Problem 6.47 Determine i2 in the circuit of Fig. P6.47 for t 0, given that Vs =
10 V, Rs = 0.1 M, R = 1 M, C1 = 1 F, and C2 = 2 F.
i2
Rs
t=0
+
Vs _
R
C2
C1
Figure P6.47: Circuit for Problem 6.47.
Solution: The circuit containing C1 and C2 contained no sou
RLC Circuits
EECS 215: Intro.
Second Order Circuits
A second order circuit is characterized
by a second order differential equation
Resistors and two energy storage elements
Determine voltage/current as a function of time
Initial/final values of voltage/c
Laboratory 1 DC Circuits
EECS 215
LABORATORY 1 DC CIRCUITS
OUTLINE
1 Basic Measurement of Electric Circuits
Voltage Measurements
Current Measurements
Resistance Measurements
2 Background for Laboratory
Agilent E3631A Power Supply
Thvenin Equivalent Circui
EECS 215 Lab Supplementary Materials / DC Lab Cover page
DC Lab Report
Students Name _
Date of Lab Work _
I have neither given nor received aid on this report, nor have I concealed any violations of the Honor Code. _ (students signature)
Lab Section # _
C
EECS 215 Lab Supplementary Materials / Op Amp Lab Cover page
Op Amp Lab Report
Students Name _
Date of Lab Work _
I have neither given nor received aid on this report, nor have I concealed any violations of the Honor Code. _ (students signature)
Lab Secti
Problem 5.65 Show that the op-amp circuit in Fig. P5.65 (in which R = 10 k, and
C = 20 F) simulates the differential equation
dv
+ 5v = 10vs .
dt
v
R
C
R
_
R
+
R
_
v1
R
+
v2
R
_
+
v3
2R
R
vs
_
+
v4
Figure P5.65
Solution: We recognize the rst stage as an i
Problem 1.6 A certain cross section lies in the xy plane. If 3 1020 electrons
go through the cross section in the z-direction in 4 seconds, and simultaneously,
1.5 1020 protons go through the same cross section in the negative z-direction, what
is the mag
Circuits by Fawwaz T. Ulaby and Michel M. Maharbiz
Solutions to the Exercises
Fawwaz T. Ulaby and Michel M. Maharbiz, Circuits
c 2009 National Technology and Science Press
ISBN-10: 1-934891-00-2 ISBN-13: 978-1-934891-00-1 Publisher: Tom Robbins General Ma
Problem 3.32 The circuit in Fig. P3.32 includes a dependent current source. Apply
mesh analysis to determine Ix .
5
Ix
+
+
+
12.3 V _
10
I1
I4
4
20
I2
2Ix
I3
2
Figure P3.32: Circuit for Problem 3.32.
Solution:
Mesh 1:
Supermesh 2/3:
Mesh 4:
Auxiliary 1:
Problem 9.21 A series RLC bandpass lter has half-power frequencies at 1 kHz
and 10 kHz. If the input impedance at resonance is 6 , what are the values of R, L,
and C?
Solution: At resonance, the input impedance of the series RLC circuit is equal to R.
Hen
Problem 5.13 The voltage across a 0.2-mF capacitor was 20 V until a switch in the
circuit was opened at t = 0, causing the voltage to vary with time as
v(t) = (60 40e5t ) V
(a)
(b)
(c)
(d)
for t > 0.
Did the switch action result in an instantaneous change
Problem 3.82 Use the DC Operating Point Analysis in Multisim to nd the power
dissipated or supplied by each component in the circuit in Fig. P3.82 and show that
the sum of all powers is zero.
R1
R4
+
_
25
R2
R3
5
5
5
R5 10
I
R6 10
+
2.5I
10 V _
Figure
Problem 4.47 An instrumentation amplier with R1 = R3 = 10 k, R4 = 1 M,
and R5 = 1 k, uses a potentiometer for the gain-control resistor R2 . If the
potentiometer resistance can be varied between 10 and 100 , what is the
corresponding variation of the circ
MSE 330 Thermodynamics of Materials
Department of Materials Science and Engineering
University of Michigan
Homework #7 100 points
1- (25 points)
For the phase diagram shown below:
(a) Sketch the Gibbs
Problem 4.14 For the op-amp circuit shown in Fig. P4.14:
(a) Obtain an expression for the current gain Gi = iL /is .
(b) If RL = 12 k, choose Rf so that Gi = 15.
Rf
_
is
+
Rs
vo
iL
RL
Figure P4.14: Circuit for Problem 4.14.
Solution: (a) This is an invert
Problem 3.59 Find the Norton equivalent circuit of the circuit in Fig. P3.58 after
increasing the magnitude of the voltage source to 38 V.
5
Ix
10
V2
+
V1
20
4
_ 38 V
2
V3
8
2Ix
a
+
Voc
b _
Solution:
V1 = 38 V
V2 V1 V2 V2 V3
+ +
=0
10
4
20
V3 V2 V3 V3 V
Problem 5.44 Given that in Fig. P5.44, I1 = 4 mA, I2 = 6 mA, R1 = 3 k,
R2 = 6 k, and C = 0.2 mF, determine v(t). Assume the switch was connected to
terminal 1 for a long time before it was moved to terminal 2.
Solution:
1
(a)
I1
2
t=0
R1
I2
R2
C
R2
I2
v
1
Problem 7.2
Express the current waveform
i(t) = 0.2 cos(6 109 t + 60 ) mA
in standard cosine form and then determine the following:
(a) Its amplitude, frequency, and phase angle.
(b) i(t) at t = 0.1 ns.
Solution:
i(t) = 0.2 cos(6 109t + 60 )
(mA)
= 0.2 co
Problem 6.25 Determine iL (t) in the circuit of Fig. P6.25, given that the switch
was moved to position 2 at t = 0 (after it had been in position 1 for a long time) and
then back to position 1 at t = 0.5 s. The element values are Vs = 36 V, R1 = 4 ,
5
R2
Problem 9.3 For the circuit shown in Fig. P9.3, determine (a) the transfer function
H = Vo /Vi , and (b) the frequency o at which H is purely real.
C
L2
V1
+
+
L1
Vi
_
R
Vo
_
Figure P9.3: Circuit for Problem 9.3.
Solution:
(a) KCL at node V1 gives:
V1 Vi
Determine the power dissipated in RL of the circuit in Fig. P8.16.
2IC
j3
_
IC
3
6
j1
+
_ 8
45o
a
+
Problem 8.16
RL = 4
V
b
Figure P8.16: Circuit for Problem 8.16.
Solution:
2IC
_
IC
3
45o
+
8
j1
I1
a
+
j3
6
I2
V _
I3
RL = 4
b
8e j45 + 3I1 + j3I1 j(
Problem 3.2
Apply nodal analysis to determine Vx in the circuit of Fig. P3.2.
2
2
V
1
3A
+
4 Vx
_
Figure P3.2: Circuit for Problem 3.2.
Solution: At node V , application of KCL gives
V
V
3+
= 0,
2+1
2+4
which leads to
V = 6 V.
By voltage division,
Vx =
V
Problem 2.4 A resistor of length consists of a hollow cylinder of radius a
surrounded by a layer of carbon that extends from r = a to r = b, as shown in
Fig. P2.4.
(a) Develop an expression for the resistance R.
(b) Calculate R at 20 C for a = 2 cm, b = 3
Problem 7.39 As we will learn in Chapter 8, to maximize the transfer of power
from an input circuit to a load ZL , it is necessary to choose ZL such that it is equal
to the complex conjugate of the impedance of the input circuit. For the circuit in
Fig. P
Problem 2.32
Determine A if Vout /Vs = 9 in the circuit of Fig. P2.32.
Solution:
3
+
_ Vs
I1
12
3
+
_ Vs
AI1
+
6 Vout
_
AI1
12
3
Figure P2.32: Circuit
for Problem 2.32.
2 Vout
I
6
+
_
Vs
9
I
Vs
I1 = =
2 18
I=
Vout = AI1 2 =
AVs
AVs
2 =
18
9
Vout A
= = 9
Yourname:w Sciti'lim E3
EECS 215.
Final Exam
April 25, 2016
This text consists of 8 problems with points as indicated to total 90 points.
Please note that Laplace tables are attached at the end of the exam.
Read through the entire exam before beginning.
Yourname: ilQSlAKl %
EECS 215-001
Quiz #11, Chapter 11 (Complex Power)
December 9, 2016
I. As advice for students taking this class in the future, please answer the following question (please
limit your response to three concrete ideas full credit awarded
Problem 1 (20 points)
Assuming the opamps are ideal, determine vaut / 21,-.
NH)
Figure 1: Circuit for Problem 1.
"-u 5| * is: o
.k cook
1. L3. out 0. ,_ o
3 7.1 * a 7:; * an
_L.- - v i
\
= . / 7. 03H
.31 + i
go
, 12 ., 1-5154 *c.
1 Problem 2 (10 point
EECS 215 Winter Semester 2015 Midterm Exam Iece
Name (Last, First):
Uniqname:
Rules:
a) Nominal exam time: Wednesday, February 11, 2015, 3:30 to 5:30 PM.
Due to medical issues, a smaller number of students may be taking this
exam as late as Friday. Do not
4. Given the circuit below
a. (5 points) Find the transfer function () = /
b. (5 points). Find |()| at = 0 and and () at = 0 and
C
+
+
Vi
L
R
Vo
Write your answer here:
a. () _
b. |()| at = 0 _
Write your
answer
()
at here:
= 0 _
|()| at _
a. () = _
() a