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Exam 2 Solution

# Exam 2 Solution - ENME 350 Electronics and Instrumentation...

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Unformatted text preview: ENME 350 Electronics and Instrumentation | Fall 2011 Problem 1 [20 points] a. The circuit below is used to perform a test on two capacitors C1 and C2 (one capacitor at a time). Each capacitor has an initial voltage of 5 V. The voltage across C1 is v10) and the voltage across C2 is v2 (t) and both are plotted in the figure on the left. X 10000 Q W) C R: (i) [5 pts] Circle the correct statement (a) C1 = C2 A f“ /\ L : Q C L 2 7 (- l (b) C1 > C2 <5)“ :7 c2 x. --va.—- any (d) Sometimes C1 > C2 and sometimes Cl < C2. (ii) [5 pts] The time constant for the circuit when C2 is connected is approximately Jim-94:35; \V\ 7:2 Tim (m5), \J a ‘m it)? 7;? a a. (5)3215 sec g x ’37 : LgS' VON“ “A Z’ l 3,5 MA ‘27, (d) 3.5 sec (e) 5.0 sec Exam 2 Page 2 of9 2 Prof D Barker ENME 350 Electronics and Instrumentation | Fall 2011 Problem 1 - continued b. (5pts) Increasing the value of w in the circuit causes what change in the magnitude ofVc i _. W l V311: 'JLQC. “ + VC(t) _ A Increase N m L Decrease o 0 ‘w If No Change vs (I) c. (5pts) . If KG) =12€05(24t+30”) and i(t) = 25in(24t + 60°). The impedance of the circuit is i V5 0 ' Circuit , _ m V A « a ~. «’7‘ 4— 45m (24t+ 17;}: 2,9943%.413- i) Z '3: J "/ - 5e -: 5:4 L‘LL; Q) J /3 L , __ - I {Z 2 Q, J ‘9 —j6 Q Exam 2 Page 3 of 9 . Prof D Barker ENME 350 Electronics and instrumentation l Fall 2011 Problem 2 [30 pts]. A battery with an open circuit voltage Vb = 6V and an internal resistance Rb = 40 is used to charge a supercapacitor (Cm = 1F). The supercapacitor is used to power a wireless mouse. A. (5pts) Draw a circuit representing this charging circuit in the box below. ASL , rmwwmmlxﬁAqf‘xuwm ‘ con) B. (10pts) How long will it take (in seconds) to charge the supercapacitor to 95% of Vb? Assume the initial capacitor voltage is zero, VCm(0)=0 T95%charge : \ ‘1 l 9;?) “:2. I \ 1 .— “£7? \ \) - "ii/z“: C m .- ‘— 1: ‘35:) "Z l "' “Z4 (5. 1‘: -— /2':“ n, (Z; ‘ AD 6;} t;’ _ ﬂ l )a\ R»... 1 Exam 2 Page 4 of 9 » Prof D Barker ENME 350 Electronics and Instrumentationl Fall 2011 C. D. (5pts) You disconnect the charged supercapacitor from the battery and connect it to your wireless mouse modeled by a resistor Rm = lOkQ. Draw a circuit diagram representing this new circuit in the box below. (lOpts) How long will it take (in seconds) before a fully charged ( 100% charged) supercapacitor discharges to half if its initial voltage (at which point your mouse will cease to function)? T50% discharge : (b 9 % \ ‘27:. .I> \f‘” ‘ 1 q . ’5: VA 1, Mt), "L t; 5; Vt: Vt, Q. \/ vii/a?" (1:.L37—{Z U. L Exam 2 Page 5 of 9 . Prof D Barker ENME 350 Electronics and Instrumentation I Fall 2011 Problem 3 [20 points] For the circuit shown below, the circuit is in steady state prior to closing the switch. The switch is closed at t = 0. Circle the correct answer to each following guestion. 10 A10 20V a. [5 pts] The voltage across the capacitor at t = 0+ b. [5 pts] The steady state voltage across the capacitor (i.e., vc(t) as t ——> 00) is “VLV‘UL “'QE‘sig-f-or Q g V — 20 , + IQ — 1mm 2 559 “7.0 : —Z_0 1((0 )=1o A 1 3 3 ‘ (0+) 10 A .— M IF 2'— LC = - 7 d. [5 pts] Themtime constant for the circuit for t > 0, t = KM» w uh a: w; 0.333 sec 1 sec 15 sec 2 sec 3 sec none of these K Exam 2 Page 6 of 9 . Prof D Barker ENME 350 Electronics and Instrumentation | Fall 2011 Problem 4 [30 pts]. Your headphones are suffering from high frequency interference. Design a circuit consisting of a resistor (R) and an inductor (L) that passes low frequency signals from Vin to Vout and attenuates high frequency signals. A. (5pts) Draw a diagram of a circuit with these characteristics using one resistor (R) and one inductor (L). Clearly mark the input and output voltages Vin and Vout, including plus and minus signs. B. (5pts) Find the transfer function H060) = I:fl‘téjjzaﬂterms of R, L, and 0). ill . ”Q ........ l ............ HlJCOl = m». 2 L/ SmL‘l’Q Am 1;: Jr l V0l+¢( a) \Vl A1? Exam 2 Page 7 of 9 _ "MM wwmwwnw X \ l (VOL/EY— Prof D Barker ENME 350 Electronics and Instrumentation I Fall 2011 C. (10pts) Draw the magnitude portion of the Bode plot (piece-wise approximation) for the circuit you drew in part A. Label two different points (frequency in terms of R and L and magnitude) and any slopes. If you make a mistake on this Bode plot put a big X through the plot, as more plots are included on the last page of this exam. Circle the Bode plot with your answer. i [l D. (10pts) Derive a value for the inductor L as a function of R that results in a 40dB attenuation at f=100kHz. Exam 2 Page 8 of 9 . Prof D Barker ...
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Exam 2 Solution - ENME 350 Electronics and Instrumentation...

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