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”

Electric circuit theory Electromagnetic theory

- Electrical engineering • Power • Electric machines • Control • Electronics • Communications • Instrumentations

- Other branches of physical sciences

• Understanding of theory • To use correctly certain mathematical principles

- Problem solving

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 self-inductance

— 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_8/118/30460/7797848.cw/index.html

—http://www.mhhe.com/

Methods

• Read – Review – Demonstration – Examples and concept tests – Read again and Make summary – Homework

• Electric Circuits —Basic concepts and laws of electrical elements

—The analysis of the circuit: the behaviour of an interconnection of the elements

—Applications

Continually looking up material you though you

had acquire

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: — amperes (A) (one of the seven principal units)

• Charge — an electrical property of the atomic particles of which matter consists — coulombs (C)

• Voltage (potential difference) — the energy required to move a unit charge through an element: — volts (V) — Ground: reference point

• Energy — the capacity to do work: — joules(J)

• Power — the time rate of expending or absorbing energy: — watts (W)

ivdtdq

dqdw

dtdwp ⋅=⋅==

dqdwvab =

dtdqi =

]TimeCurrent[[Charge] and have we, ,definitionBy 0

⋅=== ∫t

t

idtqdtdqi

∫∫∫ ===t

t

t

t

q

q

vidtpdtvdqw000

Electrical quantities

Voltage: Volts (V), vab

Current: Amperes(A), i

Charge: Coulombs (C), q

Moving charges

Energy: Joules (J), w

Power: Watts (w), p

Time rate Time rate

Unit Charge

Unit Time Unit Time

dtdqi =∫=

t

t

idtq0

dqdwvab =

∫=q

q

vdqw0

∫=t

t

pdtw0

dtdwp =

ivdtdq

dqdw

dtdwp ⋅=⋅==

Electrical quantities – Reference

• Current

+3 A -3 A

• Voltage

Assign reference direction by arrows…

a b

vab = 3V

+ -

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

10V

2V 8V

0 V

c

0 V

c 0 V

c

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

RGiRv

ivab

/1==∝

The voltage v across a resistor is directly proportional to the current i flowing through the resistor (linear resistor):

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)

Prove: Assume a set of current flow into a node. The algebraic sum of currents at the node is Integrating both side Conservation of electric charge requires: the

node stores no net charge

∑=

=N

nni

10

( )tik

( ) ( ) ( ) ( ) ...321 +++= titititiT

( ) ( ) ( ) ( ) ...321 +++= tqtqtqtqT

( ) ( ) 00 =→= titq TT

General Case: KCL also applies to a closed boundary.

Kirchhoff’s voltage law (KVL)

A closed path/loop ∑=

=M

mmv

10

• Conservative force: the work, W, is zero for any simple closed path • Voltage: the energy required to move a unit charge through an element

015432 =−+−+ vvvvv

• Taking either a clockwise or a counter-clockwise trip around the loop • Passive elements: voltage drop (plus sign) • Active elements: voltage rise (negative sign)

034512 =+−+− vvvvv

Techniques: Voltage Divider

• The same current —Ohm’s law:

—KVL:

• Equivalent resistance

• Voltage v divided among the resistors

, 11 iRv = 22 iRv =

021 =++− vvv 21 RRvi+

=

21 RRReq += ∑=

=N

nneq RR

1 resistors, NFor

vRR

Rv21

11 += v

RRRv

21

22 += v

R

Rv N

nn

nn

∑=

=

1

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:

—KCL:

• Equivalent resistance

• Current i divided among the resistors

2211 RiRiv ==

21 iii += v

RRRv

Rvi

+=+=

2121

11

21

111RRReq

+=21 GGGeq += ∑

=

=N

nneq GG

1 :resistors NFor

iGGG

GivG

Rvi

eqeq

111

11 ====

Principle of current division In parallel circuits, the total current i is divided among the resistors in direct proportion to their conductances;

Electrical Safety

• 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.

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:

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 • 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)

— Vacuum tube diodes • 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 • 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 • 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 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

Quantity Basic unit Symbol

Length meter m

Mass kilogram kg

Time second s

Electric current ampere A

Thermodynamic temperature kelvin K

Luminous intensity candela cd

Amount of substance mole mol

Electrical Units

Quantity Symbol SI unit Symbol

Capacitance C farad F

Charge Q coulomb C

Conductance G siemens S

Current I ampere A

Energy or work W joule J

Frequency f hertz Hz

Impedance Z ohm Ω

Inductance L henry H

Power P watt W

Reactance X ohm Ω

Resistance R ohm Ω

Voltage V volt V

To derive the unit of a quantity:

( )2

2

smkg1pa 1

ime][length][T[Mass]

Length][[Length]]Time][Time[

]Length[[Mass]

Length][[Length]]Time[

]Velocity[[Mass]

Length][[Length]n]Accelratio[[Mass]

[Area][Force] [Pressure]

⋅=

=⋅

⋅=

⋅

⋅=

=⋅

⋅==

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

kWh ]Time(hour)(kW)[Power [Energy] ,0

=⋅== ∫t

t

pdtw

Theory of metallic conduction

• Objective: Calculate the current density • Model: Free electron gas

—Valence electrons • a sea of conduction electrons, Charge density:

—Steady State: • 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)

dVdqne =−

Em

nedSdtdqJ

τ2==

dL = vddt

dV = dS dL = vddtdS

dS n ( ) 0 : 0 ,0 0 ==< avvEt

, : ,0m

EemFaEeFt

−

==−=≥

( ) ( ) ( ) davavav vEmeaavvt

=−

==+==ττττ 0 ,

Calculate the drifting velocity

dSdtdqJ =

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):

Resistance, R, of an element denotes its ability to resist the flow of electric current (Ω).

AL

nemR

iRv

ab

ab

τ2=

⋅=

ivab ∝Lab

a b

A J i

F -e

Conductance, G, is the ability of an element to conduct electric current (S, 1S = 1Ω-1);

,2

Em

nedSdtdqJ

τ== J

nemEτ2

=

, charge aFor dq

AJAndJi ⋅=⋅•=

:Current

, :Force EdqF

=

abababab LEdqLEdqLFdw ⋅⋅=•=•=

:Work

( ) iA

Lne

mAJA

Lne

m

LA

AJne

mLJne

mLEdq

dwv

abab

abababab

ab

ττ

ττ

22

22

1

=⋅=

⋅⋅=⋅=⋅==

Resistance of the material • Resistivity: a material property

— Carrier density, n Metal > Semiconductor > insulator

— n and τ : Temperature dependence

• Energy transform and power consumption — Electrical energy → thermal kinetic energy →

internal energy — The power dissipated in a resistor

ρσ

τρρ

τ1 , , 22 ====

nem

AL

AL

nemR

e Electrical force

Drift displacement

Work welectric > 0

a b

ivdtdw

tR

vtRitividtvdqv

ab

abab

t

tab

q

qab

=

∆=∆=∆== ∫∫2

22

1

2

1

Electric field

Current

à b

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