Download 10 - Electrical and Computer Engineering

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EE-0001
PEEE Refresher Course
Week 1: Engineering
Fundamentals
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Engineering Fundamentals
• Bentley Chapters 1 & 2
• Camara Chapters 1, 2, & 3
• Electrical Quantities
– Energy (work), power, charge, current
– Electrostatic pressure, resistance
• Circuit Elements
– Resistor, Inductor, Capacitor
• Circuit Equations
–
–
–
–
–
Series, Parallel, Wye-Delta Conversions
Norton Equivalent
Thevenin Equivalent
Kirchhoff’s Laws
Loop and Node equations
• Complex Algebra
• Transients & Resonance
• R, C, RC, RLC
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Fundamental Electrical Units
Quantity
Units
Symbol
Formula
energy (work)
joule
W
W = ∫ Pdt
power
watt
P
P=
charge
coulomb
Q
Q = CV
current
ampere
I
electrostatic
pressure
volt
V
V = IR
resistance
ohm
R
R=
dW
dt
I=
V
R
V
I
Equivalent Units
watt-second
volt-ampere or
joule/second
ampere-second
coulomb/second
joule/coulomb
volt/ampere
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Voltage
• Energy gained or lost when a charge is
moved from one point to another.
• Potential difference
• EMF
W
Vab =
Q
dw
=
dq
⎡ joule ⎤
⎢⎣ coulomb ⎥⎦
dw P
= =V
dq I
E = energy given up or generated
E=
V = potential difference between two terminals
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Power
• Time rate of doing work
– BTU/second
– Joule/second
– watts
– horsepower
P = VI [watts]
V = voltage
I = current
1 t
Pavg = ∫ vi dt [watts]
t 0
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Energy (work)
W = ∫ P dt [watt - sec]
t2
t1
where P = watts
- or W = Pt
if power is constant
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Ohm’s Law
I
V = IR
V
I=
R
V
R=
I
-
+
V
V
I
R
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Resistance
The resistance of a section of conductor
of uniform cross section is:
R=
ρl
A
l
A
where
A=cross-sectional area (square meters or circular mils)
l = length (meters or feet)
R = resistance (ohms)
ρ = resistivity of material (ohm-meters) = 1/conductivity
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Resistivity for Typical Conductive
Materials
Material
Resistivity,
ohm-meters
-8
aluminum
copper
cast iron
2.6 x 10
-8
1.7 x 10
-8
9.7 x 10
lead
silver
steel
tin
nichrome
22 x 10
-8
1.6 x 10
-8
(11-90) x 10
-8
11 x 10
-8
100 x 10
-8
Resistivity,
ohm-circular mills per
foot
17
10
58
132
9.9
66-540
69
602
Note: The area of a circle one mill (0.001 inch) in diameter is one circular mil;
the area of any circle in circular mils equals the square of its diameter in mils.
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Circuit Element Characteristics
Element Schematic
Symbol
resistor
Current
Through
- I =V
I +
R
Voltage
Drop
V = IR
Power
Dissipation
V2
or I 2 R
R
Stored
Energy
zero
V
inductor
-
I +
V
capacitor
I=
φ
L
1
= ∫ V dt
L
I
-
+
V
I =C
dV
dt
V =L
V=
dI
dt
1
I dt
C∫
zero
zero
W=
W=
1 2
LI
2
1
CV 2
2
Units
ohm
Ω, K Ω,
MΩ
henry
h, mh, µh
farad
f, µf, pf
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Metric Prefixes
Multiplier
Prefix
Symbol
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
100 = 1
101
102
103
106
109
1012
1015
1018
atto
femto
pico
nano
micro
milli
centi
deci
---deka
hecto
kilo
mega
giga
tera
peta
exa
a
f
p
n
µ
m
c
d
---da
h
k
M
G
T
P
E
Note the use of
lower case letters
for multipliers less
than one and the
use of upper case
letters for multipliers
greater than 106.
Inconsistent usage on
“kilo”.
Commonly used
multipliers shown
in bold.
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Inductance
The inductance of a coil is:
L = KN
2
where
N = number of turns
L = inductance in henries
K = a constant dependent upon geometry and material