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Unformatted text preview: ECE 110  ' . September 17, 2007
Professors Brunet and Loui ' HOUR EXAMINATION #1 1) Write your:
Last Name (use capital letters): 30g“ ll 0 N S First Name (use capital letters):
 _ Signature: » 2) Write your name and section at the back of the test. DONOT TURN THIS PAGE UNTIL YOU ARE TOLD A. Write or print clearly. Answer each problem on the exam itself. If you
need extra paper, there is an extra sheet at the end of thisexam. Clearly
identify" the problem number on any additiOnal page‘s. ' ' B. In order to receive partial or full credit, you must show all your work,
e. g., your solution process, the equation(s) that you use, the values of the
variables used in the equation(s), etc. You must also include the unit of
measurement in each answer. Students caught cheating on this exam will earn a grade of F for the
entire course. Other penalties may include suspension and/or dismissal
' from the university. Problem 1 (20 points) Consider the circuit below. a (a) [2 pts.] Write a KCL equation for node a.
r“
(b) [2 pts.] Write a KVL equation that relates V1 and V2.
V \ 2 \' 7. + Cl (c) [4 pts.] Use Ohm’s Law to write equations that relate the currents I 1 and 12 to the voltages V1 and V2. \J\ 3' 51‘
(d) [8 pts.] Determine the voltage V2 and the currents I 1 and I2 and I3.
: \I
325 Km. \I c, . W,
I: \I /§2 G/Szl 2A
1': \I [2 =  [.524 1:43:  — —m
31.4% °~ m =m (e) [4 pts.] Is the 4 A current source a load or source of power? Ex lain our reasonin .
In SR8, tag. \I Masada. Cwnuft we: £4 ‘40",
4031; SR3 (A (a x4=~gzl+w. 52cm W%Wuﬂm)ﬁwz¢wu Problem 2 (20 points) A periodic voltage is applied to a DC motor whose efﬁciency is 78%.
Shown below are the graphs of motor voltage Vm and current 1",. I". (amPS) '0 I 21 31 51 61 _L_ ‘
F“ “3: goms=30xw’3.s
(a) [6 pts.] Determine the period and frequency of Vm. Period = Frequency = 33 . .73 “Z (bzlf6pts'1 Determine the RMS voltage Vrm . 8‘ x20 + Gal(”MO
V‘“ Av (‘13 '= 30 27533
‘3\ (a 94‘ \Ivms : '75. 33 )
o 10 30 M“ w— (c) [8 pts. ] Determine the time— a—veraged electrical power consumed by the motor. Show your work. , a (w
a, v, I 3 ”Wk“, M3263“:— ~36,“ (9.3M 3380“! ﬁnaCmS)
> 7» ‘Slavd Paver= 3.? w Problem 3 (20 points) The three identical dashboard lights in a car are controlled by a dimer.
We model the car battery by a 12 V ideal voltage source, the dashboard
lights by three identical resistors in parallel, and the dimer by a variable resistor R1. Suppose the equivalent resistance of the three dashboard lights is R; = 15 Q.
dimmer """""""""""""""""""""" dashboard
lights Rd=15 Q  (a) [5 pts.] Determine the value of R2. PW rwfom “a“ “1 ‘1‘ “1 = ”I I” R::(5x3‘: '45“— I)
my» (b) [6 pts. ] Using the Voltage Divider Rule, show that R1: 153—9 — 15.
R‘ d lgx W
343 V912) Vat: 12R: 1J7. :: ”2+6“
W 9 K. ‘ R" ‘ So (R +6)de (erz :\80 ‘
(8‘0 _‘g
Rug: lgO/Vd , and 2.: ”at (c) [9 pts.] Using (b), determine the value of R1 for which the total power Pd consumed by the
dashboard lights is 0.4 W. Show your work. Th [9W P4=VaIJ=V4(Va/m\=\/}/RJ =O.4 W
Wat VE=O~4W31g.,W \ld‘i O.4$l§':ﬁ w g8 FW£(b), R 23422—492: 1:9. ~(S__ ".S—g S—{L =— Problem 4 (15 points) 1.
1) 3Q IZVG 29 A value of R was given to Sam Genius, who solved the circuit and found that the SRS power
supplied by the voltage source is (—60 W). ' (a) [9 pts.] Find the current 1,, and voltage V1, and the SRS power p1 = V1 x 1,.
Since, {M 5115 (2‘10: ~60, mwmd’ Io =§ﬁ,
M I:  Io = 57*. “Men. \I; 1: x 7: ...stz — «le Vt; V‘XI‘: (55;: VSW (b) [6 pts.] Something does not seem to make sense. Sam must have made a mistake. Explain
what does not make sense in two sentences (provide a clear, detailed argument). In ’Olu. 3.9.— (Mfof "ISW 04.42 diléipmd and sz
LA Jiuim‘ﬁﬁd Wm 0'60! I’m/(3'66 ﬁ‘lﬁn ijwwg‘ WW raJJJCZJK 6 mVleageyaa—w «9.3 60W.
(MSW MM 6;; Wm! 1.391111% QUESILQIS ["0 Points}
What is the maximum power possible that can be supplied by the voltage source (in magnitude)
for any possible value of R? For‘ﬁm’di/m resident», Via. a NM (Manes: {A Problem 5 (10 points) The component C below has the I—V characteristic shown; the units are
amps and volts. C V I=0.4V~—7.2 (a) [5 pts.] Determine the current Im measured (b) [5 pts.] Determine the voltage Vm measured by the ideal ammeter below. Explain your by the ideal voltmeter below. Explain
reasoning. your reasoning.
I.
C‘ a
*—
c v a y»:
b Problem 6 (15 points) Answer the following questions (check one choice for each). net
(a) [2 pts.] The direction of a positive current indicates the direction of the glow of the electrons. 0 Always True UAIways False 0 It depends (b) [3 pts.] An ideal voltage source generates energy. 0 Always True 0 Always False Mt depends (c) [2 pts.] A resistor dissipates energy. Q/Always True 0 Always False 0 It depends (d) [3 pts.] KVL can be used on any circuit (with any circuit elements). ®/Always True 0 Always False 0 It depends (e) [2 pts.] The IV graph for a resistor is linear. Q/Always True 0 Always False Q It depends (f) [3 pts.] The RMS value of a signal is the peak value multiplied by «5 / 2 . 0 Always True 0 Always False (B/It depends ...
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