ECE 20100 Spring 2015 Final Exam May 7, 2015 Section (circle below) Jung (1:30) 0001 Qi (12:30) 0002 Peleato (9:30) 0004 Allen (10:30) 0005 Zhu (4:30) 0006 Name PUID Instructions 1. DO NOT START UNTIL TOLD TO DO SO. 2. Write your name, section, professor, and student ID# on your Scantron sheet. We may check PUIDs. 3. This is a CLOSED BOOKS and CLOSED NOTES exam. 4. The use of a TI-30X IIS calculator is allowed, but not necessary. 5. If extra paper is needed, use the back of test pages. 6. Cheating will not be tolerated. Cheating in this exam will result in, at the minimum, an F grade for the course. In particular, continuing to write after the exam time is up is regarded as cheating. 7. If you cannot solve a question, be sure to look at the other ones, and come back to it if time permits. Course Learning Objective Exam Questions Total Points Possible Minimum Points Required to Satisfy Learning Objective i 1 6 54 27 ii 7 10 36 18 iii 11 16 54 27 1
Question 1: In the circuit below, the power absorbed by the voltage controlled current source, P dep, is: (1) P dep = 10 W (2) P dep = 6 W (3) P dep = 4 W (4) P dep = 2 W (5) P dep = 0 W (6) P dep = 2 W (7) P dep = 4 W (8) P dep = 6 W (9) P dep = 8 W (10) P dep = 10 W 2
Question 2: Find the value of the voltage source, V s, in the circuit below: V s (1) V s = -20 V (2) V s = -10 V (3) V s = -5 V (4) V s = 0 V (5) V s = 2 V (6) V s = 3 V (7) V s = 5 V (8) V s = 10V (9) V s = 20V (10) V s = 35V 3
Question 3. The loop current I 1 in the circuit below is (note the resistors are marked by their conductance): 0.2S -3A I 4 I 2 0.15S 440V -8A 0.05S 0.25S I O I 1 I 3 25A GND (1) I 1 = 3 A (2) I 1 = 0 A (3) I 1 = 4.5 A (4) I 1 = 5.0 A (5) I 1 = 5.5 A (6) I 1 = 6.0 A (7) I 1 = 6.5 A (8) I 1 = 7.0 A (9) I 1 = 7.5 A (10) I 1 = 8.0 A 4
Question 4: A device is connected to a circuit that has only two independent sources. Two identical measurements are made on the device with different independent sources turned on: Measurement A Source 1 is turned ON Source 2 is turned OFF Voltage drop across the device: V = 2V 1 Power absorbed by the device: P = 6 W 1 Measurement B Source 1 is turned OFF Source 2 is turned ON Voltage drop across the device: V = 1V 2 Current through the device: I = 1 A 2 Assume that the measured voltage drop and current through the device follow the passive sign convention. What is the power absorbed by the device when both sources are ON? (1) 6 W (2) 5 W (3) 4 W (4) 3 W (5) 1 W (6) 1 W (7) 3 W (8) 4 W (9) 5 W (10) 6 W 5
Question 5: In the circuit below, I 0 = 1 A, find I s and V s : (1) I s = 2 A; V s = 4 V (2) I s = 3 A; V s = 5 V (3) I s = 2 A; V s = 6 V (4) I s = 1 A; V s = 4 V (5) I s = 5 A; V s = 2 V (6) I s = 3 A; V s = 6 V (7) I s = 7 A; V s = 3 V (8) I s = 1 A; V s = 3 V (9) I s = 5 A; V s = 5 V (10) I s = 2 A; V s = 7 V 6
Question 6: In the circuit below, find R L so that V L =20 V: (1) R L = 1 Ω (2) R L = 2 Ω (3) R L = 4 Ω (4) R L = 7 Ω (5) R L = 10 Ω (6) R L = 13 Ω (7) R L = 15 Ω (8) R L = 18 Ω (9) R L = 20 Ω (10) R L = 25 Ω 7
Question 7: Find the Thevenin equivalent voltage seen by the inductor in the circuit below. (1) VTH (2) VTH (3) VTH (4) VTH (5) VTH (6) VTH (7) VTH (8) VTH (9) VTH (10) VTH 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 V 9 V 12 V 8
Question 8: What is the time constant,, of the following circuit? (1) 1 ms (2) 2 ms (3) 3 ms (4) 4 ms (5) 5 ms (6) 6 ms (7) 7 ms (8) 8 ms (9) 9 ms (10) 10 ms 9
Question 9: Find the zero-input component of the voltage across the capacitor for t > 0 if the voltage at time t = 0 - is V c (0 - ) = 15 V (with the plus sign on top). The zero-input component is due to only initial conditions. V C (t) + - (1) Vc(t) = 15 (2) Vc(t) = 15 exp(- t / 3) (3) Vc(t) = 15 exp(- 4*t / 3) (4) Vc(t) = 15 exp(- 2*t ) (5) Vc(t) = 15 exp(- 2*t / 3) (6) Vc(t) = 11 + 4 exp(- t / 2) (7) Vc(t) = 11-11 exp(- 3*t / 2) (8) Vc(t) = 11 + 22 exp(- 3*t) (9) Vc(t) = 11-4 exp(- t / 3) (10) None of the above 10
Question 10: Find the current through the inductor, I L, at t = (1) I L = - 1 A (2) I L = - 0.75 A (3) I L = - 0.5 A (4) I L = - 0.25 A (5) I L = 0 A (6) I L = 0.25 A (7) I L = 0.5 A (8) I L = 0.75 A (9) I L = 1 A (10) None of the above 11
Question 11: Find the voltage OUT. Assume the op-amps are ideal. 3cos t V 1 1 2 k 1 k 1 k 2 k 2cos t V 1 1 2 k 2 k 1 k OUT (1) 1t 1 (2) 1t 1 (3) 1t 1 (4) 1t 1 (5) 1t 1 (6) 1t 1 (7) 1t 1 (8) 1t 1 (9) t 1cos V 2cos V 3cos V 4cos V 5cos V 6cos V 7cos V 8cos V 9cos V 1 1 12
Question 12: In the circuit above, the switch has been closed for a long time and opens at t = 0 +, find at t = 0 + (1) (3) (5) (7) (9) dv dv dv dv dv C dt C dt C dt C dt C dt t t t t t t0 t0 t0 t0 t0 = 2 A/s (2) = 6 A/s (4) = 10 A/s (6) = 4 A/s (8) = 8 A/s (10) dv dv dv dv C dt C dt C dt C dt dv t t t t C dt t t0 t0 t0 t0 t0 = 4 A/s = 8 A/s = 2 A/s = 6 A/s = 10 A/s dvc dt t 13
Question 13: In the circuit below, i ( t) cos(5 t) A. In sinusoidal steady state, what is the phasor of the current through the inductor, I, in Amps? L s (1) 10-90 (2) 1090 (3) 5-90 (4) 590 (5) 0.2-90 (6) 0.290 (7) 0.1-90 (8) 0.190 14
Question 14: Find I out in the following circuit: (1) 0 ma (2) 5 ma (3) 15 ma (4) 30 ma (5) 45 ma (6) 60 ma (7) 90 ma (8) 150 ma (9) 300 ma (10) None of the above 15
Question 15: Which one of the plots is the most accurate one for the frequency response of the circuit below? (V out and V in are phasor voltages, and observe the numbers at the axis) (1) (2) (3) (4) (5) (6) (7) (8) 16
Question 16: Find the Thevenin equivalent voltage, TH, and resistance, R TH, of the following circuit as seen from nodes A B. Assume the op-amp is ideal. 4 k 4 k 4 k 900 A IN 4 k 900 900 B IN t 2cos V TH (1) TH t (2) TH t (3) TH t (4) TH t (5) TH t (6) TH t (7) TH t (8) TH t (9) t 3cos V, R 450 TH 3cos V, R 600 TH 3cos V, R 900 TH 2cos V, R 450 TH 2cos V, R 600 TH 2cos V, R 900 TH 1cos V, R 450 TH 1cos V, R 600 TH 1cos V, R 900 TH TH 17
Question 17: Find the reactive power absorbed by the load if V load = 3 2 cos(10t + 45 ) V. Amps (1) 1.5 W (2) 1.5 VAR (3) 3 W (4) 3 VA (5) 4.5 VAR (6) 4.5 VA (7) 9 W (8) 9 VAR (9) 0 VA (10) None of the above 18
Question 18: What is the effective voltage of the periodic signal plotted below? 2 1 2 1 3 4 3 1 2 4 5 6 1 (1) 0.25 V (2) 0.5 V (3) 0.75 V (4) 1 V (5) 1.25 V (6) 1.5 V (7) 1.75 V (8) 2 V (9) 2.25 V (10) 2.5 V 19
Question 19: What is the apparent power generated by the voltage source in the circuit below? S i, where i = 1,2,3,4,5, are the complex power absorbed by the circuit elements. S2 2 j2 VA S3 1 j VA S1 1 j VA S4 2 j2 VA V S S5 2 j2 VA (1) 2 2 VA (2) 2 VA (3) 4 2 VA (4) 4 VA (5) 6 2 VA (6) 6 VA (7) 8 2 VA (8) 8 VA (9) 10 2 VA (10) 10 VA 20
Question 20: An inductor of L 5 nh is put in series with a source that has an internal 9 resistance of 50 and an antenna. In sinusoidal steady state at 636 MHz ( 4 10 rad/s), what impedance Z should the antenna have in order to ensure maximum power delivered to Ant the antenna? (Note: 1 nh = 1 10 9 H) (1) 20 (2) 30 (3) 50 (4) 80 (5) j20 (6) j50 (7) 50 j20 (8) 50 j20 (9) 50 j0.05 (10) 50 j0.05 21
Question 21: You have built a startup which produces cool plasma TVs that consume 150W when connected to a wall outlet (V rms = 120 V, ω = 2 60 rad/sec). You would like to start selling in California but their laws require a power factor above 0.9, while your current product has a power factor of 0.75 (lagging). Which of the following elements, when added in parallel at the input as shown below, can make the plasma TV to satisfy the California law? (1) 100 Ω resistor (2) 210 Ω resistor (3) 0.9 F capacitor (4) 11 F capacitor (5) 137 F capacitor (6) 1 mf capacitor (7) 0.9 m inductor (8) 11 mh inductor (9) 137 mh inductor (10) 1 H inductor 22
Question 22: In the circuit below, i s (t) = 5 2 cos(2000t) A, find R and L so that maximum power is transferred to R: (1) R = 1 Ω; L = 1 mh (2) R = 1 Ω; L = 2 mh (3) R = 6 Ω; L = 1 mh (4) R = 2 Ω; L = 2 mh (5) R = 4 Ω; L = 2 mh (6) R = 2 Ω; L = 4 mh (7) R = 2 Ω; L = 1 mh (8) R = 1 Ω; L = 4 mh (9) R = 1 Ω; L = 6 mh (10) R = 4 Ω; L = 6 mh 23
Potentially Useful Formulas (2 nd Midterm) ( t t0 )/ 0 x( t) x( ) x( t ) x( ) e, where RTHC or L R TH dil () t vl() t L dt 1 t il ( t) il( t0) vl( t ) dt L t0 L WL ( t0, t1) il( t1) il( t0) 2 2 2 dvc () t ic () t C dt 1 t vc ( t) vc ( t0) ic ( t ) dt C t0 C WC ( t0, t1) vc ( t1) vc ( t0) 2 2 2 1 ln x ln x Elapsed time formula: t 2 - t 1 = ln[(x 1 - x( ))/(X 2 - x( ))] 24
Potentially Useful Formulas (3 rd midterm) First order circuit: tt o / x(t) x( ) x(t o ) x( ) e, = L/R or = RC Series RLC: Parallel RLC: 2 R 1 s s 0 L LC 2 1 1 s s 0 RC LC t x(t) x( ) Acos dt Bsin dt e t x(t) x( ) A Bt e s1t s2t x(t) x( ) Ae Be 2 b b 4c 2 s 1,s 2 for s bs c 0 2, where c LC 1 R / 2L (series) b 1 2 (parallel) 2RC o 1 LC 2 2 s1,2 o 2 4c b 2 2 d o 2 25
Potentially Useful Formulas (since Exam 3) P p( t) dt VI cos( ) V I cos( ) V I cos( ) T 1 m m ave V I eff eff V I rms rms V I T 2 0 1 S = V I V I V I = VA * * * P jq 2 m m eff eff rms rms pf P P cos( ) 2 2 V I S P Q, pfa ( ) V I 26