EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
KEY
Closed'Book/Closed'Notes'
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75'minutes'
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1. There'are'8'problems'on'this'exam'worth'a'total'of'100'points.''5$bonus$points$
are$available$for$question$5.$
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2. Calculators'without'communication'capability'are'allowed'on'the'exam,'but'
NO'laptops,'iPads,'iPods,'or'any'PDAs.'
3. You'must'circle'or'box'your'answers'to'get'full'credit.''Show'all'work'neatly'
and'clearly.'
4. Partial'credit'will'be'awarded,'provided'your'work'is'organized'and'readable.'
5. No'collaboration'is'allowed'during'the'exam!'Only'the'proctors'can'be'
consulted'for'clarification.''Cell'phones'must'be'turned'off!''
6. For'additional'work'space,'use'the'backside'of'exam'sheets'marking'clearly'and'
neatly'the'problem'#'and'circle'or'box'your'answer.''
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After'completing'the'exam,'please'sign'below.''You'MUST'
sign'this'statement'to'receive'credit'for'this'exam!'
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I'hereby'testify'that'I'have'neither'provided'nor'received'information'during'
this'exam,'and'that'this'exam'is'the'sole'product'of'my'efforts.'
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Signed:'
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Date:'
NOTICE:''All'work'must'be'shown'on'these'exam'sheets'for'credit'to'be'given.'
No'credit'will'be'given'for'work'not'shown.'Closed'Book.''One'8'½'x'11'Page'of'Notes.'
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
'
KEY
YOU'MAY'USE'THE'FOLLOWING'LAPLACE'TRANSFORM'TABLES'AND'THEOREMS'AS'REQUIRED'
BY'THE'QUESTION.'
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
Question'1.''
KEY
a. [5#points]#Convert#21710#to#binary.##Show#your#work#below.##
#
21710%% =%
=%
=%
=%
128%+%64%+%16%+%8%%+%1%
1*27%+%1*26%+%1*24%+%1*%23%+%1*20%
1*27%+%1*26%+%0*25%+%1*24%+%1*%23%+%0*22%+%0*%21%+%1*20%
110110012%
%
Grading%Rubric:%
%
If%correct%
%
%
%
%
(5%points)%
Else%%
If%highest%order%digit%is%1%% %
(1%point)%
%
%
If%lowest%order%digit%is%1%% %
(1%point)%
%
%
If%final%answer%is%wrong,%but%correct%powers%of%two%are%shown%(1%point)%%
#
Write#your#answer#here:###110110012%
#
b. [5#points]#Convert#001011002#to#decimal.##Show#your#work#below.##
#
001011002% =%%
0*27%+%0*26%+%1*25%+%0*24%+%1*%23%+%1*22%+%0*%21%+%0*20%
%
%
=%
1*25%+%1*%23%+%1*22%%%(zero%bits%have%not%value,%so%drop%them)%
%
%
=%
32%+%8%+%4%%
%
%
=%
4410%
%
Grading%Rubric:%
%
If%correct%
%
%
%
%
%
%
%
%
Else%If%answer%is%wrong%but%correct%powers%of%2%shown%% %
Else%If%wrong%answer%is%between%42%and%46%inclusive% %
#
Write#your#answer#here:%4410#
(5%points)%
(3%point)%%
(2%points)%
#
#
Question'2.'
You#are#building#a#robot#that#fires#Nerf®#darts#at#professors#when#they#walk#through#the#Hall#of#
Flags#in#the#College#of#Engineering.##The#robot#has#one#cannon.##The#cannon#holds#two#darts#but#
can#only#fire#one#a#time.#When#the#cannon#is#empty#(meaning,#it#has#0#darts),#the#robot#shuts#
down#and#waits#for#a#student#to#come#over#to#reload#the#cannon.#Your#job#is#to#design#the#
digital#control#circuit#that#decides#when#to#fire#the#cannon,#and#when#the#cannon#needs#to#be#
reloaded.##
#
#
#
The#control#circuit#outputs#are:#
• F#=#1#if#the#cannon#should#fire,#else#F=0.##
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
• R#=#1#if#the#cannon#need#to#be#reloaded,#else#R=0.#
#
#
The#control#circuit#inputs#are:#
• A1#=#1#if#one#dart#is#in#the#cannon,#else#A1#=##0.##
• A2#=#1#if#two#darts#are#in#the#cannon,#else#A2#=##0.###
• L#=#1#if#cannon#is#locked#on#to#a#professor,#else#L=0.#If#a#cannon#is#locked#on#to#a#
professor,#then#the#next#time#a#dart#is#fired,#the#dart#will#hit#the#professor.#
#
Answer#the#questions#below.#
a. [5#points]#Fill#in#the#truth#table#below.#
##
INPUTS'
OUTPUTS'
''''''A2'
'''''A1'
''''L'
''''''''F'
'''''''R'
0#
0#
0#
0#
1#
0#
0#
1#
0#
1#
0#
1#
0#
0#
0#
0#
1#
1#
1#
0#
1#
0#
0#
0#
0#
1#
0#
1#
1#
0#
1#
1#
0#
0#
0#
1#
1#
1#
1#
0#
#
Grading%Rubric:%
If%all%values%of%F%are%correct%%%
%
%
%
else%if%at%least%two%values%of%F%are%correct%
If%all%values%of%R%are%correct%%%
%
%
%
else%if%at%least%two%values%of%R%are%correct%
#
#
#
#
#
#
#
#
(2%points)%
(1%point)%
(2%points)%
(1%point)%
4
EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
b. [5#points]#Write#out#Boolean#equations#for#F#and#R.#Show#your#work#below.#
There is more than one right answer, depending on how you approach the problem.
Answer 1: F = A2’A1L + A2A1’L + A2A1L
Answer 2: F = L(A1+A2)
R = A2’A1’L’ + A2’A1’L
R = A1’A2’
Here are your options.
Answer 1: Sum of Products. OR the minterms where F = 1.
F = A2’A1L + A2A1’L + A2A1L
Repeat this for R.
R = A2’A1’L’ + A2’A1’L
It turns out these equations are more complex than necessary. There are some rules and axioms
that you can apply to the above equations to simplify them. Unfortunately, we haven’t covered
them in class. What else can we try?
Answer 2: Stare at the table. Make some observations. Note any patterns. See if you can
summarize the rows in words. For example:
We only fire when L=1 AND either A1 OR A2 or both are 1.
This means F = L(A1+A2)
R = 1 if both A1 AND A2 are 0.
This means R = A1’A2’
You can prove this to yourself by trying different values of the inputs and seeing that the outputs
match the truth table. Here is the final circuit:
Grading Rubric:
If F is correct
(2 points)
If R is correct
(2 points)
Note: full credit should be given if answers match the truth table above, even if
the truth table is wrong
#
Write#answers#here:#
#
Answer 1: F = A2’A1L + A2A1’L + A2A1L
R = A2’A1’L’ + A2’A1’L
Answer 2: F = L(A1+A2)
R = A1’A2’
5
EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
#
c. [5#points]#Draw#a#digital#circuit#for#the#equations#you#derived#in#part#b.##You#may#use#
inverters#as#well#as#2#and#3#input#AND#and#OR#gates.#
Answer 1: F = A2’A1L + A2A1’L + A2A1
R = A2’A1’L’ + A2’A1’L
#
#
#
Answer 2: F = L(A1+A2)
#
#
R = A1’A2’
#
If%F%is%correct%%%
%
%
(2%points)%
If%R%is%correct%%
%
%
(2%points)%
Note:%full%credit%should%be%given%if%answers%match%the%equations%above,%even%
if%the%equations%are%wrong%
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
'
Question'3.'
#
[10#points]#Complete#the#schematic#of#the#simple#microprocessor#shown#below.#Include#the#
major#components#discussed#in#class#and#the#wires#that#connect#those#components#together.##
Label#all#the#components.##
#
NOTE:#You#do#not#need#to#label#the#wires.##Do#not#add#input/output#to#the#diagram.#
Grading%Rubric:%
%
Presence%of%memory%%/%storage%%%%%%%% (2%points)%
%
Presence%of%(sequence)%controller%% (2%points)%
%
Presence%of%ALU%%
%
%
%
%
%
Presence%of%two%inputs%to%ALU%
If%both%inputs%are%from%memory% %
%
%
If%just%one%input%is%from%memory% %
%
%
If%just%one%input%is%from%seq.%controller%%
%
%
If%both%b%and%c%%
%
%
%
%
Wire%from%Seq.%Controller%to%Memory%
%
%
Wire%from%Seq.%Controller%to%SIDE%of%ALU%% %
#
#
(2%points)%
(2%points)%
(1%point)%
(1%point)%
(2%points)%
(1%point)%
(1%point)%
#
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
Question'4.'
'[15'points,'a`h'1'pt.'each,'i`j'2'pts.,'k'3'pts.]#Given#the#sinusoidal#voltage#and#current#below,#
answer#the#questions#a#through#k.'
################## #
#
#
#
## #
v(t)#=#20#cos#(100πt#]#45°)#V### #
###i(t)#=#10#cos#(100πt#+#60°)##A#
a.
What#is#the#maximum#amplitude?##Vm#=#####20#V##
###Im#=######10#A###############'
b.
What#is#the#RMS#value?#Vrms=##Vm/#√2#=#14.1#V####Irms#=##Im/#√2#=#7.07#A'
c. What#is#the#angular#frequency#in#rad/s?#ωv#=#100π#=#314#rad/s'''ωi#=#100π#=#314#rad/s''''
d.
What#is#the#frequency#in#Hz?##fv#=#######50#Hz########fi#=#####50#Hz########'
e.
What#is#the#phase#angle#in#degrees?#θv#=#####]#45#°########_##θi#=######60#°#########'
f.
What#is#the#phase#angle#in#radians?#θv#=#]0.785________###θi#=#_1.04________###'
Radians#=#Degrees/180##X#π#
g.
What#is#the#period#in#ms?#Tv#=#######20#ms#########Ti#=########20#ms######'
h.
What#is#the#phasor#voltage#and#current#in#polar#form?#V#=#####20∠]45°####I#=#####10∠60°####'
i.
State#the#phase#relationship#between#V#and#I#(lead,#lag).#########I#leads#V#by#105#°#####
j.
At#what#time,#t,#after#t=0s#does#I#=#]10A?#_####6.67#ms#####
I#=#]10#=#10#cos#(100π#t#+#60°)#
cos#(100π#t#+#60°)#=#]1##when#100πt#+#60°#=#180°,#since#cos#(180°)#=#]1#
then#t#=#120°/100π###X###π/180°#=#6.67#ms#
k.
Find#the#average#power#of#a#circuit#element#having#these#voltage#and#current#values.##
#
Resistive#Load##Pav#=#Irms#X##Vrms#=##99.687#W#
Capacitive#Load##Pav#=#Irms#X##Vrms#cos(θv#]#θi)#=##24.9#W#when#(θv#]#θi)#is#
negative#
Inductive#Load##Pav#=#Irms#X##Vrms#cos(θv#]#θi)#when#(θv#]#θi)#is#positive#
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
Question'5.'
KEY
Answer#the#following#questions#for#the#circuit#below.#
#
#
#
#
#
#
#
#
a.#[1#point]#What#is#the#RMS#magnitude#of#the#voltage#source?#
#
#
#
#
#
b.##[1#point]#Express#the#voltage#source#(100cos#(104t))#as#a#phasor##
in#polar#form#with#RMS#magnitude.#
#
#
#
#
#
c.##[2#points]#What#is#the#complex#impedance#of#the#inductor,#
ZL?#(in#ohms)#
#
#
#
#
#
#
#
#
d.##[2#points]#What#is#the#complex#impedance#of#the#capacitor,#
ZC?#(in#ohms)#
#
#
#
70.7 V
70.7∠0° V
ZL = j100 Ω
ZC = -j100 Ω
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
#
#
e.##[2#points]#What#is#the#complex#impedance#of#the##
resistor#and#capacitor#in#parallel,#ZRC?#(in#ohms)#
Hint:'100'–'j100'`>'141/`45°'
KEY
ZRC = 70.7∠-45° Ω
#
#
f.##[2#points]#What#is#the#phasor'polar'form#of#the#total#impedance,#Ztotal,#of#the#circuit?#
Hint:'70.7/`45°'`>'50'–'j50'
#
#
# Z
total = 70.7∠45° Ω
#
#
g.#[5#points]#What#is#phasor#i'in#polar#form#and#corresponding#i(t)#in#time#domain?###
'[5'bonus'points'question]#Also#find#ir(t)#and#ic(t)#in#time#domain#if#radial#frequency,#ω#=#0?##
#
I'='V/'ZTotal'='100∠0°/'70.7'∠45°##=#1.41∠]45°##A#
I(t)#=#1.41#cos#(104t#–#45°)#A#
For#ω#=#0,##Voltage#divider#gives#Vr#=##[ZR#/#(ZR#+#ZL)]#x#100#=#100#since'ZL#=#
jϖL#=#0#for#ϖ#=#0#;#then#Ir#=#Vr/Zr#=#1A,##
then#ir(t)#=##cos#(104t)#A;#for#w#=0,#ir(t)#=#1#A#
and#Ic#=#Vr/Zc#=#0,#since##Zc#=#1/jϖC##does#not#exist#for#ϖ#=#0#
then#for#w=0,#ic(t)#=#0#A#
i'
i#(t)#
4
1.41∠]45°##A' 1.41#cos#(10 t#–#45°)#A#
'
[3#points]#
[2#points]#
ir#(t)#for#w#=#0#
ic#(t)#for#w#=#0#
1#A#
#0#A#
[3'bonus'points]'
[2'bonus'points]'
'
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
Question'6.'
KEY
[10#points]#For#the#given#circuit#below,#find#the#loop#current#i(t)#when#the#input#f(t)#=#10u(t),#
i.e.,#f(t)#=#10,#for#t≥0,#f(t)#=#0#otherwise.##Show#your#work#and#circle#your#answer#below.'
#
#
#
#
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
Name ________________________________________________(U Number)
#
Question'7.'
For#the#system#block#diagram#below,#answer#the#following#questions.#
KEY
#
a. [10#points]#Find#the#transfer#function#T(s)#=#Y(s)/R(s).##Show#your#work#below.#
#
#
#
#
#
b. [5#points]#Use#Final#value#theorem#to#find#the#output#of#the#system#if#the#input#is
f1 (t) = 3, t ≥ 0 #when#t#]>#∞.#
#
#
#
#
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EGN 3373, Introduction to Electrical Systems I
EXAM #2 (Fall, 2013)
KEY
Name ________________________________________________(U Number)
Question'8.'
#
State#the#stability#–#stable#or#unstable#–#of#the#system#given#below.##You'have'to'show'all'your'
work'clearly'to'get'credit.#
#
#
#
a. [5#points]#If#K#=#10?#
1
1
Y (s)
1
= s −3 s +5 = 2
1
R( s) 1 + 1
K s + 2 s − 15 + K
s −3 s +5
#
#
1
s 2 + 2s − 15 + K
=
with K =10
1
, s = -3.4495 and1.4495
s 2 + 2s − 5
#
One'pole'has'positive'real'part.'This'will'make'system'unstable'
b. [5#points]#If#K#=#20?#
#
1
s 2 + 2s − 15 + K
with K = 20
1
= 2
, s = -1 ± 2 j
s + 2s + 5
#
Both'Poles'have'negative'real'part.'This'system'is'stable.#
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