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Name: Instructor: ID #: Class Time:
EE 201/201C Final Exam December 11, 1996
General Instructions:
- The exam is closed book, closed notes, no calculator.
- Do not open the exam until you are told to begin.
- Put your name, student identification number, and instructor name in the blanks above. Fill in your name, student identification number, and section number in the appropriate places on the computer scan forms.
Time Instructor Section Number 7:30 am Krogmeier (EE201C) 0001 8:30 am Nyenhuis (EE201) 0002 11:30 am Doerschuk (EE201) 0003 2:30 pm Krogmeier (EE201C) 0004
- The exam consists of 14 multiple choice questions (10 points each) and 4 workout problems (15 points each).
- Please keep your computer scan sheets covered while you are working on the exam.
- An official crib sheet will be handed out separately.
Problem 1. Consider the circuit shown. The switch has been closed for a long time before it is opened at time t = 0. What is the current iC (0+) into the capacitor at time t = 0+^ (in Amperes)?
(1) 1 (2) 2 (3) 0 (4) 0.5 (5) -2 (6) -0. (7) 7
t = (^) 0
15 V^ +-- 20 Ω
10 Ω
1 F
i (^) C
Problem 2. Consider the circuit shown below. The switch has been closed for a long time before it is opened at time t = 0. What is the voltage vL(0+) across the inductor just after the switch is opened (in Volts)?
(1) -20 (2) -10 (3) 0 (4) 10 (5) 5 (6) 15 (7) 20
+
--
t = 0 10 V^ +--
10 Ω
1 H vL^ 10 Ω
Problem 5. For the following circuit, choose the correct set of nodal equations. Answers:
−i(t) + va(t) R− 1 v b^ (t) = 0 vb(t)−va (t) R 1 +^
vb(t)−v(t) R 2 +^ C^
dvb(t) dt =^0
i(t) + va(t) R− 1 v b^ (t) = 0 vb(t)−va (t) R 1 +^
vb(t)−v(t) R 2 +^ C^
dvb(t) dt =^0
−i(t) + va(t) R− 1 v b^ (t) = 0 vb(t)−va (t) R 1 +^
vb(t)−v(t) R 2 −^ C^
dvb(t) dt =^0
−i(t) + va(t) R− 1 v b^ (t) = 0 vb(t)−va (t) R 1 +^
vb(t)−vc (t) R 2 +^ C^
dvb(t) dt =^0 vc(t)−vb (t) R 2 +^ v(t)^ =^0
i(t) + va(t) R− 1 v b^ (t) = 0 vb(t)−va (t) R 1 +^
vb(t)−vc (t) R 2 +^ C^
dvb(t) dt =^0 vc(t)−vb (t) R 2 +^ v(t)^ =^0
i(t) + vb(t R)− 2 v(t)+ C dvdb(t t) = 0
i(t) + vb(t R)− 2 v(t)− C dvdbt( t) = 0
i ( t ) C^^ +-- v ( t )
R 1
va vb vc
R 2
Problem 6. Compute the Thevenin equivalent of the circuit drawn below at the a-b termi- nals. Answers:
(1) Voc = 4V, Rth = 2Ω (2) Voc = 2V, Rth = −1Ω (3) Voc = 0V, Rth = 4Ω (4) Voc = 4V, Rth = −4Ω (5) Voc = 2V, Rth = 1Ω (6) Voc = 6V, Rth = 4Ω (7) Voc = 1V, Rth = 1Ω
8 V^ +--
2 Ω a
b
1 Ω
2 Ω 2 Ω
Problem 7. Compute the Thevenin equivalent of the circuit drawn below at the a-b termi- nals. Answers:
(1) Voc = 4V, Rth = 2Ω (2) Voc = 2V, Rth = −1Ω (3) Voc = 0V, Rth = 4Ω (4) Voc = 4V, Rth = −4Ω (5) Voc = 2V, Rth = 1Ω (6) Voc = 6V, Rth = 4Ω (7) Voc = 1V, Rth = 1Ω
+ (^) --
2 A
2 Ω
a
b
Vx
2 Ω^2 Vx
Problem 10. The capacitor voltage in the RLC circuit shown below is of the form
vC (t) = (A + Bt)e−σt^ for t > 0.
Find the value of R (in Ohms).
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5 (6) 6 (7) 7
10 A
1/4 Ω
t = 0 (^) 1 mF vC 16 mH
R
Problem 11. Determine the effective (rms) value (in V rms) of the voltage waveform:
v(t) = 5(1 + cos ωt) V.
(1) 5
Problem 12. Compute Vo for the circuit drawn below. Answers:
(1) V 0 = − Rf Rs Vs^ (2)^ V^0 = +
Rf Rs Vs
(3) V 0 = −Rf R^ +sR oVs (4) V 0 = +Rf R^ +sR oVs
(5) V 0 = − (^) (RfR +fR^ Roo)Rs Vs (6) V 0 = + (^) (RfR +f^ RRoo)Rs Vs
(7) V 0 = − (^) (RL+RRLf )Rs Vs
+
--
+--
+
-- ideal
Rs
Rf
Ro
Vs RL Vo
Problem 13. Compute Va for the circuit drawn below. Answers (in Volts):
(1) 1 (2) 2 (3) 3 (4) 0 (5) -3 (6) -2 (7) -
+
--
+--
+ -- + --
3 Ω
3 V
Va 2 Ω
4 Ω
2 Ω
1 Ω
2 V
1 V
Workout Problems. There are four workout problems contained in the following pages. Each is worth 15 points. In order to receive credit for these problems, your work must be shown and your final answers must be in the boxes provided.
Workout Problem 1. (15 points) In the circuit shown below assume an ideal OP AMP. Find the correct expression for the voltage v 0 (t) for t ≥ 0. Assume that the capacitor voltage is zero at t = 0−.
+
--
+--
+
-- ideal
R 1
R 2
R 3
C vo ( t )
t = 0
1 V
v 0 (t) =
Workout Problem 2. (15 points) The source in the circuit below is operating at 10 Vrms with radian frequency 40 radi- ans/second. The load in the box is 3000 W at a power factor of 0.6 lagging (i.e., the angle of the load current is smaller than the angle of the load voltage). See the figure. Find:
(a) the reactive power absorbed by the load in the box (in VAR).
(b) the value of the capacitor C (in F) to adjust the power factor of the combined load to unity (i.e., PF = 1).
10 V rms 40 rad/sec
Load 3000 W 0.6 power factor lagging
+ --
C
Qload =
C =
Workout Problem 4. (15 points) The circuit shown below operates in the sinusoidal steady state at frequency ω = 1000 radians per second.
(a) Compute the input impedance Zin = Rin + jXin.
Rin =
Xin =
(b) If you could choose any positive values for R, L, and C in the circuit below, is it possible to achieve Rin < 0? Give a reason (think average power).
Yes/No, Reason:
2 mH
0.5 mF
4 Ω
Z (^) in
