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EENG 3305
Linear Circuit Analysis II
Final Exam
December 14, 2013
Name:
Answer the questions in the spaces provided on the question
sheets. If you run
out of room for an answer, continue on the back of the page.
Please complete
the exam in pencil and clearly denote the final answer. Except
where trivial,
show all work!
Question Points Bonus Points Score
1 10 0
2 5 0
3 5 0
4 5 0
5 5 0
6 10 0
7 10 0
8 4 0
9 6 0
10 10 0
11 5 0
12 10 0
13 5 0
14 10 0
15 0 8
16 0 7
Total: 100 15
EENG 3305 Final Exam - Page 1 of 11 December 12, 2013
1. [10 points] Determine the Fourier coefficients a1, a2, a3, a4
and b1, b2, b3, b4 of the rectified
cosine wave shown below
−2 2 4 6 8 10 12
2
4
t
f(t)
EENG 3305 Final Exam - Page 2 of 11 December 12, 2013
2. [5 points] If the rectangular pulse shown below is applied to
the circuit, also shown
below, find v0 at t = 1s.
1 2 3
2
4
6
t
vs(t)
+
−vs(t)
2 Ω
2 Ω 1 H
+
−
v0
Page 2
EENG 3305 Final Exam - Page 3 of 11 December 12, 2013
3. [5 points] Find the transfer function
Io(ω)
Is(ω)
for the following circuit
is(t) 2 Ω 1 H 4 Ω
i0(t)
Page 3
EENG 3305 Final Exam - Page 4 of 11 December 12, 2013
4. [5 points] Obtain the Fourier Transform of the following
function
−4 −1 1 4
−2
2
t
vs(t)
Page 4
EENG 3305 Final Exam - Page 5 of 11 December 12, 2013
5. [5 points] Use the convolution integral to find e−2tu(t) ∗
e−3tu(t)
6. [10 points] Given that the circuit is initially at rest use the
Laplace transform to solve
the differential equation
d2v(t)
dt2
+ 12
dv(t)
dt
+ 35v(t) = e−2t
.
Page 5
EENG 3305 Final Exam - Page 6 of 11 December 12, 2013
7. For the circuit below
+
−60u(t)
2 Ω
+ −
vo(t)
2 H 2 Ω
(a) [2 points] Write the integrodifferential equation for vo(t)
assuming no initial condi-
tions in the circuit.
(b) [2 points] Convert the equation you obtained in the previous
part to the Laplace
domain.
(c) [2 points] Find the transfer function if the output of interest
is the 1Ω resistor
voltage.
(d) [2 points] Calculate the impulse response of the system.
(e) [2 points] Calculate the step response of the system.
Page 6
EENG 3305 Final Exam - Page 7 of 11 December 12, 2013
8. A circuit consisting of a coil with inductance 10mH and
resistance 20Ω is connected in
series with a capacitor and a generator with an RMS voltage of
120V. Find:
(a) [2 points] the value of the capacitance that will clause the
circuit to be in resonance
at 15kHz
(b) [2 points] the current through the coil at resonance
9. The circuit parameters for a series RLC bandstop filter are R
= 2kΩ, L = 1H, C = 40pF.
Calculate
(a) [2 points] the center frequency
(b) [2 points] the half-power frequencies
(c) [2 points] the quality factor
Page 7
EENG 3305 Final Exam - Page 8 of 11 December 12, 2013
10. [10 points] Find the y parameters for the following circuit
4 Ω 6 Ω
ix
2 Ω
3ix
11. [5 points] A balanced delta-connected load has line current
Ia = 5 −30◦A. Find the
phase currents IAB, IBC, ICA.
Page 8
EENG 3305 Final Exam - Page 9 of 11 December 12, 2013
12. Three 230V generators form a delta-connected sourced that
is connected to a balanced
delta-connected load of ZL = 10 + j10 Ω per phase.
(a) [5 points] Determine the value of IAC
(b) [5 points] Is the load inductive or capacitive?
13. [5 points] A three-phase balanced system with a line voltage
of 300V RMS feeds a delta-
connected load with ZP = 75 70
◦Ω. Find the line current.
Page 9
EENG 3305 Final Exam - Page 10 of 11 December 12, 2013
14. [10 points] Sketch the magnitude and phase plots for
G(s) =
s
(s + 2)
2
(s + 10)
Page 10
EENG 3305 Final Exam - Page 11 of 11 December 12, 2013
15. [8 points (bonus)] In the ideal transformer circuit in the
circuit below, find Vo and the
complex power supplied by the source
+
−240 0◦
2 Ω 16 Ω
−j24
1 : 8
16. [7 points (bonus)] Find the input impedance of the circuit
below and the current from
the voltage source
+
−240 60◦
4 Ω 16 Ω
6 Ω
j4Ω
j3Ω
Page 11
Appendix D
Present value interest factor of an (ordinary) annuity of $1 per
period at i% for n periods, PVIFA(i,n).
P
e
rio
d
s
Rate per period
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
16% 17% 18% 19% 20%
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917
0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847
0.840 0.833
2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759
1.736 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566
1.547 1.528
3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531
2.487 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174
2.140 2.106
4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240
3.170 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690
2.639 2.589
5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890
3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127
3.058 2.991
6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486
4.355 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498
3.410 3.326
7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033
4.868 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812
3.706 3.605
8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535
5.335 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078
3.954 3.837
9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995
5.759 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303
4.163 4.031
10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418
6.145 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494
4.339 4.192
11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139
6.805 6.495 6.207 5.938 5.687 5.453 5.234 5.029 4.836
4.656 4.486 4.327
12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536
7.161 6.814 6.492 6.194 5.918 5.660 5.421 5.197 4.988
4.793 4.611 4.439
13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904
7.487 7.103 6.750 6.424 6.122 5.842 5.583 5.342 5.118
4.910 4.715 4.533
14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244
7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229
5.008 4.802 4.611
15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559
8.061 7.606 7.191 6.811 6.462 6.142 5.847 5.575 5.324
5.092 4.876 4.675
16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851
8.313 7.824 7.379 6.974 6.604 6.265 5.954 5.668 5.405
5.162 4.938 4.730
17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122
8.544 8.022 7.549 7.120 6.729 6.373 6.047 5.749 5.475
5.222 4.990 4.775
18 16.398 14.992 13.754 12.659 11.690 10.828 10.059
9.372 8.756 8.201 7.702 7.250 6.840 6.467 6.128 5.818
5.534 5.273 5.033 4.812
19 17.226 15.678 14.324 13.134 12.085 11.158 10.336
9.604 8.950 8.365 7.839 7.366 6.938 6.550 6.198 5.877
5.584 5.316 5.070 4.843
20 18.046 16.351 14.877 13.590 12.462 11.470 10.594
9.818 9.129 8.514 7.963 7.469 7.025 6.623 6.259 5.929
5.628 5.353 5.101 4.870
25 22.023 19.523 17.413 15.622 14.094 12.783 11.654
10.675 9.823 9.077 8.422 7.843 7.330 6.873 6.464 6.097
5.766 5.467 5.195 4.948
30 25.808 22.396 19.600 17.292 15.372 13.765 12.409
11.258 10.274 9.427 8.694 8.055 7.496 7.003 6.566 6.177
5.829 5.517 5.235 4.979
35 29.409 24.999 21.487 18.665 16.374 14.498 12.948
11.655 10.567 9.644 8.855 8.176 7.586 7.070 6.617 6.215
5.858 5.539 5.251 4.992
40 32.835 27.355 23.115 19.793 17.159 15.046 13.332
11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233
5.871 5.548 5.258 4.997
50 39.196 31.424 25.730 21.482 18.256 15.762 13.801
12.233 10.962 9.915 9.042 8.304 7.675 7.133 6.661 6.246
5.880 5.554 5.262 4.999
Appendix C
Present value interest factor of $1 per period at i% for n
periods, PVIF(i,n).
P
e
rio
d
s
RATE PER PERIOD
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
16% 17% 18% 19% 20%
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917
0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847
0.840 0.833
2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842
0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718
0.706 0.694
3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772
0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609
0.593 0.579
4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708
0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516
0.499 0.482
5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650
0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437
0.419 0.402
6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596
0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370
0.352 0.335
7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547
0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314
0.296 0.279
8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502
0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266
0.249 0.233
9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460
0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225
0.209 0.194
10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422
0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191
0.176 0.162
11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388
0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162
0.148 0.135
12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356
0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137
0.124 0.112
13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326
0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116
0.104 0.093
14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299
0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099
0.088 0.078
15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275
0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084
0.074 0.065
16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252
0.218 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071
0.062 0.054
17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231
0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060
0.052 0.045
18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212
0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051
0.044 0.038
19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194
0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043
0.037 0.031
20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178
0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037
0.031 0.026
25 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116
0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016
0.013 0.010
30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075
0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007
0.005 0.004
35 0.706 0.500 0.355 0.253 0.181 0.130 0.094 0.068 0.049
0.036 0.026 0.019 0.014 0.010 0.008 0.006 0.004 0.003
0.002 0.002
40 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.032
0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001
0.001 0.001
50 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013
0.009 0.005 0.003 0.002 0.001 0.001 0.001 0.000 0.000
0.000 0.000
Appendix A
Future value interest factor of $1 per period at i% for n periods,
FVIF(i,n).
P
e
rio
d
s
RATE PER PERIOD
1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.100
2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188
1.210
3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
1.331
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412
1.464
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539
1.611
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677
1.772
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828
1.949
8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993
2.144
9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172
2.358
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367
2.594
11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580
2.853
12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813
3.138
13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066
3.452
14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342
3.797
15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642
4.177
16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970
4.595
17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328
5.054
18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717
5.560
19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142
6.116
20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604
6.727
25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623
10.835
30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063
13.268 17.449
35 1.417 2.000 2.814 3.946 5.516 7.686 10.677 14.785
20.414 28.102
40 1.489 2.208 3.262 4.801 7.040 10.286 14.974 21.725
31.409 45.259
50 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902
74.358 117.391
Future value interest factor of $1 per period at i% for n periods,
FVIF(i,n).
P
e
rio
d
s
RATE PER PERIOD
11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190
1.200
2 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416
1.440
3 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685
1.728
4 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005
2.074
5 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386
2.488
6 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840
2.986
7 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379
3.583
8 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021
4.300
9 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785
5.160
10 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.695
6.192
11 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777
7.430
12 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064
8.916
13 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596
10.699
14 4.310 4.887 5.535 6.261 7.076 7.988 9.007 10.147
11.420 12.839
15 4.785 5.474 6.254 7.138 8.137 9.266 10.539 11.974
13.590 15.407
16 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129
16.172 18.488
17 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672
19.244 22.186
18 6.544 7.690 9.024 10.575 12.375 14.463 16.879 19.673
22.901 26.623
19 7.263 8.613 10.197 12.056 14.232 16.777 19.748 23.214
27.252 31.948
20 8.062 9.646 11.523 13.743 16.367 19.461 23.106 27.393
32.429 38.338
25 13.585 17.000 21.231 26.462 32.919 40.874 50.658
62.669 77.388 95.396
30 22.892 29.960 39.116 50.950 66.212 85.850 111.065
143.371 184.675 237.376
35 38.575 52.800 72.069 98.100 133.176 180.314 243.503
327.997 440.701 590.668
40 65.001 93.051 132.782 188.884 267.864 378.721
533.869 750.378 1,051.668 1,469.772
50 184.565 289.002 450.736 700.233 1,083.657 1,670.704
2,566.215 3,927.357 5,988.914 9,100.438
ACC206 Week Five Problems
Please complete the following 5 exercises below in either Excel
or a word document (but must be single document). You must
show your work where appropriate (leaving the calculations
within Excel cells is acceptable). Save the document, and
submit it in the appropriate week using the Assignment
Submission button.
1. Basic present value calculations
Calculate the present value of the following cash flows,
rounding to the nearest dollar:
a. A single cash inflow of $12,000 in five years, discounted at a
12% rate of return.
b. An annual receipt of $16,000 over the next 12 years,
discounted at a 14% rate of return.
c. A single receipt of $15,000 at the end of Year 1 followed by
a single receipt of $10,000 at the end of Year 3. The company
has a 10% rate of return.
d. An annual receipt of $8,000 for three years followed by a
single receipt of $10,000 at the end of Year 4. The company has
a 16% rate of return.
2. Cash flow calculationsand net present value
On January 2, 20X1, Bruce Greene invested $10,000 in the
stock market and purchased 500 shares of Heartland
Development, Inc. Heartland paid cash dividends of $2.60 per
share in 20X1 and 20X2; the dividend was raised to $3.10 per
share in 20X3. On December 31, 20X3, Greene sold his
holdings and generated proceeds of $13,000. Greene uses the
net-present- value method and desires a 16% return on
investments.
a. Prepare a chronological list of the investment's cash flows.
Note: Greene is entitled to the 20X3 dividend.
b. Compute the investment's net present value, rounding
calculations to the nearest dollar.
c. Given the results of part (b), should Greene have acquired the
Heartland stock? Briefly explain.
3. Straightforwardnet present value and internal rate of return
The City of Bedford is studying a 600-acre site on Route 356
for a new landfill. The startup cost has been calculated as
follows:
Purchase cost: $450 per acre
Site preparation: $175,000
The site can be used for 20 years before it reaches capacity.
Bedford, which shares a facility in Bath Township with other
municipalities, estimates that the new location will save
$40,000 in annual operating costs.
a. Should the landfill be acquired if Bedford desires an 8%
return on its investment? Use the net-present-value method to
determine your answer.
4. Straightforward net-present-value and payback computations
STL Entertainment is considering the acquisition of a sight-
seeing boat for summer tours along the Mississippi River. The
following information is available:
Cost of boat
$500,000
Service life
10 summer seasons
Disposal value at the end of 10 seasons
$100,000
Capacity per trip
300 passengers
Fixed operating costs per season (including straight-line
depreciation)
$160,000
Variable operating costs per trip
$1,000
Ticket price
$5 per passenger
All operating costs, except depreciation, require cash outlays.
On the basis of similar operations in other parts of the country,
management anticipates that each trip will be sold out and that
120,000 passengers will be carried each season. Ignore income
taxes.
Instructions:
By using the net-present-value method, determine whether STL
Entertainment should acquire the boat. Assume a 14% desired
return on all investments- round calculations to the nearest
dollar.
5. Equipment replacement decision
Columbia Enterprises is studying the replacement of some
equipment that originally cost $74,000. The equipment is
expected to provide six more years of service if $8,700 of major
repairs are performed in two years. Annual cash operating costs
total $27,200. Columbia can sell the equipment now for
$36,000; the estimated residual value in six years is $5,000.
New equipment is available that will reduce annual cash
operating costs to $21,000. The equipment costs $103,000, has a
service life of six years, and has an estimated residual value of
$13,000. Company sales will total $430,000 per year with either
the existing or the new equipment. Columbia has a minimum
desired return of 12% and depreciates all equipment by the
straight-line method.
Instructions:
a. By using the net-present-value method, determine whether
Columbia should keep its present equipment or acquire the new
equipment. Round all calculations to the nearest dollar, and
ignore income taxes.
b. Columbia's management feels that the time value of money
should be considered in all long-term decisions. Briefly discuss
the rationale that underlies management's belief.

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EENG 3305Linear Circuit Analysis IIFinal ExamDecembe.docx

  • 1. EENG 3305 Linear Circuit Analysis II Final Exam December 14, 2013 Name: Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Please complete the exam in pencil and clearly denote the final answer. Except where trivial, show all work! Question Points Bonus Points Score 1 10 0 2 5 0 3 5 0 4 5 0 5 5 0 6 10 0
  • 2. 7 10 0 8 4 0 9 6 0 10 10 0 11 5 0 12 10 0 13 5 0 14 10 0 15 0 8 16 0 7 Total: 100 15 EENG 3305 Final Exam - Page 1 of 11 December 12, 2013 1. [10 points] Determine the Fourier coefficients a1, a2, a3, a4 and b1, b2, b3, b4 of the rectified cosine wave shown below −2 2 4 6 8 10 12 2 4
  • 3. t f(t) EENG 3305 Final Exam - Page 2 of 11 December 12, 2013 2. [5 points] If the rectangular pulse shown below is applied to the circuit, also shown below, find v0 at t = 1s. 1 2 3 2 4 6 t vs(t) + −vs(t) 2 Ω 2 Ω 1 H + −
  • 4. v0 Page 2 EENG 3305 Final Exam - Page 3 of 11 December 12, 2013 3. [5 points] Find the transfer function Io(ω) Is(ω) for the following circuit is(t) 2 Ω 1 H 4 Ω i0(t) Page 3 EENG 3305 Final Exam - Page 4 of 11 December 12, 2013 4. [5 points] Obtain the Fourier Transform of the following function −4 −1 1 4 −2 2 t vs(t)
  • 5. Page 4 EENG 3305 Final Exam - Page 5 of 11 December 12, 2013 5. [5 points] Use the convolution integral to find e−2tu(t) ∗ e−3tu(t) 6. [10 points] Given that the circuit is initially at rest use the Laplace transform to solve the differential equation d2v(t) dt2 + 12 dv(t) dt + 35v(t) = e−2t . Page 5 EENG 3305 Final Exam - Page 6 of 11 December 12, 2013 7. For the circuit below + −60u(t)
  • 6. 2 Ω + − vo(t) 2 H 2 Ω (a) [2 points] Write the integrodifferential equation for vo(t) assuming no initial condi- tions in the circuit. (b) [2 points] Convert the equation you obtained in the previous part to the Laplace domain. (c) [2 points] Find the transfer function if the output of interest is the 1Ω resistor voltage. (d) [2 points] Calculate the impulse response of the system. (e) [2 points] Calculate the step response of the system. Page 6 EENG 3305 Final Exam - Page 7 of 11 December 12, 2013 8. A circuit consisting of a coil with inductance 10mH and resistance 20Ω is connected in series with a capacitor and a generator with an RMS voltage of 120V. Find: (a) [2 points] the value of the capacitance that will clause the
  • 7. circuit to be in resonance at 15kHz (b) [2 points] the current through the coil at resonance 9. The circuit parameters for a series RLC bandstop filter are R = 2kΩ, L = 1H, C = 40pF. Calculate (a) [2 points] the center frequency (b) [2 points] the half-power frequencies (c) [2 points] the quality factor Page 7 EENG 3305 Final Exam - Page 8 of 11 December 12, 2013 10. [10 points] Find the y parameters for the following circuit 4 Ω 6 Ω ix 2 Ω 3ix 11. [5 points] A balanced delta-connected load has line current Ia = 5 −30◦A. Find the phase currents IAB, IBC, ICA. Page 8
  • 8. EENG 3305 Final Exam - Page 9 of 11 December 12, 2013 12. Three 230V generators form a delta-connected sourced that is connected to a balanced delta-connected load of ZL = 10 + j10 Ω per phase. (a) [5 points] Determine the value of IAC (b) [5 points] Is the load inductive or capacitive? 13. [5 points] A three-phase balanced system with a line voltage of 300V RMS feeds a delta- connected load with ZP = 75 70 ◦Ω. Find the line current. Page 9 EENG 3305 Final Exam - Page 10 of 11 December 12, 2013 14. [10 points] Sketch the magnitude and phase plots for G(s) = s (s + 2) 2 (s + 10) Page 10
  • 9. EENG 3305 Final Exam - Page 11 of 11 December 12, 2013 15. [8 points (bonus)] In the ideal transformer circuit in the circuit below, find Vo and the complex power supplied by the source + −240 0◦ 2 Ω 16 Ω −j24 1 : 8 16. [7 points (bonus)] Find the input impedance of the circuit below and the current from the voltage source + −240 60◦ 4 Ω 16 Ω 6 Ω j4Ω j3Ω Page 11
  • 10. Appendix D Present value interest factor of an (ordinary) annuity of $1 per period at i% for n periods, PVIFA(i,n). P e rio d s Rate per period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589
  • 11. 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533
  • 12. 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 6.604 6.265 5.954 5.668 5.405 5.162 4.938 4.730 17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 6.729 6.373 6.047 5.749 5.475 5.222 4.990 4.775 18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812 19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843 20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 7.025 6.623 6.259 5.929 5.628 5.353 5.101 4.870 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 30 25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.694 8.055 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.979
  • 13. 35 29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567 9.644 8.855 8.176 7.586 7.070 6.617 6.215 5.858 5.539 5.251 4.992 40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 50 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 9.042 8.304 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999 Appendix C Present value interest factor of $1 per period at i% for n periods, PVIF(i,n). P e rio d s RATE PER PERIOD 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
  • 14. 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194
  • 15. 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054 17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038
  • 16. 19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 25 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 35 0.706 0.500 0.355 0.253 0.181 0.130 0.094 0.068 0.049 0.036 0.026 0.019 0.014 0.010 0.008 0.006 0.004 0.003 0.002 0.002 40 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001 50 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0.009 0.005 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 Appendix A
  • 17. Future value interest factor of $1 per period at i% for n periods, FVIF(i,n). P e rio d s RATE PER PERIOD 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210
  • 18. 3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797
  • 19. 15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.835 30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 17.449 35 1.417 2.000 2.814 3.946 5.516 7.686 10.677 14.785 20.414 28.102 40 1.489 2.208 3.262 4.801 7.040 10.286 14.974 21.725 31.409 45.259 50 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902 74.358 117.391 Future value interest factor of $1 per period at i% for n periods,
  • 20. FVIF(i,n). P e rio d s RATE PER PERIOD 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200 2 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 3 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 4 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 5 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488 6 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986 7 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 8 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021
  • 21. 4.300 9 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 10 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.695 6.192 11 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430 12 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916 13 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 14 4.310 4.887 5.535 6.261 7.076 7.988 9.007 10.147 11.420 12.839 15 4.785 5.474 6.254 7.138 8.137 9.266 10.539 11.974 13.590 15.407 16 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.172 18.488 17 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186 18 6.544 7.690 9.024 10.575 12.375 14.463 16.879 19.673 22.901 26.623 19 7.263 8.613 10.197 12.056 14.232 16.777 19.748 23.214 27.252 31.948 20 8.062 9.646 11.523 13.743 16.367 19.461 23.106 27.393
  • 22. 32.429 38.338 25 13.585 17.000 21.231 26.462 32.919 40.874 50.658 62.669 77.388 95.396 30 22.892 29.960 39.116 50.950 66.212 85.850 111.065 143.371 184.675 237.376 35 38.575 52.800 72.069 98.100 133.176 180.314 243.503 327.997 440.701 590.668 40 65.001 93.051 132.782 188.884 267.864 378.721 533.869 750.378 1,051.668 1,469.772 50 184.565 289.002 450.736 700.233 1,083.657 1,670.704 2,566.215 3,927.357 5,988.914 9,100.438 ACC206 Week Five Problems Please complete the following 5 exercises below in either Excel or a word document (but must be single document). You must show your work where appropriate (leaving the calculations within Excel cells is acceptable). Save the document, and submit it in the appropriate week using the Assignment Submission button. 1. Basic present value calculations Calculate the present value of the following cash flows, rounding to the nearest dollar: a. A single cash inflow of $12,000 in five years, discounted at a 12% rate of return. b. An annual receipt of $16,000 over the next 12 years, discounted at a 14% rate of return.
  • 23. c. A single receipt of $15,000 at the end of Year 1 followed by a single receipt of $10,000 at the end of Year 3. The company has a 10% rate of return. d. An annual receipt of $8,000 for three years followed by a single receipt of $10,000 at the end of Year 4. The company has a 16% rate of return. 2. Cash flow calculationsand net present value On January 2, 20X1, Bruce Greene invested $10,000 in the stock market and purchased 500 shares of Heartland Development, Inc. Heartland paid cash dividends of $2.60 per share in 20X1 and 20X2; the dividend was raised to $3.10 per share in 20X3. On December 31, 20X3, Greene sold his holdings and generated proceeds of $13,000. Greene uses the net-present- value method and desires a 16% return on investments. a. Prepare a chronological list of the investment's cash flows. Note: Greene is entitled to the 20X3 dividend. b. Compute the investment's net present value, rounding calculations to the nearest dollar. c. Given the results of part (b), should Greene have acquired the Heartland stock? Briefly explain. 3. Straightforwardnet present value and internal rate of return The City of Bedford is studying a 600-acre site on Route 356 for a new landfill. The startup cost has been calculated as follows: Purchase cost: $450 per acre Site preparation: $175,000 The site can be used for 20 years before it reaches capacity. Bedford, which shares a facility in Bath Township with other
  • 24. municipalities, estimates that the new location will save $40,000 in annual operating costs. a. Should the landfill be acquired if Bedford desires an 8% return on its investment? Use the net-present-value method to determine your answer. 4. Straightforward net-present-value and payback computations STL Entertainment is considering the acquisition of a sight- seeing boat for summer tours along the Mississippi River. The following information is available: Cost of boat $500,000 Service life 10 summer seasons Disposal value at the end of 10 seasons $100,000 Capacity per trip 300 passengers Fixed operating costs per season (including straight-line depreciation) $160,000 Variable operating costs per trip $1,000 Ticket price $5 per passenger All operating costs, except depreciation, require cash outlays. On the basis of similar operations in other parts of the country, management anticipates that each trip will be sold out and that 120,000 passengers will be carried each season. Ignore income taxes. Instructions: By using the net-present-value method, determine whether STL Entertainment should acquire the boat. Assume a 14% desired
  • 25. return on all investments- round calculations to the nearest dollar. 5. Equipment replacement decision Columbia Enterprises is studying the replacement of some equipment that originally cost $74,000. The equipment is expected to provide six more years of service if $8,700 of major repairs are performed in two years. Annual cash operating costs total $27,200. Columbia can sell the equipment now for $36,000; the estimated residual value in six years is $5,000. New equipment is available that will reduce annual cash operating costs to $21,000. The equipment costs $103,000, has a service life of six years, and has an estimated residual value of $13,000. Company sales will total $430,000 per year with either the existing or the new equipment. Columbia has a minimum desired return of 12% and depreciates all equipment by the straight-line method. Instructions: a. By using the net-present-value method, determine whether Columbia should keep its present equipment or acquire the new equipment. Round all calculations to the nearest dollar, and ignore income taxes. b. Columbia's management feels that the time value of money should be considered in all long-term decisions. Briefly discuss the rationale that underlies management's belief.
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