Summer09 Midterm1
~McGill ,,"'-/
April 2009
Midterm 1 Examination
y
Fundamentals of Electrical Engineering
ECSE 200
Section 1
19 May 2009, 9:35
Examiner: Thomas Szkopek
I Student Name: I
I
McGilIID:
III IIII IJJ
INSTRUCTIONS: • This is a CLOSED BOOK examination.
• SPACE IS PROVIDED on the examination to answer all questions. • STANDARD FACULTY CALCULATOR permitted ONLY. • This examination consists of 3 questions, each with multiple parts, for a total of 13 numbered pages, including the cover page. • Show ALL your work and indicate your final answer CLEARLY. • This examination is PRINTED ON BOTH SIDES of the paper. • This examination paper MUST BE RETURNED.
ECSE-200
Page 1 of 13
1. A battery is charged according to the plots below of the delivered charge and voltage. Note that "hrs"
=hours. [12pts]
Q
+ V
v
Q
--... I 2Ahrs battery
I
.....~-----I----+ t Ohrs
10 hrs
-1------1--+ t 10 hrs Ohrs
a) What is the total charge delivered to the battery during the charge cycle? Express your answer in SI units. [lpt] b) Plot the current (defined with a reference direction obeying passive sign convention on the battery) versus time over the interval-lhour < t < Ilhours. label the current axis in SI units. [2pts] c) Plot the instantaneous power absorbed by the battery over the interval -lhour < t < Ilhours? label the power axis in SI units. [2pts] d) What is the algebraic expression for the instantaneous power absorbed by the battery (expressed in terms of the time variable t alone) over the interval 0 < t < 10hours? [2pts] e) What is the total energy delivered to the battery during this charge cycle? Give your answer in SI units. [2pts] f) At what time t has the battery absorbed 50% of the total energy delivered to it by the charge cycle? [3pts]
ECSE-200
Page 2 of 13
work space
Q=
~ A ~~ ~ ~~o 0
So
=-
f ~~ kC
~V"
~OO....J~~.... _
0(&< \O'-'n
[+\1
__
----~------~--~~f
~ 0::: :l A~rs. ':. ~oo VI-\ A
--~--------~--~~ o \O~""s.
ECSE-200
Page 3 of 13
work space
e..)
LJ
--to-W
~
S
\a"w,
b
--
--
S
(1-l)
to\.,.,
" ( 'd..oO ....W + a.OO~W ~ \O~ys
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-.:
f q,1o, (-f-I) dt I
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'+-
\
-
~
aaow..vJ • \O~r~
-t ( ) J-t'
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( \OhrS')'
\O~Yi
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o = o
~
.'J..o o ""'W \Ohr~
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-c. '- -\" ~oo w-.w' -t - S ."\ k.. T
-t L.
+ ~oo~w t -
s. '-\ k:"S
5
ECSE-200 Page 4 of 13
C+ \]
work space
e. 't.u...""-\'-aV\
a..=
!
0
-=
0...
t '-~ \o-i. 1... + C
a."8)("\o-'
c..= -5.4x-\o
3
ECSE-200
Page 5 of 13
2. Consider the circuit below. [12pts]
+
3A 4V
a) What is the power absorbed by the 20 resistor? [2pts]
b) What is the power absorbed by the 170 resistor? [3pts]
c) What is the power absorbed by the 90 resistor? [lpt]
d) How much power does the 3A source deliver or absorb? Indicate clearly power
absorption or delivery. [2pts]
e) How much power does the SV source deliver or absorb? Indicate clearly power
absorption or delivery. [2pts]
f) How much power does the 4V source deliver or absorb? Indicate clearly power absorption or delivery. [2pts]
ECSE-200
Page 6 of 13
work space t.\"').
- ~ V -+ v~ -+ '-\ V ~ 0
kVl '.
v\ --:. 5\/ - 4\} ~ \ V
[+\j
o.SA
\,)
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+
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0
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I
~ \
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V
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6::, = 3A - ("
a...
\\1 - 3A· ~Jt-
'::.
1 f\
-\~.n..- ~~
ECSE-200
Page 7 of 13
work space
Co")
[t- \j
d)
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- 4v-
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"4
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~
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-- 4 V ~
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(4\]
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V
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[-\-\J
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= \ 1\ -
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'P o..'b s::' ~)
S\J. t
April 2009
Midterm 1 Examination
y
Fundamentals of Electrical Engineering
ECSE 200
Section 1
19 May 2009, 9:35
Examiner: Thomas Szkopek
I Student Name: I
I
McGilIID:
III IIII IJJ
INSTRUCTIONS: • This is a CLOSED BOOK examination.
• SPACE IS PROVIDED on the examination to answer all questions. • STANDARD FACULTY CALCULATOR permitted ONLY. • This examination consists of 3 questions, each with multiple parts, for a total of 13 numbered pages, including the cover page. • Show ALL your work and indicate your final answer CLEARLY. • This examination is PRINTED ON BOTH SIDES of the paper. • This examination paper MUST BE RETURNED.
ECSE-200
Page 1 of 13
1. A battery is charged according to the plots below of the delivered charge and voltage. Note that "hrs"
=hours. [12pts]
Q
+ V
v
Q
--... I 2Ahrs battery
I
.....~-----I----+ t Ohrs
10 hrs
-1------1--+ t 10 hrs Ohrs
a) What is the total charge delivered to the battery during the charge cycle? Express your answer in SI units. [lpt] b) Plot the current (defined with a reference direction obeying passive sign convention on the battery) versus time over the interval-lhour < t < Ilhours. label the current axis in SI units. [2pts] c) Plot the instantaneous power absorbed by the battery over the interval -lhour < t < Ilhours? label the power axis in SI units. [2pts] d) What is the algebraic expression for the instantaneous power absorbed by the battery (expressed in terms of the time variable t alone) over the interval 0 < t < 10hours? [2pts] e) What is the total energy delivered to the battery during this charge cycle? Give your answer in SI units. [2pts] f) At what time t has the battery absorbed 50% of the total energy delivered to it by the charge cycle? [3pts]
ECSE-200
Page 2 of 13
work space
Q=
~ A ~~ ~ ~~o 0
So
=-
f ~~ kC
~V"
~OO....J~~.... _
0(&< \O'-'n
[+\1
__
----~------~--~~f
~ 0::: :l A~rs. ':. ~oo VI-\ A
--~--------~--~~ o \O~""s.
ECSE-200
Page 3 of 13
work space
e..)
LJ
--to-W
~
S
\a"w,
b
--
--
S
(1-l)
to\.,.,
" ( 'd..oO ....W + a.OO~W ~ \O~ys
~ -- _. ;;t
-.:
f q,1o, (-f-I) dt I
;)..COw..W \O~r ...
'+-
\
-
~
aaow..vJ • \O~r~
-t ( ) J-t'
~OO~W
( \OhrS')'
\O~Yi
. 3Goos
"'...
\0. ~
k."J
L +\ '1 \o .. 8k."'"S .;t
o = o
~
.'J..o o ""'W \Ohr~
~ ~.l f"'J 81"W
-c. '- -\" ~oo w-.w' -t - S ."\ k.. T
-t L.
+ ~oo~w t -
s. '-\ k:"S
5
ECSE-200 Page 4 of 13
C+ \]
work space
e. 't.u...""-\'-aV\
a..=
!
0
-=
0...
t '-~ \o-i. 1... + C
a."8)("\o-'
c..= -5.4x-\o
3
ECSE-200
Page 5 of 13
2. Consider the circuit below. [12pts]
+
3A 4V
a) What is the power absorbed by the 20 resistor? [2pts]
b) What is the power absorbed by the 170 resistor? [3pts]
c) What is the power absorbed by the 90 resistor? [lpt]
d) How much power does the 3A source deliver or absorb? Indicate clearly power
absorption or delivery. [2pts]
e) How much power does the SV source deliver or absorb? Indicate clearly power
absorption or delivery. [2pts]
f) How much power does the 4V source deliver or absorb? Indicate clearly power absorption or delivery. [2pts]
ECSE-200
Page 6 of 13
work space t.\"').
- ~ V -+ v~ -+ '-\ V ~ 0
kVl '.
v\ --:. 5\/ - 4\} ~ \ V
[+\j
o.SA
\,)
\ -= •
G~
+
i~
-
~A
0
\I
I
~ \
L-t\IJ..J
V
[. -\-l(~' ]
=0
v;J.. -:;
'"(..
~.
liSL
e'" \(~ "1
"6
v~·
9J1
(+'r~J
t
=.
-\\1 -\r"jSl-' Ld-, + (tn. ~:?:,-= 0
6::, = 3A - ("
a...
\\1 - 3A· ~Jt-
'::.
1 f\
-\~.n..- ~~
ECSE-200
Page 7 of 13
work space
Co")
[t- \j
d)
kV L :
- 4v-
V3 -T
"4
=0
v\{ ~
~
4'-1
~ \/3
-- 4 V ~
~de\ -- 3A e.-)
'\1'1
=
~.I\
. d. a v
Z3'~J'-
'iV -\-
=-
-t
~'J..
~A .
(4\]
'.n
V
Gf;;; W
[-\-\J
kCL:
= \ 1\ -
0"
S- A
= o. S" A
'P o..'b s::' ~)
S\J. t
