PY2011 Current Electricity
Dr. Hongzhou Zhang (张洪洲)
hozhang@tcd.ie
SNIAM 1.06
http://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/
SF-Circuit/2011.php
The goal…
“an ability to apply knowledge of mathematics,
science, and engineering”
Electromagnetic theory
Electric circuit theory
- Electrical engineering
• Power
• Electric machines
• Control
• Electronics
• Communications
• Instrumentations
- Other branches of physical sciences
- Problem solving
• Understanding of theory
• To use correctly certain
mathematical principles
Course content
•
•
•
DC Circuits (6)
— Basic concepts and laws: Elements of Electrical Circuits, Serials/parallel resistors,
Voltage/current dividers, Kirchhoff’ laws,
— Analysis methods: Nodal and mesh analysis
— Circuit Theorems: Linearity property, Superposition, Source transformation, Thevenin's
theorem and Norton's theorem, Maximum power transfer
— Capacitors and Inductors
— Transient analysis: Capacitors and Inductors, integration and differentiation
AC Circuits (5)
— Sinusoids and phasors: Sinusoids, Phasors, Complex representation, Phasor relationships
for circuit elements, Frequency domain, Impedance combinations
— Sinusoidal steady-state analysis: Superposition Theorem, Source transformation,
Thevenin and Norton Equivalent
— AC Power Analysis: Instantaneous and average power, Maximum average power transfer,
effective RMS value, Apparent power and power factor
— Transformers: Review of electromagnetic induction, mutual inductance and selfinductance
— Frequency response: Resonance, low and high pass filters and active filters, L-R-C circuits
Review (1)
Resources
• Textbook
— Fundamentals of Electric Circuits, Charles K. Alexander
and Matthew N. O. Sadiku, 4th edition, McGRAW-HILL
—Electronics Fundamentals, Thomas L. Floyd and David M.
Buchla, 8th edition, Pearson/Prentice Hall
—University Physics, Young and Freedman, 12th edition,
Addison-Wesley
—Fundamental Electrical and Electronic Principles,
Christopher R Robertson, 3rd edition, Elsevier
—The Art of Electronics, Paul Horowitz and Winfield Hill, 2nd
edition, Cambridge
• Web
— http://wps.prenhall.com/chet_floyd_electfun_8/118/30460/7
797848.cw/index.html
— http://www.mhhe.com/
Methods
• Read – Review – Demonstration – Examples
and concept tests – Read again and Make
summary – Homework
Continually looking up
material you though you
• Electric Circuits
had acquire
—Basic concepts and laws of electrical elements
—The analysis of the circuit: the behaviour of an
interconnection of the elements
—Applications
Time Table
Week #
12
13
14
15
16
Lectures
2
3
3
2
2
Tues 12:00-13:00
Wed 16:00-17:00
Fri 10:00-11:00
Lecture 1 DC Circuits
Basic Concepts and Basic Laws
Lecture Objectives
• Basic Concepts
—Electrical quantities: Charge, Current, Voltage, Energy, and
Power
—Passive convention
—Elements of electric circuit
• Ideal elements
• Linear elements
• Ground
—Network topology: Nodes, Branches, and Loops
• Basic Laws:
—Ohm’s Law
—Kirchhoff’ laws
—Series, parallel, series-parallel circuits and voltage(current)
dividers
• Safety
Electrical quantities
• Electric Current
— the time rate of change of charge: i =
dq
dt
— amperes (A) (one of the seven principal units)
• Charge
— an electrical property of the atomic particles of which matter consists
— coulombs (C)
t
dq
By definition, i =
, we have q = ∫ idt and [Charge] = [Current ⋅ Time]
dt
t0
• Voltage (potential difference)
dw
— the energy required to move a unit charge through an element: vab =
dq
— volts (V)
— Ground: reference point
• Energy
q
t
t
— the capacity to do work: w = ∫ vdq = ∫ pdt = ∫ vidt
q0
t0
t0
— joules(J)
• Power
dw dw dq
=
⋅
= v ⋅i
— the time rate of expending or absorbing energy: p =
dt dq dt
— watts (W)
Electrical quantities
Unit Charge
Voltage: Volts (V), vab
Moving charges
q
w = ∫ vdq
q0
dw
vab =
dq
Charge: Coulombs (C), q
Energy: Joules (J), w
t
q = ∫ idt
i=
dq
dt
t0
Time rate
dw dw dq
p=
=
⋅
= v ⋅i
dt dq dt
dw
p=
dt
t
w = ∫ pdt
Time rate
Current: Amperes(A), i
Power: Watts (w), p
Unit Time
Unit Time
t0
Electrical quantities – Reference
• Current
+3 A
-3 A
Assign reference direction by arrows…
• Voltage
vab = 3V
a
+
b
-
Assign reference polarity by plus/minus signs…
a
b
-
+
vab = -3V
Passive and Active Elements
• Passive sign convention
The current enters:
—Positive terminals
• Passive elements
• Absorbing power
• p = vi > 0
—Negative terminals
• Active elements
• Supplying power
• p = -vi < 0
Quiz 1: Passive or Active?
Voltage: Electrical Potential Difference
c
2V
8V
10V
0V
c
0V
c
0V
Elements of electric circuit
• Sources
— DC voltage sources: Batteries, Fuel Cells, Solar Cells, Generator, Power
Supplies, Thermocouples, Piezoelectric Sensors
— DC current sources
— AC generators (Alternators)
• Wires
• Loads
—
—
—
—
—
Resistors
Capacitors
Inductors
Transformers
Devices: diodes, transistors, amplifiers …
• Current Control and Protection
— Mechanical Switches
— Protective Devices: Fuses and Circuit breakers
• Ground
— Earth
— reference(common)
• Circuit Measurement
— Multimeter: Voltmeter, Ammeter, Ohmmeter, Capacitance meter
Basic Concepts: Schematic Circuit Symbols
Ideal Sources
• An Ideal Independent
Source
— an active element
— provides a specific
voltage/current
completely independent
of other circuit elements
• An ideal
dependent/control source
— an active element
— source quantity
controlled by another
voltage or current
— A VCVS/CCVS/VCCS/CCCS
*-Controlled-*-Source
(*C*S)
Example
Calculate the power supplied or absorbed by each element:
Ideal Resistor - Ohm’s Law
The voltage v across a resistor is directly proportional to the current i flowing through
the resistor (linear resistor):
vab ∝ i
v = iR
G = 1/ R
Ideal Wires
• Wire resistance is negligible
—Voltage drop: Vw= iR = 0
—Perfect conductor: the electric
potential is the same at every
point of the surface.
—Current path: no charge
accumulation (steady state)
• Open and Short Circuit
—Open: no current
—Short: zero voltage drop
Circuits: Some basic concepts of network topology
• Branch (b = 5)
— a single element such as a voltage source
or a resistor
• Node (n = 3)
— the point of connection between two or
more branches
• Loop
— any closed path in a circuit
— independent Loop (l = 3): if it contains a
branch which is not in any other loop
• Fundamental theorem of network topology: b
= l+n-1
• Connection
— Series: elements are cascaded or
connected sequentially: exclusively share
a single node
— Parallel: elements are connected to the
same two nodes
Kirchhoff’s current law (KCL)
N
∑i
n =1
n
=0
Prove:
Assume a set of current ik (t ) flow into a node.
The algebraic sum of currents at the node is
iT (t ) = i1 (t ) + i2 (t ) + i3 (t ) + ...
Integrating both side
qT (t ) = q1 (t ) + q2 (t ) + q3 (t ) + ...
Conservation of electric charge requires: the
node stores no net charge
qT (t ) = 0 → iT (t ) = 0
General Case: KCL also applies to a closed boundary.
Kirchhoff’s voltage law (KVL)
M
A closed path/loop ∑ vm = 0
m =1
• Conservative force: the work, W, is zero for any simple closed path
• Voltage: the energy required to move a unit charge through an element
v2 + v3 − v4 + v5 − v1 = 0
v2 − v1 + v5 − v4 + v3 = 0
• Taking either a clockwise or a counter-clockwise trip around the loop
• Passive elements: voltage drop (plus sign)
• Active elements: voltage rise (negative sign)
Techniques: Voltage Divider
• The same current
—Ohm’s law: v1 = iR1 , v2 = iR2
− v + v1 + v2 = 0
—KVL:
v
i=
R1 + R2
}
• Equivalent resistance
Req = R1 + R2
N
For N resistors, Req = ∑ Rn
n =1
• Voltage v divided among the resistors
R1
v1 =
v
R1 + R2
R2
v2 =
v
R1 + R2
vn =
Rn
N
∑R
n =1
v
n
Principle of voltage division In series circuits, the source voltage v is divided among
the resistors in direct proportion to their resistances;
Techniques: Current Dividers
• The same voltage
— Ohm’s law: v = i1 R1 = i2 R2
i = i1 + i2
—KCL:
}
v
v 1 1 
i= +
=  + v
R1 R2  R1 R2 
• Equivalent resistance
1
1
1
= +
Req R1 R2
Geq = G1 + G2
For N resistors : Geq = ∑ Gn
• Current i divided among the resistors
i1 =
N
n =1
i
G
v
= vG1 =
G1 = 1 i
R1
Geq
Geq
Principle of current division In parallel circuits, the total current i is divided among
the resistors in direct proportion to their conductances;
Electrical Safety
Safety is always a concern with electrical circuits. Knowing the rules
and maintaining a safe environment is everyone’s job. A few
important safety suggestions are:
•
•
•
•
•
•
•
Do not work alone, or when you are drowsy.
Do not wear conductive jewelry.
Know the potential hazards of the equipment you
are working on; check equipment and power
cords frequently.
Avoid all contact with energized circuits; even
low voltage circuits.
Maintain a clean workspace.
Know the location of power shutoff and fire
extinguishers.
Don’t have food or drinks in the laboratory or
work area.
Electrical Safety
• Electrical hazards: shocks, burns, electrocution, fire hazard
—Current not the voltage is the cause
Electrical Safety: What should you do, if…?
• an overhead wire falls across your vehicle
while you are driving. What if the engine
stalls?
• you are standing in water and are asked to
operate electrical equipment.
• you work at heights or hand long objects.
• another person cannot let go of an energized
conductor.
Appendix
Milestones in Electronics
•
The Beginning of Electronics
—
Electric currents in vacuum tubes
•
•
•
•
—
Vacuum tube diodes
•
•
•
—
•
A binary machine envisioned, John Atanasoff, 1937
A binary machine called ABC constructed (based on vacuum tubes and capacitors), John Atanasoff and Clifford Berry, 1939
The first stored program computer, the Eniac, John von Neumann, 1946
Microwave oscillators and microwave tubes: 1939
Radar, high-frequency communication, Cathode ray tubes, World War II
Solid State Electronics
—
—
—
—
—
—
—
—
•
The first licensed broad-cast radio station, Herbert Hoover, 1921
Super-heterodyne radio solved high-frequency communication, Edwin Armstrong, end of 1920s
The first TV picture tube, Vladimir Zworykin, 1923
A complete television system, Philo T. Farnsworth, 1927
Many developments in radio (metal tubes, automatic gain control, directional antennas, …), 1930s
Electronic Computers
•
•
•
—
—
Forerunner of vacuum tube diodes: Fleming valve, John A. Fleming, 1904
Gridded vacuum tube could amply a weak signal: Audiotron, Lee DeForest, 1907
Improved version of Audiotron enabled transcontinental telephone service and radios, 1912
Radio and TV
•
•
•
•
•
—
Glowing tube with flowing current, Heinrich Geissler (1814-1879)
Current in the tube consists of particles, Sir William Crookes (1832-1919)
Carbon filament bulbs-current flow to positive charged plate, Thomas Edison (1847-1931)
Properties of electrons measured, Sir Joseph Thompson (1856-1940)
The Invention of the transistor, Walter Brattain, John Bardeen, and William Shockley, Bell Labs, 1947
Commercial manufacturing of transistors, 1951
The first Integrated circuit, Jack Kilby, Texas Instruments, 1958
The first ‘’op-amp’’ (µA709) and Industry standard op-amp (741), Bob Widlar, Fairchild Semiconductor, 1965
The first microprocessor (4004 chip), Intel (a group from Fairchild Semiconductor), 1971
The Internet, 1990s
Digital Audio Radio Service, 1995
Wireless broadband, 2001
Nanotechnology … recent research and development
—
New devices and applications of technology
A systems of units
• To communicate results of physical measurement in a standard language
• Metric: SI, MKS, CGS
The six basic SI units
Electrical Units
Symbol
SI unit
Symbol
Basic unit
Length
meter
m
Capacitance
C
farad
F
Mass
kilogram
kg
Charge
Q
coulomb
C
Time
second
s
Conductance
G
siemens
S
Electric current
ampere
A
Current
I
ampere
A
Thermodynamic temperature
kelvin
K
Energy or work
W
joule
J
Luminous intensity
candela
cd
Frequency
f
hertz
Hz
Amount of substance
mole
mol
Impedance
Z
ohm
Ω
Inductance
L
henry
H
To derive the unit of a quantity:
Power
P
watt
W
[Force] [Mass] ⋅ [Accelration]
=
=
[Area]
[Length] ⋅ [Length]
[Velocity]
[Length]
[Mass] ⋅
[Mass] ⋅
[Mass]
[Time][Time]
[Time]
=
=
=
[Length] ⋅ [Length]
[length][Time]2
[Length] ⋅ [Length]
1 pa = 1 kg
m ⋅ s2
Reactance
X
ohm
Ω
Resistance
R
ohm
Ω
Voltage
V
volt
V
[Pressure] =
(
)
Symbol
Quantity
Quantity
Sense the units
•
Charge
— The Coulomb is a large unit: In 1C of charge, 6.24×1024 electrons
•
Voltage
— Utility Voltage: 240 V
•
Resistance
— Human body: 10 kΩ - 50 kΩ
•
Current
— Physical effect
•
•
16 mA: Painful shock!
23 mA: Severe painful shock, muscular contractions, breathing difficulty!
— Household
•
•
•
•
•
A Light bulb and a typical motor in drill, eggbeater etc: ½ - 1 A
A microwave oven and a toaster: ~ 6 A
Hair dryers and electric heaters: ~ 12 A
Fuses/circuit breakers: 15 to 20 A
Power
— Microwave oven: 800 watts
— Clock: 2 watts
— TV: 250 watts
•
Energy
— Monthly consumption of household appliances: TV 10 kWh
t
w = ∫ pdt ,
t0
[Energy] = [Power (kW) ⋅ Time(hour)] = kWh
Theory of metallic conduction

dq
J=
dSdt
• Objective: Calculate the current density
• Model: Free electron gas
—Valence electrons
• a sea of conduction electrons, Charge density: − ne =
—Steady State:
•
•
•
•
dq
dV
Constant electric field: electron velocity gains
Collisions of electrons: electron velocity losses
Velocity gains = velocity losses… average drifting velocity vd
The free time τ between collisions (during which the field acts on
the carrier)
2


Calculate the drifting velocity


t < 0, E = 0 : (v0 )av = 0
J=
dq
ne τ
=
E
dSdt
m



  F − eE
=
t ≥ 0, F = −eE : a =
,
m
m

 

− eτ  
t = τ , (v )av = (v0 + aτ )av = (aτ )av =
E = vd
m
n
dV = dS dL = vddtdS
dS
dL = vddt
Ohm’s Law
•
•
Objective: Calculate Resistance R
The voltage v across a resistor is directly proportional to the current i flowing
through the resistor (linear resistor): vab ∝ i

dq
ne 2τ 
J=
E,
=
dSdt
m
m
E= 2 J
ne τ
 
Current : i = J • dn ⋅ A = J ⋅ A
Lab
b
a
J
For a charge dq,


Force : F = dqE ,
 
 
Work : dwab = F • Lab = dqE • Lab = dq ⋅ E ⋅ Lab
dwab
m
m
 1
= E ⋅ Lab = 2 J ⋅ Lab = 2 J ⋅  A ⋅  Lab
dq
ne τ
ne τ  A 
m L
m L
= 2 ab ( J ⋅ A) = 2 ab i
ne τ A
ne τ A
vab =
i
A
F
-e
vab = R ⋅ i
m Lab
R= 2
ne τ A
Resistance, R, of an element denotes its ability to resist the flow of electric current (Ω).
Conductance, G, is the ability of an element to conduct electric current (S, 1S = 1Ω-1);
Resistance of the material
• Resistivity: a material property
— Carrier density, n
Metal > Semiconductor > insulator
— n and τ : Temperature dependence
R=
m L
L
,
=
ρ
ne 2τ A
A
ρ=
1
m
,
=
σ
ne 2τ
ρ
• Energy transform and power consumption
— Electrical energy → thermal kinetic energy →
internal energy
— The power dissipated in a resistor
a
q2
Electric field
b
Electrical force
t2
2
vab
∫q vab dq = ∫t vabidt = vabi∆t = i R∆t = R ∆t
1
1
Drift displacement
2
dw
= vabi
dt
Current
Work welectric > 0
à
b
e
Resistors
• Linear/Nonlinear (Ohmic/nonohmic) resistor
• Power rating
— the maximum power without being damaged by excessive heat
build-up
• Fixed and variable resistors
– Fixed
• Colour/label code
• Types: Carbon-composition, chip resistors, film resistors,
wriewound (high power rating)
– Variable
• Potentiometer: divide voltage
• Rheostat: control current
P854 Young, P40-48, P90-93 Thomas
Lecture 2 DC Circuits
Circuit Analysis Methods