Download post-midterm HWs and solutions

Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 7
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: August 20, 8:59 AM
Instructions
1.
2.
3.
4.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
Questions
1) [Alexander and Sadiku, 2009, Q6.13] Find the voltage across the capacitors in the circuit
of Fig. 6.49 under dc conditions.
Figure 1
2) [Alexander and Sadiku, 2009, Q6.19] Find the equivalent capacitance between terminals
a and b in the circuit of Figure 2. All capacitances are in F.
Figure 2
3) [Alexander and Sadiku, 2009, Q6.20] Find the equivalent capacitance at terminals a-b of
the circuit in Figure 3.
Figure 3
4) [Alexander and Sadiku, 2009, Q6.46] Find vC, iL, and the energy stored in the capacitor
and inductor in the circuit of Figure 4 under dc, steady-state, conditions.
Figure 4
5) [Alexander and Sadiku, 2009, Q6.49] Find the equivalent inductance of the circuit in
Figure 5. Assume all inductors are 10 mH.
Figure 5
[Alexander and Sadiku, 2009, Q6.13]
Monday, August 12, 2013
9:24 PM
2013 HW7 Page 1
Capacitor Combination
Monday, August 12, 2013
9:20 PM
2013 HW7 Page 2
[Alexander and Sadiku, 2009, Q6.19]
Monday, August 12, 2013
9:23 PM
2013 HW7 Page 3
2013 HW7 Page 4
[Alexander and Sadiku, 2009, Q6.20]
Monday, August 12, 2013
9:24 PM
2013 HW7 Page 5
[Alexander and Sadiku, 2009, Q6.46]
Monday, August 12, 2013
9:24 PM
2013 HW7 Page 6
2013 HW7 Page 7
[Alexander and Sadiku, 2009, Q6.49]
Monday, August 12, 2013
9:24 PM
2013 HW7 Page 8
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 8
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: August 27, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
v.
All phasor should be answered in polar form where the magnitude is positive and the phase is
vi.
between 180 and 180 .
All sinusoid should be answered in the cosine form where the amplitude is positive and the phase is
between 180 and 180 .
Questions
1) [Alexander and Sadiku, 2009, Q6.9] The current through a 0.5-F capacitor is 6(1-e-t) A.
Determine the voltage and power at t = 2 s. Assume v(0) = 0.
2) [Alexander and Sadiku, 2009, Q6.73] Show that the circuit in Figure 1 is a noninverting
integrator.
Figure 1
3) [Alexander and Sadiku, 2009, Ex 9.1] Find the amplitude, phase, period, and frequency of
the sinusoid
v  t   12cos  50t  10  .
4) (*) Consider the signal x(t) in Figure 2 below. Suppose x  0   3.356 . Find its phasor.
Figure 2
5) Find the phasors (in standard form) corresponding to the following signals.
a) v(t) = 120 sin (10t –50o ) V
b) i(t) = -60cos(30t +10o) mA
c) i(t) = -8 sin(10t+70o) mA
6) [F2010] Find the sinusoid x  t  which is represented by a phasor X = 7  7 j . Assume
  100 rad/s. (Your answer should be a time-dependent sinusoid in standard form.)
[Alexander and Sadiku, 2009, Q6.73]
Monday, August 12, 2013
9:24 PM
2013 HW8 Page 1
2013 HW8 Page 2
[Alexander and Sadiku, 2009, Q6.9]
Tuesday, August 20, 2013
7:31 PM
2013 HW8 Page 3
[Alexander and Sadiku, 2009, Ex 9.1]
Tuesday, August 20, 2013
7:35 PM
2013 HW8 Page 4
Finding phase of a sinusoid
Tuesday, August 20, 2013
8:37 PM
2013 HW8 Page 5
2013 HW8 Page 6
Sinusoids to Phasors
Tuesday, August 20, 2013
8:01 PM
2013 HW8 Page 7
Phasor to Sinusoid
Tuesday, August 20, 2013
8:25 PM
2013 HW8 Page 8
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 9
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: September 3, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
v.
All phasor should be answered in polar form where the magnitude is positive and the phase is
vi.
between 180 and 180 .
All sinusoid should be answered in the cosine form where the amplitude is positive and the phase is
between 180 and 180 .
Questions
1) [F2010] Simplify x  t   7 cos  t  777   7sin  t  77  . (Your answer should be a timedependent sinusoid in standard form.)
2) [Alexander and Sadiku, 2009, Q9.24a] Find v(t) in the following integrodifferential
equation using the phasor approach:
v  t    vdt  5cos  t  45  .
3) [Alexander and Sadiku, 2009, Q9.56] At  = 377 rad/s, find the input impedance of the
circuit shown in Figure 1.
Figure 1
Remark: Impedance value should be answered in rectangular form. Unit is .
4) [Alexander and Sadiku, 2009, Q10.7] Use nodal analysis to find V in the circuit of Figure
2
Figure 2
5) [F2010] In this question, you must use the specified techniques to solve the problem.
There will be no credit given if you do not follow the instructions. As always, your score
depends strongly on your explanation of your answer. If the explanation is incomplete,
zero score may be given even when the final answer is correct.
Consider the circuit below.
+ v1(t) -
R1
vs(t)
R2
+
v2(t)
-
L
Figure 3
Suppose
vs  t   7 cos  200t  30
 V,
iL(t)
R1 = 6 , R2 = 4 , and L = 5 mH.
a. Find Vs (which is the phasor representation of vs(t)).
b. Find the impedance of the inductor.
c. Use nodal analysis to find the voltage v2  t  across the resistor R2.
d. Find the voltage v1  t  across the resistor R1.
[F2010] Combining Sinusoids
Sunday, August 25, 2013
10:16 PM
2013 HW 9 Page 1
[Alexander and Sadiku, 2009, Q9.24a]
Tuesday, August 27, 2013
7:32 PM
2013 HW 9 Page 2
[Alexander and Sadiku, 2009, Q9.56]
Sunday, August 25, 2013
9:59 PM
2013 HW 9 Page 3
[Alexander and Sadiku, 2009, Q10.7] Nodal Analysis
Saturday, February 27, 2010
3:04 PM
2013 HW 9 Page 4
[F2010] AC Analysis
Monday, August 26, 2013
11:05 AM
2013 HW 9 Page 5
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 10
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: September 10, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
v.
All phasor should be answered in polar form where the magnitude is positive and the phase is
vi.
between 180 and 180 .
All sinusoid should be answered in the cosine form where the amplitude is positive and the phase is
between 180 and 180 .
Questions
1) [Alexander and Sadiku, 2009, Q10.43] Using the superposition principle, find ix in the
circuit of Figure 1.
Figure 1
2) [Alexander and Sadiku, 2009, Q10.58] For the circuit depicted in Figure 2, find the
Thevenin equivalent circuit at terminals a-b.
Figure 2
3) [Alexander and Sadiku, 2009, Q11.1] If we have v(t) = 160 cos 50t V across an element
and i(t) = - 20 sin (50t - 30) A through that element,
a) Calculate the instantaneous power. Express your answer in two parts, the constant part
and the sinusoidal part, as discussed in lecture.
b) Calculate the average power.
4) [Alexander and Sadiku, 2013, Q11.3] A load consists of a 60- resistor in parallel with a
90-F capacitor. If the load is connected to a voltage source vs(t) = 160 cos 2000t V, find
the average power delivered to the load.
5) [F2010] In this question, you must use the specified techniques to solve the problem.
There will be no credit given if you do not follow the instructions. As always, your score
depends strongly on your explanation of your answer. If the explanation is incomplete,
zero score may be given even when the final answer is correct.
Consider the circuit below.
+ v1(t) -
R1
vs(t)
R2
+
v2(t)
-
L
iL(t)
Figure 3
Suppose
vs  t   7 cos  200t  30
 V,
R1 = 6 , R2 = 4 , and L = 5 mH.
Remark: Note that this is a continuation of a question from the previous assignment.
a. Use mesh analysis to find all mesh currents (in the clockwise direction) in phasor
form.
b. Use the mesh current(s) to find the current iL  t  through the inductor.
c. Use source transformation(s) and/or impedance combination(s) to transform
the part of the circuit to the left of the inductor
into
a phasor voltage source VA in series with an impedance ZA.
d. Use VA, ZA, and the impedance of the inductor to find iL(t).
[Alexander and Sadiku, 2009, Q10.43] Superposition
Sunday, August 25, 2013
9:59 PM
2013 HW10 Page 1
[Alexander and Sadiku, 2009, Q10.58] Thevenin
Sunday, August 25, 2013
9:59 PM
2013 HW10 Page 2
[Alexander and Sadiku, 2009, Q11.1] Average Power
Sunday, August 25, 2013
9:59 PM
2013 HW10 Page 3
[Alexander and Sadiku, 2009, Q11.3] Average Power
Tuesday, September 03, 2013
7:15 PM
2013 HW10 Page 4
[F2010] ac Analysis
Tuesday, September 03, 2013
7:09 PM
2013 HW10 Page 5
2013 HW10 Page 6
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 11
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: September 17, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
Questions
1. [Alexander and Sadiku, 2009, Q11.5] Assuming that vs = 16 cos(2t - 40) V in the circuit
shown in Figure 1, find the average power delivered to each of the passive elements.
Figure 1
2. [F2010] Consider the circuit below.
+ v1(t) -
R1
vs(t)
R2
+
v2(t)
-
L
iL(t)
Figure 2
Suppose
vs  t   7 cos  200t  30
 V,
R1 = 6 , R2 = 4 , and L = 5 mH.
Remark: Note that this is a continuation of a question from the previous assignments.
You may use the answers from the solutions of the previous assignments.
a. Find the instantaneous power absorbed by R1
b. Find the average power absorbed by R1
c. Find the average power absorbed by L
d. Find the average power absorbed by the voltage source.
3. [Alexander and Sadiku, 2009, Q11.12] For the circuit shown in Figure 3, determine the
load impedance Z for maximum power transfer (to Z). Calculate the maximum power
absorbed by the load.
Figure 3
4. [F2010] Consider the circuit in Figure 4 below.
6
vs(t)
ZL
Figure 4
0.2 H
Suppose
vs  t   7 cos  200t  30
 V,
a. Determine the load impedance ZL for maximum power transfer (to ZL).
b. How can you build the optimal ZL which you got in part (a) from a combination of
resistor(s)/inductor(s)/capacitor(s)? Draw and explain your answer. Indicate the
values of each component (in /H/F).
c. Calculate the maximum power absorbed by the load ZL.
5. [Alexander and Sadiku, 2012, Q11.26] Find the effective value of the voltage waveform
in Figure 5.
Figure 5: [Alexander and Sadiku, 2012, Figure 11.57]
6. [Alexander and Sadiku, 2012, Q11.36a-c] Calculate the rms value for each of the
following functions:
d. i(t) = 10 A
e. v(t) = 4 + 3 cos 5t V
f. i(t) = 8 - 6 sin 2t A
[Alexander and Sadiku, 2009, Q11.5]
Tuesday, September 10, 2013
8:56 PM
2013 HW11 Page 1
2013 HW11 Page 2
[F2010] ac power analysis
Tuesday, September 10, 2013
9:54 PM
2013 HW11 Page 3
[Alexander and Sadiku, 2009, Q11.12]
Tuesday, September 10, 2013
8:56 PM
2013 HW11 Page 4
2013 HW11 Page 5
[F2010] ac power analysis: max power transfer
Tuesday, September 10, 2013
9:54 PM
2013 HW11 Page 6
2013 HW11 Page 7
[Alexander and Sadiku, 2012, Q11.26]
Tuesday, September 10, 2013
8:56 PM
2013 HW11 Page 8
[Alexander and Sadiku, 2012, Q11.36]
Tuesday, September 10, 2013
8:56 PM
2013 HW11 Page 9
2013 HW11 Page 10
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 12
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: September 24, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
Questions
1. Find the solution of the following (first order) differential equations
d
(a)
x  t   5x  t   0 , x  0  5
dt
d
(b)
x  t   3x  t   2 , x  0   0
dt
2. [Alexander and Sadiku, 2009, Q7.8] For the circuit in Figure 1 if
v(t) = 10e-4t V and i(t) = 0.2e-4t A, t > 0
(a) Find R and C.
(b) Determine the time constant .
(c) Calculate the initial energy in the capacitor.
(d) Obtain the time it takes to dissipate 50 percent of the initial energy.
Figure 1
3. [Alexander and Sadiku, 2009, Q7.10] For the circuit in Figure 2, find vo(t) for t > 0.
Determine the time necessary for the capacitor voltage to decay to one-third of its value
at t = 0.
Figure 2
4. [Alexander and Sadiku, 2009, Q7.3] Determine the time constant for the circuit in Figure
3.
Figure 3: [Alexander and Sadiku, 2009, Figure 7.83]
5. [Alexander and Sadiku, 2009, Q7.11] For the circuit in Figure 4, find io for t >0.
Figure 4: [Alexander and Sadiku, 2009, Figure 7.91]
Solution of the first order ODE
Tuesday, September 17, 2013
9:17 PM
2013 HW12 Page 1
2013 HW12 Page 2
[Alexander and Sadiku, 2012, Q7.8]
Tuesday, September 10, 2013
8:56 PM
2013 HW12 Page 3
2013 HW12 Page 4
[Alexander and Sadiku, 2012, Q7.10]
Tuesday, September 10, 2013
8:56 PM
2013 HW12 Page 5
2013 HW12 Page 6
[Alexander and Sadiku, 2012, Q7.3]
Tuesday, September 10, 2013
8:56 PM
2013 HW12 Page 7
[Alexander and Sadiku, 2012, Q7.11]
Tuesday, September 17, 2013
9:53 PM
2013 HW12 Page 8
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 13
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: October 1, 8:59 AM
Instructions
i.
ii.
iii.
iv.
Solve all problems. (5 pt)
ONE sub-question will be graded (5 pt). Of course, you do not know which part will be selected; so you should
work carefully on all of them.
Late submission will be heavily penalized.
Write down all the steps that you have done to obtain your answers. You may not get full credit even when your
answer is correct without showing how you get your answer.
Questions
1. [Alexander and Sadiku, 2009, Q7.2] Determine the time constant for the circuit in Figure
1.
Figure 1
Page 1 of 3
2. [Alexander and Sadiku, 2009, Q7.7] Assuming that the switch in Figure 2 has been in
position A for a long time and is moved to position B at t = 0, find vo(t) for t  0.
Figure 2
3. [Alexander and Sadiku, 2009, Q7.40] Find the capacitor voltage for t < 0 and t > 0 for
each of the circuits in Figure 3.
Figure 3
4. [Alexander and Sadiku, 2009, Q7.42]
(a) If the switch in Figure 4 has been open for a long time and is closed at t = 0, find
vo(t).
(b) Suppose that the switch has been closed for a long time and is opened at t = 0.
Find vo(t).
Figure 4
Page 2 of 3
5. [Alexander and Sadiku, 2009, Q7.44] The switch in Figure 5 has been in position a for a
long time. At t = 0, it moves to position b. Calculate i(t) for all t > 0.
Figure 5
Page 3 of 3
[Alexander and Sadiku, 2012, Q7.2]
Tuesday, September 24, 2013
7:46 PM
2013 HW13 Page 1
[Alexander and Sadiku, 2012, Q7.7]
Tuesday, September 10, 2013
8:56 PM
2013 HW13 Page 2
2013 HW13 Page 3
[Alexander and Sadiku, 2012, Q7.40a]
Tuesday, September 24, 2013
7:51 PM
2013 HW13 Page 4
2013 HW13 Page 5
[Alexander and Sadiku, 2012, Q7.40b]
Tuesday, September 24, 2013
7:51 PM
2013 HW13 Page 6
[Alexander and Sadiku, 2012, Q7.42]
Tuesday, September 24, 2013
7:51 PM
2013 HW13 Page 7
2013 HW13 Page 8
[Alexander and Sadiku, 2012, Q7.44]
Tuesday, September 24, 2013
7:51 PM
2013 HW13 Page 9
2013 HW13 Page 10
Sirindhorn International Institute of Technology
Thammasat University at Rangsit
School of Information, Computer and Communication Technology
ECS 203: Problem Set 14
Semester/Year:
Course Title:
Instructor:
Course Web Site:
1/2013
Basic Electrical Engineering
Asst. Prof. Dr. Prapun Suksompong ([email protected])
http://www2.siit.tu.ac.th/prapun/ecs203/
Due date: Not Due
Questions
1. Consider the circuit in Figure 1 below. Let
Vs = 10 V, R1 = 30 k, R2 = 10 k, and C = 4 F.
Figure 1
Assume that the switch has been in position 1 during time t < 0. Then, during time t  0 the
switch changes its position five times: at t1 = 0 ms, t2 = 25 ms, t3 = 50 ms, t4 = 75 ms, t5 = 100
ms.
(At time t1, the switch changes to position 2. At time t2, the switch changes back to position
1. At time t3, the switch changes again to position 2….)
Plot the voltage v(t) for time t > 0.
Hint: You should have v(t5)  4.59 V.
Page 1 of 2
2. [F2010] Consider the circuit in Figure 2 below. Assume the switch has been at position
1 for a long time and moves to position 2 at t = 0 sec.
R1 Ω
R2 Ω
1
2
Vs1
t=0
Vs2
+
v(t)
-
C
Figure 2
Let
Vs1 = 5 V, Vs2 = 0 V, R1 = 6 , R2 = 3 , and C = 10 F.
a. (3 pt) Find v(0-). Do not forget to justify your answer.
b. (1 pt) Find v(0). Do not forget to justify your answer.
c. (4 pt) Find v(t) for t > 0.
3. [F2010] Consider the circuit in Figure 3 below. Assume the switch has been at position 1
for a long time and moves to position 2 at t = 5 sec.
R1 Ω
1
2
Vs1
t=5
R2 Ω
Vs2
C
+
v(t)
-
Figure 3
Let
Vs1 = 16 V, Vs2 = 8 V, R1 = 3 , R2 = 5 , and C = 8 F.
a.
b.
c.
d.
(3 pt) Find v(0).
(2 pt) Find v(5).
(4 pt) Find v(t).
(1 pt) Evaluate v(t) at t = 7.
Page 2 of 2
Step Response: Alternating Switch Positions
Tuesday, February 23, 2010
8:40 PM
2013 HW14 Page 1
2013 HW14 Page 2
2013 HW14 Page 3
Q2
Monday, September 30, 2013
9:34 PM
2013 HW14 Page 4
Q3
Monday, September 30, 2013
9:45 PM
2013 HW14 Page 5
2013 HW14 Page 6