fundamentals of engineering exam review...
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THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA
171 Moultrie Street, Charleston, SC 29409
Dr. Gregory J. Mazzaro
Spring 2018
Fundamentals of Engineering
Exam Review
Electromagnetic Physics
(currently 5-7% of FE exam)
2
FE Exam – Subjects
3
Charge vs. Current
• charge is the basic unity of electricity (a property of protons & electrons)
particles that attract each other (opposite “charge”)
or repel each other (same “charge”)
• as EEs, we focus on the behavior of electrons
• fundamental unit of charge (SI system) = coulomb
1 electron holds a charge of
q = –1.602 x 10-19 C
1 proton holds a charge of
q = +1.602 x 10-19 C
• current = the flow of charge
• unit of current = ampere
1 ampere = 1 C / s (1 coulomb flowing past a point per second,
usually within a wire)
4
Electric Field & Coulomb’s Law
• a field is a vector (with magnitude & direction)
defined at all points in space, (x, y, z)
• an electric field (E) is the force that a unit charge
experiences (N/C) due to the presence of other
charges nearby governed by Coulomb’s Law
1Q
r
Q2
E
ar12
field vectors
flux lines
D
5
Example: Electric Field
(A) 0.431 mN, away from the 2-nC charges
(B) 0.719 mN, away from the 2-nC charges
(C) 0.431 mN, towards the 2-nC charges
(D) 0.719 mN, towards the 2-nC charges
The correct answer is (A).
6
Example: Electric Field & Potential
VF QE Q
d The correct answer is (B).
7
Gauss’ Law
-- 1 of Maxwell’s Equations which governs
the behavior of electric fields Qencl = charge contained in a
“Gaussian” surface
E = electric field intensity
dS is normal to the surface
and directed outward
(sphere)
an alternative to Coulomb’s Law for determining electric field, under symmetry
8
Example: Gauss’ Law
9
Example: Gauss’ Law
10
Resistivity
All real wires have a non-zero resistance.
• when current flows along a non-zero resistance,
voltage drops and energy is dissipated (as heat)
r = resistivity,
a material property (W-m)
Also, real materials become more
current-resistant as they heat up.
L
11
Example: Resistivity
2
22
22 2100 .05 0.1 7.85 W
RP I R
L A
IJ I J A
A
P RI J A
L L A
J A
r
r
r
The correct answer is (C).
12
Capacitance & Stored Energy
12
A capacitor is a linear circuit element which stores energy
in the electric field in the space between two conducting bodies
occupied by a material with permittivity e .
13
Example: Capacitance
13
1414
Example: Electrostatic Energy
22
2 2
0 0
Qd QV E
A Ae e
15
Voltage / Potential / Work
• energy must be expended to move charge
• work required to move charge through an
element or through a field, per charge = voltage
• unit of voltage = volt = 1 J/C
• can exist even when no current
is flowing “potential”
Circuit theory
Electromagnetic
theory
QV
16
Example: Electromagnetic Work
17
Magnetic Fields
18
Inductance & Stored Energy
18
An inductor is a linear circuit element which stores energy
in the magnetic field in the space between current-carrying wires
occupied by a material with permeability m .
19
Example: Magnetostatic Energy
20
Example: Magnetostatic Energy
21
induced electro-motive force (EMF), vemf (in volts)
-- potential difference generated in a loop by
applying a time-varying magnetic field B to the loop (“transformer EMF”)
and/or changing the area seen by the B field over time (“motional EMF”)
(B applied)
(v induced) indI
indI
emfv
Lenz’s Law ( Bind and Iind , for Vemf )
-- the current induced in the loop generates a magnetic
field to oppose the change in magnetic flux
Lenz’s Law / Induced Voltage
22
Example: Lenz’s Law / Induced Voltage
23
Free-Space EM Waves
Far away from a radiating antenna, the traveling fields
may be approximated as a plane wave, with E and H in
phase, whose vector directions are related by the right-
hand-rule, and whose magnitudes are related by the
characteristic impedance of free space, h :
377E
Hh W
S E H
24
Example: Free-Space EM Waves
S E H
310 V cm377 2.6 μA cm
377
EH
H
W W
E is parallel to the antenna
H is perpendicular to the antenna
(A) 2.6 mA/cm, parallel to the antenna
(B) 3.8 mA/cm, parallel to the antenna
(C) 2.6 mA/cm, perpendicular to the antenna
(D) 3.8 mA/cm, perpendicular to the antenna
The correct answer is (C).
THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA
171 Moultrie Street, Charleston, SC 29409
Dr. Gregory J. Mazzaro
Spring 2018
Fundamentals of Engineering
Exam Review
Selected Advanced
Circuit-Theory Concepts
26
Example: RC Circuit
26
/
0
10
010
0
t RC
C
C
v t V e
v RC V e
almost completely discharged
all energy stored in C = 10 mF
was dissipated by R = 25 W
22 61 1
10 10 150 0.11J2 2
W CV
The correct answer is (B).
27
Example: RL Circuit
27
/
2.5 2.5
1
10 V1 2 1 A
5
Rt L
L
t t
L
Vi t e
R
i t e e
W
The correct answer is (D).
28
Example: Thevenin Equivalent
29
RMS or Effective Value
Root-mean-squared (or effective)
values are an alternative
representation of the magnitude of
time-varying and periodic signals.
They allow us to calculate equivalent
V/I/P for AC circuits as if the V/I/P
quantities were DC values.
30
Example: Power, AC Circuit
2
4
2
1
2
4
14.4 A 4
829 W
rms rms rms
rms
P I V I R
I
W
W
The correct answer is (B).
31
Example: Op Amp
a bv v 2 1 0i i va
vb
1
2 1
21
1
1
0
0
20040
5
o a a
b a
o
o
v v v v
R R
v v
Rv v
R
v
v
The correct answer is (C).
32
a bv v 2 1 0i i va
vb
42 2 2
3 4
2 1
22
1
2
200 40
205 41
00
200 401 1
5 41
4041 40
41
b
o a a
o a
o
Rv v v v
R R
v v v
R R
Rv v v
R
v
v
The correct answer is (C).
Example: Op Amp
33
Gain / Decibels
Gain (A) refers to the ratio of output-to-input
voltage, current, or power.
out outv
in in
p
V PA A
V P
“differential” gain = outv,diff
in,1 in,2
VA
V V
Av,1 Av,2VoutVin
outv v,1 v,2
in
VA A A
V
dB dB dB
v v,1 v,2A A A
Decibels are a convenient mathematical form
used to express very high/low gain
(up/down to very high/low values of V, I, P).
34
Example: Op Amp, Decibels
dB outv,diff 10
in,1 in,2
20logV
AV V
0 1 2
dB
v,diff 10
40
20log 40 32 dB
V V V
A
The correct answer is (A).
dB dB dB dB
p p,1 p,2 p,3
100 25 9 134 dB
A A A A
35
Transfer Function
y t h t x t
Y j H j X j
Many calculations on linear circuits,
assuming the circuit has reached
sinusoidal steady-state, are easier to
perform in the frequency (j) domain:
by the Fourier Transform, where h is the impulse response of the circuit
and H is the transfer function of the circuit
10sin 30 Vt
L
0.1 || 3 kΩ1030
0.1 || 3 kΩ 1kΩ2
Sv v H j
j
j
input (x) = voltage, output (y) = voltage,
system (h) = voltage divider
36
Example: Transfer Function
37
Example: Transfer Function
1 in 11 20 0
20 MΩ ||1 5MΩ
oV v V vv v
j C
v1
v2
in
6 6
in
20 MΩ ||1
5 MΩ
1 2 60 .001 10 2.7 10
20 2.71
5 20 2.7
0.53 82
o
o
j CV V
j C j j
jV
V j
The correct answer is (B).
THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA
171 Moultrie Street, Charleston, SC 29409
Dr. Gregory J. Mazzaro
Spring 2018
Grimsley Hall, Room 312
843-953-0429
http://ece.citadel.edu/mazzaro