the amplifier: 5 V x Vs 6
Chapter 10: Magnetically Coupled Networks
Problem 10.FE-3
2
Irwin, Basic Engineering Circuit Analysis, 9/E
5 4 x10 4 Vs V 6 100 10k Rout oc I sc 5 4 Vs 6 100 16a 2 10k a 25
Problem 10.FE-3
Chapter 10: Magnetically Coupled Networks
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c. Z1
ZL 2 2 (1 j1) 4 j 4 n2
1200 11.7711.31 A 6 j2 4 j4 I I2 1 n I 2 23.5411.31 A I1
Chapter 10: Magnetically Coupled Networks
Problem 10.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a. I1
V1 Z1
ZL n2 N n 2 2 N1 10 j10 Z1 2.5 j 2.5 22 1200 I1 24 j 24 A 2.5 j 2.5 I 24 j 24 I2 1 n 2 I 2 12 j12 A 16.97 45 A Z1
Chapter 10: Magnetically Coupled Networks
Problem 10.FE-5
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>
.
-
> 3
-
AN
AN
-
an
PF
36
o
A
/
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is d.
I 6 A rms VR 84.85V rms VL 84.85V rms
R
VR
L
I VL I
84.85 14.14 6
84.85 14.14 6
Z load 14.14 j14.14 2
S 3 3 I Z load S 3 36 14.14 j14.14 2
S 3 2.1645 kVA
Chapter 11: Polyphase Circuits
Problem 11.FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a.
Z 12 j12 Finding the equivalent per-phase wye: Z Y 4 j 4 5.6645 V AB 230 V rms
V AN
I aA
230 3
V AN ZY
132.79V rms
132.79 23.5 A rms 5.66
P3 3 V AN I aA cos Z 3(132.79)(23.5) cos 45 6.62kW
Chapter 11: Polyphase Circuits
Problem 11.FE-2
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is b. 24 j18 8 j 6 3 6 j 4
ZY1 ZY 2
V AB 208V rms
V AN
208
120V rms 3 1200 I aN 1 12 36.87 A 8 j6 1200 I aN 2 16.64 33.69 A 6 j4 I aA I aN 1 I aN 2 28.63 35.02 A rms
Chapter 11: Polyphase Circuits
Problem 11.FE-3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c. S 3 2430 kVA 20784.61 j12000 VA P3 20.78kW P1 6.93kW
Chapter 11: Polyphase Circuits
Problem 11.FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is d. By use of the power triangle: S 2 P2 Q2
Q S 2 P2
Q (100k ) 2 (90k ) 2 Q 43.59k var
Chapter 11: Polyphase Circuits
Problem 11.FE-5
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-/
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4
4
4
. .
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION:
The correct answer is a.
0
1 LC
1 1m(10 )
10,000
rad s
1 1 Z ( j 0 ) 60 60 90V V0 ( j 0 ) 120 c 60 2 10,000(10 )90 0 C90
Chapter 12: Variable – Frequency Network Performance
Problem 12. FE-1
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is c.
0
BW
1 LC
1 20m(50 )
1000
rad s
R rad 200 L s
R 200(20m) 4
Chapter 12: Variable – Frequency Network Performance
Problem 12. FE-2
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is d. 1 1 V0 ZC jC RC Gv ( j ) 1 1 VI Z C R R j jC RC at DC, Gv=1=0dB at 3dB down,
1 RC
rad 1 200 s (5k )(1 )
2f f
31.83 32 Hz 2
Chapter 12: Variable – Frequency Network Performance
Problem 12. FE-3
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is b.
0 L
1 LC
1000
rad s
1 1 100mH 2 0 C (1000) 2 (10 )
BW
R rad 100 L s
R 100m(100) 10
Chapter 12: Variable – Frequency Network Performance
Problem 12. FE-4
Irwin, Basic Engineering Circuit Analysis, 9/E
1
SOLUTION: The correct answer is a.
f 8 Hz , 1 16
rad s
1 j 2 k jC 1 1 j C RC Gv ( j 1 ) 1 1 R j jC RC ZC
For f=8Hz and 1=16 V0 ZC j 2000 G v ( j 1 ) 0.707 45 VS Z C R 2000 j 2000 Gv ( j16 ) 0.707 45
fC
1 1 7.96 8 Hz 2RC 2 (2k )(10 )
Chapter 12: Variable – Frequency Network Performance
Problem 12. FE-5
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S
C
C
S
C
S
C t
l
C
S
sC
C
S
C
C
S
C
S
C
C
S
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