Solutions Manual
INTRODUCTION TO
MECHATRONICS AND
MEASUREMENT
SYSTEMS
4th edition
2012(c)
SOLUTIONS MANUAL
David G. Alciatore
and
Michael B. Histand
Department of Mechanical Engineering
Colorado State University
Fort Collins, CO 80523
Introduction to Mechatronics and Measurement Systems 1
,Solutions Manual
This manual contains solutions to the end-of-chapter problems in the third edition of
"Introduction to Mechatronics and Measurement Systems." Only a few of the open-ended
problems that do not have a unique answer are left for your creative solutions. More information,
including an example course outline, a suggested laboratory syllabus, MathCAD files for examples
in the book, and other supplemental material are provided on the Internet at:
mechatronics.colostate.edu
We have class-tested the textbook for several years, and it should be relatively free from
errors. However, if you notice any errors or have suggestions or advice concerning the textbook's
content or approach, please feel free to contact us via e-mail at .
We will post corrections for reported errors on our Web site.
Thank you for choosing our book. We hope it helps you provide your students with an
enjoyable and fruitful learning experience in the cross-disciplinary subject of mechatronics.
2 Introduction to Mechatronics and Measurement Systems
,Solutions Manual
2.1 D = 0.06408 in = 0.001628 m.
2
D - = 2.082 10–6
A = ---------
4
= 1.7 x 10-8 m, L = 1000 m
R = -- -L
-- = 8.2
A
2.2
(a) R1 = 21 104 20% so 168k R1 252k
(b) R2 = 07 103 20% so 5.6k R2 8.4k
(c) Rs = R1 + R2 = 217k 20% so 174k Rs 260k
R1R2
(d) Rp = ------------------
R1 + R2
R1 R2
Rp = ----------M--I-N--------M--I--N--- = 5.43k
MIN R1 + R
MIN 2 MIN
R1 R2
Rp = ----------M--A--X---------M--A--X---- = 8.14k
MAX R1 +R
MAX 2 MAX
2.3 R1 = 10 102 , R2 = 25 101
R1R2 (10 102)(25 101) 1
R = = = 20 10
R1 + R2 10 102 + 25 101
a = 2 = red, b = 0 = black, c = 1 = brown, d = gold
2.4 In series, the trim pot will add an adjustable value ranging from 0 to its maximum value to
the original resistor value depending on the trim setting. When in parallel, the trim pot
could be 0 perhaps causing a short. Furthermore, the trim value will not be additive with
the fixed resistor.
2.5 When the last connection is made, a spark occurs at the point of connection as the
completed circuit is formed. This spark could ignite gases produced in the battery. The
negative terminal of the battery is connected to the frame of the car, which serves as a
ground reference throughout the vehicle.
Introduction to Mechatronics and Measurement Systems 3
, Solutions Manual
2.6 No, as long as you are consistent in your application, you will obtain correct answers. If
you assume the wrong current direction, the result will be negative.
2.7 Place two 100 resistors in parallel and you immediately have a 50 resistance.
2.8 From KCL, Is = I1 + I2 + I3
Vs V V V
so from Ohm’s Law -------- = -----s- + -----s- + ------s
Req R1 R2 R3
Therefore, --- ---- = ---- + ---- + --1-- so R
1 1 1 R1R2R3
eq = ----------------------------------------------------
Req R1 R2 R3 R2R3 + R1R3 + R1R2
2.9 Is Is
From Ohm’s Law and Question 2.8, V = ------= ----------------------------------------------------
Req R2R3 + R1R3 + R1R2
R 1 R2 R3
and for one resistor, V = I1R1
R2R3
Therefore, I1 = I
R 2R3 + R1R3 + R1R2 s
R1 R2 R1R2
2.10 lim ------------------ = ------------ = R2
R1 → R1 + R2 R1
dV dV dV
2.11 I = C eq ------ = C 1---------1 = C 2---------2
dt dt dt
From KVL,
V = V1 + V2
so
dV dV dV
------- = ---------1 + ---------2
dt dt dt
Therefore,
----I---- = ---I--- + ---I--- so ---1--- = --1-- + --1-- or C C1C2
eq = ------------------
Ceq C1 C2 Ceq C1 C2 C1 + C2
4 Introduction to Mechatronics and Measurement Systems
INTRODUCTION TO
MECHATRONICS AND
MEASUREMENT
SYSTEMS
4th edition
2012(c)
SOLUTIONS MANUAL
David G. Alciatore
and
Michael B. Histand
Department of Mechanical Engineering
Colorado State University
Fort Collins, CO 80523
Introduction to Mechatronics and Measurement Systems 1
,Solutions Manual
This manual contains solutions to the end-of-chapter problems in the third edition of
"Introduction to Mechatronics and Measurement Systems." Only a few of the open-ended
problems that do not have a unique answer are left for your creative solutions. More information,
including an example course outline, a suggested laboratory syllabus, MathCAD files for examples
in the book, and other supplemental material are provided on the Internet at:
mechatronics.colostate.edu
We have class-tested the textbook for several years, and it should be relatively free from
errors. However, if you notice any errors or have suggestions or advice concerning the textbook's
content or approach, please feel free to contact us via e-mail at .
We will post corrections for reported errors on our Web site.
Thank you for choosing our book. We hope it helps you provide your students with an
enjoyable and fruitful learning experience in the cross-disciplinary subject of mechatronics.
2 Introduction to Mechatronics and Measurement Systems
,Solutions Manual
2.1 D = 0.06408 in = 0.001628 m.
2
D - = 2.082 10–6
A = ---------
4
= 1.7 x 10-8 m, L = 1000 m
R = -- -L
-- = 8.2
A
2.2
(a) R1 = 21 104 20% so 168k R1 252k
(b) R2 = 07 103 20% so 5.6k R2 8.4k
(c) Rs = R1 + R2 = 217k 20% so 174k Rs 260k
R1R2
(d) Rp = ------------------
R1 + R2
R1 R2
Rp = ----------M--I-N--------M--I--N--- = 5.43k
MIN R1 + R
MIN 2 MIN
R1 R2
Rp = ----------M--A--X---------M--A--X---- = 8.14k
MAX R1 +R
MAX 2 MAX
2.3 R1 = 10 102 , R2 = 25 101
R1R2 (10 102)(25 101) 1
R = = = 20 10
R1 + R2 10 102 + 25 101
a = 2 = red, b = 0 = black, c = 1 = brown, d = gold
2.4 In series, the trim pot will add an adjustable value ranging from 0 to its maximum value to
the original resistor value depending on the trim setting. When in parallel, the trim pot
could be 0 perhaps causing a short. Furthermore, the trim value will not be additive with
the fixed resistor.
2.5 When the last connection is made, a spark occurs at the point of connection as the
completed circuit is formed. This spark could ignite gases produced in the battery. The
negative terminal of the battery is connected to the frame of the car, which serves as a
ground reference throughout the vehicle.
Introduction to Mechatronics and Measurement Systems 3
, Solutions Manual
2.6 No, as long as you are consistent in your application, you will obtain correct answers. If
you assume the wrong current direction, the result will be negative.
2.7 Place two 100 resistors in parallel and you immediately have a 50 resistance.
2.8 From KCL, Is = I1 + I2 + I3
Vs V V V
so from Ohm’s Law -------- = -----s- + -----s- + ------s
Req R1 R2 R3
Therefore, --- ---- = ---- + ---- + --1-- so R
1 1 1 R1R2R3
eq = ----------------------------------------------------
Req R1 R2 R3 R2R3 + R1R3 + R1R2
2.9 Is Is
From Ohm’s Law and Question 2.8, V = ------= ----------------------------------------------------
Req R2R3 + R1R3 + R1R2
R 1 R2 R3
and for one resistor, V = I1R1
R2R3
Therefore, I1 = I
R 2R3 + R1R3 + R1R2 s
R1 R2 R1R2
2.10 lim ------------------ = ------------ = R2
R1 → R1 + R2 R1
dV dV dV
2.11 I = C eq ------ = C 1---------1 = C 2---------2
dt dt dt
From KVL,
V = V1 + V2
so
dV dV dV
------- = ---------1 + ---------2
dt dt dt
Therefore,
----I---- = ---I--- + ---I--- so ---1--- = --1-- + --1-- or C C1C2
eq = ------------------
Ceq C1 C2 Ceq C1 C2 C1 + C2
4 Introduction to Mechatronics and Measurement Systems
