intended learning outcomes - lnx01lnx01.ee.polyu.edu.hk/~eewlchan/ee1d01/ee1d01_1a.pdf ·...

EE1D01 Electrical Science for Everyone

1

Subject Lecturer

Dr. W.L. Chan

Department of Electrical Engineering

[email protected] CF609, Tel 27666145lnx01.ee.polyu.edu.hk/~eewlchan/EE1D01


2

a) understand basic operation principles of some electrical devices;

b) know ways to avoid electrical accidents at home and in work place;

c) use electricity in a more energy efficient way;

d) recognize the need for life-long learning.

Intended Learning Outcomes


3

Teaching ScheduleWeek Date Lecture Topics

1 4 Sept [1] Basic electricity



4 25 Sept [2] Electrical and electronic appliances

6 9 Oct [2] Electrical and electronic appliances

7 16 Oct [2] Electrical and electronic appliances

8 23 Oct [3] Electrical safety

9 30 Oct [3] Electrical safety

10 6 Nov [4] Energy efficiency



13 27 Nov Revision

Lecture (12:30 – 14:20), Tutorial (14:30 – 15:20)3


4

20%4 assignments (5% each)Assignments (individual work)

20%report (15%) and presentation (5%) Mini-project(group work of 2 to 3 students )

PercentagesRemarksComponents

Assessment Plan

Examination Questions (60%)

Continuous Assessment (40%)


55


6

For A+, it should be over 85For A, it should be around 80For B+, it should be over 75For B, it should be over 70For C+, it should be over 65For C, it should be over 60For D+, it should be over 55For D, it should be over 50

Tentative Mark to Grade Mapping


7

What is electricity?

Proton (+)

Neutron

Electron (-)

It is a form of energy that is created from the movement of elecIt is a form of energy that is created from the movement of electrons of atoms. trons of atoms. When the electrons move from one atom to the next, energy is creWhen the electrons move from one atom to the next, energy is created. The word ated. The word electrelectricity comes from the same root word as icity comes from the same root word as electrelectron.on.


8

Electric Charge

Charge (Q)An intrinsic property of matter that establishes a force of attraction or repulsion between two particles.Unit is Coulombs (C)

Positive proton (e+)Q = +1.602 X 10-19 C

Negative electron (e-)Q = -1.602 X 10-19 C

Neutralneutron.. 0 C

Valence electrons

Atom


9

SI Units

sSecondtTimeKKelvinTTemperatureΩOhmRResistanceWWattPPowerVVoltVPotential differencesSecondTPeriodHHenryLInductance (self)HzHertzfFrequencyVVoltEElectromotive forceAAmpereICurrentCCoulombQChargeFFaradCCapacitance

Unit symbolUnitQuantity symbol

Quantity


10

PrefixPrefix SymbolSymbol FactorFactor NumericallyNumerically NameName

gigagiga GG 101099 1 000 1 000 000000 000000 billionbillion

MegaMega MM 101066 1 000 1 000 000000 millionmillion

kilokilo kk 101033 1 0001 000 thousandthousand

centicenti cc 1010--22 0.010.01 hundredthhundredth

millimilli mm 1010--33 0.0010.001 thousandththousandth

micromicro μμ 1010--66 0.000 0010.000 001 millionthmillionth

nanonano nn 1010--99 0.000 000 0010.000 000 001 billionthbillionth

Common Prefixes

I = 0.00345 A could be written as 3.45 mA


11

Investigating pairs of charges


12

Experimenting with static charge


13

Positive and Negative Charge

Electrons are stripped from one component and transferred to the other to cause both to be oppositely charged.


14

Electro-negativity

Relativeelectro-negativityranking for somecommon materialsfrom electron donatingmaterials (+, glass) toelectron acceptingmaterials (-, Teflon)

GlassHuman HairNylonSilkFurAluminumPaperCottonCopperRubberPVCTeflon

+ + + + ++ + + ++ + ++ ++

-- -- - -- - - -- - - - -


15

Classification of Materials

ConductorsMaterials with few electrons in the outermost (valance) bandThe electrons can be freed with very little external force

InsulatorsMaterials with complete valance bandsIt takes a great force to free these electrons

SemiconductorsMaterials with half-complete valance bands


16

• Room temperature values (Ohm-m)-1 = (Ω - m)-1

Conductivity: Comparison

Silver 6.8 x 10 7

Copper 6.0 x 10 7

Iron 1.0 x 10 7

METALS conductors

Silicon 4 x 10-4

Germanium 2 x 10 0

GaAs 10-6

SEMICONDUCTORS

semiconductors

Polystyrene <10-14

Polyethylene 10-15-10-17

Soda-lime glass 10

Concrete 10-9

Aluminum oxide <10-13

CERAMICS

POLYMERS

insulators

-10-10-11


17


17

Which items below act as

conductors of electricity?

Press SPACE to find out the correct answer.

COPPER WOOD SALT WATER

GLASS


18

Van De Graaff Generator


19

LightningLightning is a form of direct current (DC) produced by static electricity in clouds.The static is formed when air molecules move past each other (just like clothes in a dryer).


20

What causes you to be shocked when you rub your feet across carpet?

An electrical discharge is the passing of an electric current through the air from a negatively charged object to a positivelycharge object. This is what causes lightning!


21

Basic Electrical Quantities

In the study of electric circuits, we deal with the fundamental phenomenon of the movement of electrically charged particles or simply charged particles.

The fundamental quantities that are used to describe how rapidly charged particles move in a circuit and in what way they do so in the circuit are current and voltage.


22

Current (I)

dt

dqt

qI

t

=

ΔΔ

=→Δ 0

lim

is simply a flow of charge along a conductor and is measured as the rate of flow of charge at each particular instant.

Coulombs/second ( C/sec) or Amperes (A)

1A = 1C/s = 6,240,000,000,000,000,000 electrons per second


23

Simple Circuit with Switch


24

+++

-

-

+++

-

-

+++

-

-

+++

-

-

Voltage

(Pressure)

(Electromotive Force)

--

- - -- -

- - --

-- - -

--

The flow of the electrons is referred to as Current

How dose electricity flow?


25

Current direction

Positive terminal to negative terminal


26

Measures current in a circuit.Can be considered a flow meter.Measures the number of electrons flowing past a given point in a circuit.Must be connected in series with the loadHas a very low resistance

Ammeter


27

Potential Energy

When an object is at some height in a gravitational field it is said to have gravitational potential energy, PEg

PEg


28

Electric Potential

Any point in an electric field is said to have Electric Potential, V.

However, only a Difference in PE is measurable so we talk of electric potential difference or potential difference, ΔV.

EPEV

q=

PEV

q

ΔΔ =

unit Volt, V

J1V=1

C

→


29

Examples of “Change of state”

0 mph 50 mph

Energy

Energy

1 ton

1 ton

Energy

30ºF 78ºF

50 mph 0 mph

Energy

Note: Some changes of state release energy.

Change of state is called “Work”.


30

Work Required Energy (J)

Creation of the Universe 1068

Hiroshima Atomic Bomb Explosion

1014 (energy release)

Accelerating a 2006 Honda Accord from 0 to 60 mph

5x105

Heat up 1 kg water by 1°C 4.2x103

Hard-hit baseball 103

Lifting an apple by 1 meter 1

Hopping flea (per hop) 10-7

Examples of Work


31

Voltage = V =

Examples:

EnergyCharge

WQ

V = WQ =

56 J2 C

= 28 V

Q = WV =

84 J21 V

= 4 C

Electric Potential


32

Measures the voltage (potential difference) between two points in a circuit.

Can be considered a pressure gauge.

Voltmeter


33

Electric Power

As current passes through a resistor, the resistor becomes hot because energy is dissipated in it. The voltage measured across the resistor gives us a measure of the rate at which energy is being dissipated as heat.

VIt

qV

t

q

Power or

n dissipatioenergy of Rate

charges flowing of change of Rate

=ΔΔ

=

ΔΔ

=

Joules/second (J/s)

or Watts (W)

or Volts-Amperes (VA)


34

‘Power’ is a measure of how fast energy is

converted.

A unit of power is the WATT.

1 watt = 1 joule/second

It takes time to transform energy from one form to another (i.e. to do work)!

Power


35

The watt is a familiar unit of electric power; a 100W light bulb converts 100J of electric energy into light and heat each second.

The kilowatt-hour (kWh) is the usual commercial unit of electric energy. One kilowatt-hour is the total work done in 1 hour (3600 s) when the power is 1 kilowatt (103 J/s), so

1 kWh = (103 J/s) (3600 s) = = 3.6 MJ

The kilowatt-hour is a unit of work or energy, not power.

Our electricity bills carry the energy consumption in units of

kWh.

35

Electric Power


36

A water boiling example

2 litre of water ≈ 2 kg

Specific heat capacity of water ≈ 4.187 kJ/kg/°C

Energy required for heating from 25 °C to 100 °C

≈ 4.187 x 2 x 75 = 628.05 kJ

Specific latent heat of water ≈ 2270 kJ/kg

Energy required for converting 1.31 kg of water to steam

≈ 2270 x 1.31 = 2973.7 kJ

A heater of 2000 W operated for 30 minutes:

Heat Energy = 1 kWh = 2000 x 30 x 60 J = 3600 kJ

≈ 628.05 kJ + 2973.7 kJ

The heating coil of a hot water heater operates at 220 V with 10 A current. If electrical energy costs $0.080/kWh, what does it cost to raise the 200 kg of water in the tank from 15 °C to 80 °C? How long does it take?

The kilowatt-hour is a measure of energy equal to

The energy needed to raise the temperature of 200 kg of water from 15 C ° to 80 C ° is

and the cost of operating the heater to produce this quantity ofthermal energy is

(cost)= (energy used) (rate) = (15 kWh) ($0.080/kWh) = $1.20

Example: a 2.2 kW heater

15 kWh = t x 2.2 t = 6.8 hours


38

Choose appropriate words to fill in the gaps below:

Electrical energy is convenient to use as it is easily____________ into useful forms of energy. Electrical energy is measured in ________, symbol J.

The electrical _________ of a device is equal to the rate at which a device transforms ___________ energy to other forms of energy.

Power is measured in _________, symbol W. A one kilowatt device uses one ____________ joules of electrical energy every __________.

joules electrical

thousandtransferred power

watts

second

WORD SELECTION:

joules

electrical

thousand

transferred

power

watts

second


39

Residence Power Usage

9876543210

600 WVacuum cleaner2 WClock Radio

5000 WCentral AC500 WPC 100 WStereo170 WTV1000 WMicrowave oven700 WRefrigerator1500 WToaster60 WLight


40

A Helpful Hydraulic Analogy


41

Batteries

Secondary cells / Rechargeable batteries

Lead-acid battery

Primary cells / Dry cells / Non-rechargeable batteries


42

Battery Capacity (mAh)


43

2.8

1.5

1.25

Vol

ts

% of discharge0 50 100

Lithium (pri.)

Silver oxide

Nickel-CadmiumAlkaline(Zn/MnO2)Carbon-Zinc

Cell Characteristics


44

Battery Capacity (mAh)

Ni-MH: 1.2V/cell4.1Ah 17712J(1.2 x 4.1 x 3600)

Li-ion: 3.7V/cell3Ah 39960J(3.7 x 3 x 3600)

LiFePO4: 3.2V/cell3Ah 34560J(3.2 x 3 x 3600)

14760C

10800C

10800C


45

Batteries in Series and Parallel


46

Ni-MH: 1.2V/cell

7 x 1.2V = 8.4V

Carbon-Zinc or Alkaline: 1.5V / cell

6 x 1.5V = 9V


47

Lead-acid battery: 2V/cell

3 cells x 2V = 6V1200 mAh (4320C)25920 J

6 cells x 2V = 12V1200 mAh (4320C)51840 J


48

Ideal Voltage Source


49

Ideal Current Source


50

Solar PV SystemsCells are the building block of PV systems

Typically generate 1.5 - 3 watts of power

Modules or panels are made up of multiple cellsArrays are made up of multiple modules

Sanyo HIT Photovoltaic module temperature dependenceCell efficiency=18.7% Module efficiency=16.8%(manufacturer’s data)


52

Typical NiMH and NiCd Charge Profile


53

Types of Currents

Direct Current (DC) Alternating Current (AC)


54

0Volts

+

-

0Volts

+

-

Direct Current (DC)

Alternating Current (AC)

Time (sec.)

Time (sec.)

Alternating current or AC is what comes out of wall outlets. In Hong Kong the direction of flow of AC changes at a rate of 50 cycles/sec (hertz).

Direct current or DC flows in one direction.

Types of Currents


55

Passive sign convention : current should enter the positive voltage terminal

Consequence for P = I VPositive (+) Power: element absorbs power

Negative (-) Power: element supplies power

Sign Conventions

+

I

V


56

(a)

(b)

(c)

5A

Energy Source

Absorbs power


57

Lumped Circuit Elements


58

Wire

Connected Wire

Non connecting wire

Cell

Battery

Power supply

Switch

Voltmeter

Ammeter

Motor

Fuse

Buzzer

Diode

Bulb

Resistor

Thermistor

Variable Resistor

Light Dependant Resistor (LDR)

Circuit Symbols


59

Branch and Node

A complete electronic circuit consists of branches and nodes.

Node

Node

Branches and nodes

Branch

Every element of a network forms a branch.

A junction point between 2 or more branches.


60

Kirchhoff’s Current Law (KCL)

The algebraic sum of the currents at a node is zero, i.e. Σnin = 0.

054321 =+−−+− iiiii

i1

i5

i4

i3i2

Kirchhoff’s current law

Since charge is conserved, then we must have continuity of flow of charge.

054321 =−++− iiiiior


61

Kirchhoff’s Current Law (KCL)


62

Kirchhoff’s Voltage Law (KVL)

The algebraic sum of the voltages around a closed loop is zero. i.e. Σnvn = 0.

This law is a consequence of the necessity for an energy balance in any system.

-

+v4

-

+v1

+

-

v5

-

+

v3-

+

v2

Kirchhoff’s voltage law

I

054321 =++++− vvvvv


63

Resistance is the opposition to the flow of an electric current, causing the electrical energy to be converted to thermal energy or light.

The metal which makes up a light bulb filament or stovetop eye has a high electrical resistance. This causes light and heat to be given off.

What is electrical resistance?


64

Resistance

Depends on: Length, cross sectional area, material, and temperature

LR

Aρ=

2

resistivity, m

L length, m

A cross sectional area, m

ρ → Ω→

→


65


66

Resistance and Cross Sectional Area


67

Wiring in Homes and Buildings


68

Temperature Variation of Resistivity

For most metals, resistivity increases approximately linearly with temperature

ρo is the resistivity at some reference temperature To

To is usually taken to be 20° C

α is the temperature coefficient of resistivity

)]TT(1[ oo −α+ρ=ρ

)]TT(1[RR oo −α+=


69

Superconductors

A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC

TC is called the critical temperature

The graph is the same above TC, but suddenly drops to zero at TC


70

Superconductors discovered in 1911Require cryogenic cooling

High Temperature Superconductors (HTS) discovered in 1986 - cuprates

6X higher temperature (135 K vs 23 K)Less cooling drives commercial economics

Zero DC electrical resistanceYields high electrical efficiency

>100X more power capacity than copper wire of same dimensions

High power density - reduced size and weight

Cooling with environmentally benign liquid nitrogen

Copper, HTS @ equivalent 1000 A capacity:

Power density drives system economics

Superconductors


71

Second Generation HTS Wires - YBCO Coated Conductors

AMSC 4 cm Technology

Cu, HTS power equivalents

“344 superconductors” cross-section

Laminates – copper, stainless…

Insert – substrate, buffer, YBCO

0 100 200 300 400 5000

40

80

120

Ic o

f 3

44

su

pe

rco

nd

uct

ors

Length (m)

Average Ic = 102AStd. Dev. = +/- 2.3%Max Ic = 109 AMin Ic = 89 A

0 100 200 300 400 5000

40

80

120

Ic o

f 3

44

su

pe

rco

nd

uct

ors

Length (m)

Average Ic = 102AStd. Dev. = +/- 2.3%Max Ic = 109 AMin Ic = 89 A

AMSC wire: 4.4 mm wide, single-coat

• HTS wire in production – commercially available

72

Renewable Energy: DC “Superconductor Electricity Pipeline” for Long-Length, High Power

1000-Mile, 5 GW power equivalents: right-of-way advantage for HTS DC cables

First DC HTS cable demonstration –Chubu U., Sumitomo Electric


73

Ohm’s Law

Resistance is a measure of opposition to the flow of charge and is measured in ohms (Ω)

VI = ----

R

Georg Ohm (1787-1854)


74

Linear Resistor

R

VRIVIP

R

VI

22 ===

=


75

Resistor Examples

Resistor

Contact leads

Symbol for resistor


76

Resistor Color Codes

x.01-Silver

X10000000009White

X1000000008Grey

X100000007Purple

X10000006Blue

X1000005Green

X100004Yellow

X10003Orange

X1002Red

X101Brown

X10Black

x.1-Gold

MultiplierDigitBand color

±5%Gold

±10%Silver

±2%Red

±1%Brown

ToleranceColor

None ±20%


77


Green = 5 Blue = 6 Orange = 3 Gold = ± 5 %

56 x 103 ± 5 % = 56000 ± 5 % = 56 kΩ ± 5 %


78

4 0 0 06 4 ± 2%= 464 kΩ ± 2%



79

Non-linear Resistor


80

Variable Resistor

Photoresistor Thermistor


81


82

Calculating Resistance

R =VI =

24 V0.03 A

= 800 Ω = 0.8 k Ω

R

B1

24 V

A0.03 A


83

Calculating Current

I =VR

= 36 V1800 Ω

= 0.02 A = 20 mA

S1

SPST

R

1.8 kΩ

B1

36 V


84

Calculating Voltage

V = IR = 0.15 A x 270 Ω = 40.5 V

R

270 Ω

B1

A0.15 A


85

Calculating Power

P =270 Ω

0.2 A

IV = 0.2 A x 54 V = 10.8 W

V54 V

P = I2R = 0.2 A x 0.2 A x 270 Ω = 10.8 W

P = V2/R =(54 V x 54 V) / 270 Ω = 10.8 W

A


86

Series Circuit

A circuit that only has one path for current to flow through is called a series circuit. If the path is broken, no current flows through the circuit.


87

kΩΩmAmV V A

+ V A ΩCOM -d c a c

Series Circuit

RT = VT ÷ IT = 90 V ÷ 0.1 A = 900 Ω

PT = VT x IT = 90 V x 0.1 A = 9 W

RT = 900 Ω

PT = 9 W

B1

90 V

R1 R2 R3

0.1 A


88

kΩΩmAmV V A


R1 = VR1 ÷ IT = 20 V ÷ 0.1 A = 200 Ω

PR1 = VR1 x IT = 20 V x 0.1 A = 2 W

RT = 900 Ω

PT = 9 W

B1

90 V

R1 R2 R3

0.1 A

R1 = 200 Ω200 Ω

PR1 = 2 W

VR1 = 20 V

Series Circuit


89

kΩΩmAmV V A


R2 = VR2 ÷ IT = 40 V ÷ 0.1 A = 400 Ω

PR2 = VR2 x IT = 40 V x 0.1 A = 4 W

RT = 900 Ω

PT = 9 W

B1

90 V

R1 R2 R3

0.1 A

R1 = 200 Ω200 Ω

PR1 = 2 W

VR1 = 20 V

PR2 = 4 W

400 Ω R2 = 400 Ω

VR2 = 40 V

Series Circuit


90

kΩΩmAmV V A


R3 = VR3 ÷ IT = 30 V ÷ 0.1 A = 300 Ω

PR3 = VR3 x IT = 30 V x 0.1 A = 3 W

RT = 900 Ω

PT = 9 W

B1

90 V

R1 R2 R3

0.1 A

R1 = 200 Ω200 Ω

PR1 = 2 W

VR1 = 20 V

PR2 = 4 W

400 Ω R2 = 400 Ω

VR2 = 40 V

VR.3 = 30 V

R3 = 300 Ω

300 Ω

PR3 = 3 W

Series Circuit


91

RT = 900 Ω

PT = 9 W

B1

90 V

R1 R2 R3

0.1 A

R1 = 200 Ω200 Ω

PR1 = 2 W

VR1 = 20 V

PR2 = 4 W

400 Ω R2 = 400 Ω

VR2 = 40 V

VR.3 = 30 V

R3 = 300 Ω

300 Ω

PR3 = 3 W

9 W = 2 W + 4W + 3 W

90 V = 20 V + 40 V + 30 V

900 Ω = 200 Ω + 400 Ω + 300 Ω

Series Circuit


92

It is often possible to replace relatively complicated resistor combinations with a single equivalent resistor. This is useful when we are not specifically interested in the current, voltage, or power associated with any of the individual resistors in the combinations.

Series Circuit


93

Resistors in Series

⋅⋅⋅⋅⋅+++= 321 RRRReq

Req


94

Parallel Circuit

A type of circuit that has more than one path for current is called a parallel circuit. If the path is broken, the current continues to flow through the circuit.


95

HouseholdHouseholdwiring wiring is a kind of is a kind of parallel circuitparallel circuit

220V

220V


96

kΩΩmAmV V A


Parallel Circuit

B1R1 R2 R3

30 V

VT = VR1 = VR2 = VR3 = 30 V


97

kΩΩmAmV V A


2 A

R1 = VR1 ÷ IR1 = 30 V ÷ 2 A = 15 Ω

15 Ω

VT = VR1 = VR2 = VR3 = 30 V

B1R1 R2 R3

30 V

Parallel Circuit


98

kΩΩmAmV V A


R2 = VR2 ÷ IR2 = 30 V ÷ 1 A = 30 Ω

30 Ω

VT = VR1 = VR2 = VR3 = 30 V

B1R1 R2 R3

30 V2 A

R1 = VR1 ÷ IR1 = 30 V ÷ 2 A = 15 Ω

15 Ω

Parallel Circuit

1 A


99

kΩΩmAmV V A


R3 = VR3 ÷ IR3 = 30 V ÷ 3 A = 10 Ω

10 Ω

VT = VR1 = VR2 = VR3 = 30 V

B1R1 R2 R3

30 V2 A

R1 = VR1 ÷ IR1 = 30 V ÷ 2 A = 15 Ω

15 Ω

R2 = VR2 ÷ IR2 = 30 V ÷ 1 A = 30 Ω

30 Ω

1 A

Parallel Circuit

3 A


100

kΩΩmAmV V A


3 A

VT = VR1 = VR2 = VR3 = 30 V

B1R1 R2 R3

30 V2 A

R1 = VR1 ÷ IR1 = 30 V ÷ 2 A = 15 Ω

15 Ω

R2 = VR2 ÷ IR2 = 30 V ÷ 1 A = 30 Ω

30 Ω

1 A

R3 = VR3 ÷ IR3 = 30 V ÷ 3 A = 10 Ω

10 Ω4 A

4 A = 1 A + 3 A

Parallel Circuit


101

kΩΩmAmV V A


3 A

VT = VR1 = VR2 = VR3 = 30 V

B1R1 R2 R3

30 V2 A

R1 = VR1 ÷ IR1 = 30 V ÷ 2 A = 15 Ω

15 Ω

R2 = VR2 ÷ IR2 = 30 V ÷ 1 A = 30 Ω

30 Ω

1 A

R3 = VR3 ÷ IR3 = 30 V ÷ 3 A = 10 Ω

10 Ω4 A

4 A = 1 A + 3 A

6 A

IT = 2 A + 1 A + 3 A = 6 A

Parallel Circuit


102

kΩΩmAmV V A


B1R1 R2 R3

30 V15 Ω 30 Ω 10 Ω

Measured RT = 5 Ω

Calculated total resistance is

RT = 1

1R1

1R2

1R3

+ +=

11

15130

110

+ +=

306

= 5 Ω

Parallel Circuit


103

Resistors in Parallel

⋅⋅⋅⋅⋅+++=

⋅⋅⋅⋅⋅+++=

321

321

1111

GGGG

RRRR

eq

eq

or

Req


104

Finding Equivalent Resistance

Example:

6 kΩ

9 kΩ3 kΩ

7.5 kΩReq

15 kΩ

(a)


105


15 kΩ7.5 kΩ 5 kΩ

8 kΩ

3 kΩ

5 kΩ

(b)

(c)


106

Find the equivalent resistance by making combinations of series and parallel resistors until only one resistor is left.

1kΩ

1kΩ

2kΩ

1kΩ

2kΩ 1kΩ



107

Voltage Divider

12 for RRVV io >>≈

io

o

i

VRR

RV

RIV

RR

VI

21

2

2

21

+=

×=+

=

Series resistance with 2 elements

+

-

Vi

R1

R2Vo

I


108

Voltage Divider


109

Voltage Divider

in

nn V

RRR

RV

+++=

...21

Series resistance with n elements

Vi

+

-

Vn


110

1kΩ

1kΩ

2kΩ

1kΩ

2kΩ

1kΩ

+–

10V

+

–

V1

+

–

V3

+

–

V2

Example: Resistor Ladder

Find V1, V2, and V3


111

1kΩ

1kΩ

2kΩ

1kΩ

2kΩ

1kΩ

10V

+

–

V1

+

–

V3

+

–

V2

Find an equivalent resistance for the network with V1 across it, then find V1 using a voltage divider.

+–



112

1kΩ

1kΩ

10V

+

–

V1

V5k1k1

k1V101 =

Ω+ΩΩ

=V

+–



113

1kΩ

1kΩ

2kΩ

1kΩ

2kΩ

1kΩ

10V

+

–

5V

+

–

V3

+

–

V2

Find an equivalent resistance for the network with V2 across it, then find V2.

+–



114

1kΩ

2kΩ

1kΩ

10V

+

–

5V

+

–

V2 1kΩ

V5.2k1k1

k1V52 =

Ω+ΩΩ

=V

+–



115

1kΩ

1kΩ

2kΩ

1kΩ

2kΩ

1kΩ

10V

+

–

5V

+

–

V3

+

–

2.5V

V25.1k1k1

k1V5.23 =

Ω+ΩΩ

=V

+–



116

Current Divider

21i2 for RRII >>≈

i21

12

21i

2211

IRR

RI

III

RIRI

+=

+==

Parallel resistance with 2 elements

Ii

I1 I2


117

Current Divider

How do we find I1, I2, and I3?

I R2 V

+

–

R1

I1 I2

R3

I3


118

Current Divider

I= I1 + I2 + I3

11 R

VI =

22 R

VI =

33 R

VI =

⎟⎟⎠

⎞⎜⎜⎝

⎛++=++=

321321

111

RRRV

R

V

R

V

R

VI

321

1111

RRR

IV++

=


119

Current Divider

Parallel resistance with n elements

Ii

I1 I2 In

.....//// where 21 RRR

IR

RI

eq

in

eqn

=

=


120

Voltage & Current Divider

5.000V

6A

6.000A

31.000A2

1.500A

1

3.000A

6.000V

21.000A6V

1.000A

3.000V

2

1.500A11.000A

3.000V

V1 +V2 +V3 = 6V, I1= I2= I3= IV1 = I1 R1, V2 = I2 R2, V3 = I3 R3

1I + 2I + 3I = 6 I =6 / (1+2+3) = 1AReq = 6 / I = (R1+R2+R3) = 6ΩV1 = 1I = 1 V = 6 R1 / Req

V2 = 2I = 2 V = 6 R2 / Req

V3 = 3I = 3 V = 6 R3 / Req

I1 + I2 + I3 = 6A, V1 = V2 = V3 = Vt

V1 = I1 R1 , V2 = I2 R2 , V3 = I3 R3

V1/2 + V2/2 + V3/1 = 6Vt (1/2+1/2+1/1) = 6Vt = 6 /(1/2+1/2+1/1) = 3VReq = Vt /6 = 1/(1/R1+1/R2+1/R3)

= 0.5ΩI2 = Vt /R2 = 6 Req/R2 = 1.5A


121

Capacitor

A capacitor is a storehouse of charge and energy that can be reclaimed when needed for a specific application

A capacitor will only charge to the potential difference between the terminals of the battery


122

Charging a Capacitor


123

Capacitance

Capacitance, C: The ability of a conductor to store energy in the form of electrically separated charges

Capacitance is the ratio of charge to potential difference

QC

V=

Δ

unit Farad, F

C1F=1

V

→


124

Construction of a CapacitorLead

Lead

Plate

Plate

Dielectric

The plates and leads are conductors.

The dielectric is an insulator.


125

Capacitance

Capacitance depends on size and shape

0

AC

dε=

2-12

0 2permittivity of free space, 8.85x10

Area of one plate

d distance between plates

C

NmA

ε →

→→


126

Dielectric Constants

Assume that a capacitor uses “air” as its dielectric material and has a total capacitance of 1 mFChanging the dielectric material to “dry paper” would change the capacitance of the capacitor to 3.5 mF


127

Non-Polarized Capacitors

Not sensitive to polarity connectionMay also be referred to as AC capacitorsCan be used in AC/DC circuits


128

Capacitance Reading

•Thus, we have a 0.1μF capacitor with ±10% tolerance.

4 5 12 7 610 10 pF=10 10 F=10 F=0.1 10 F=0.1μF− − −× × ×


129

Polarized Capacitors

Also known as electrolytic capacitorsThey are sensitive to polarityUsed only in DC circuitsReversing polarity could cause capacitor damage or explosionElectrolytic capacitors can have very high capacitance in a small case


130

Energy Storage

If a capacitor stores charge and carries voltage, it also stores the energy it took to separate the charge. The formula for this is:

Estored = (1/2)QV = (1/2)CV2 ,

where in the second equation we have used the relation: C = Q/V .


131

Capacitor circuit

When a capacitor is charged through a series resistor and dc source, the charging curve is exponential.

C

RIinitial

t0(b) Charging current

Vfinal

t0(a) Capacitor charging voltage


132

Capacitor circuit

When a capacitor is discharged through a resistor, the discharge curve is also an exponential. (Note that the current is negative.)

t

t

−Iinitial

0

(b) Discharging current

Vinitial

0(a) Capacitor discharging voltage

C

R


133

Universal exponential curves

Specific values for current and voltage can be read from a universal curve. For an RC circuit, the time constant is

τ RC=

100%

80%

60%

40%

20%

00 1τ 2τ 3τ 4τ 5τ

99%98%

95%

86%

63%

37%

14%

5% 2% 1%

Number of time constants

Per

cent

of f

inal

val

ue

Rising exponential

Falling exponential


134

Capacitors in Series

Capacitors in series each charge each other by INDUCTION. So they each have the SAME charge. The electric potential on the other hand is divided up amongst them. In other words, the sum of the individual voltages will equal the total voltage of the battery or power source.


135

Capacitors in Parallel

In a parallel configuration, the voltage is the samebecause ALL THREE capacitors touch BOTH ends of the battery. As a result, they split up the charge amongst them.


136

Capacitor Combinations

Series capacitors combine like parallel resistors

1/Cser = 1/C1 + 1/C2 + 1/C3 + · · ·

Parallel capacitors combine like series resistors

Cpar = C1 + C2 + C3 + · · ·


137

Inductance

Inductance occurs when current flows through a (real) conductor.The current flowing through the conductor sets up a magnetic field that is proportional to the current.The voltage difference across the conductor is proportional to the rate of change of the magnetic field.


138

Inductor

An inductor is a passive electrical device that stores energy in a magnetic field. An inductor is usually constructed as a coil of conducting material.


139Energy Stored

)(2

1)( 2 tLitwL =

Inductor


140

Inductor circuit


141

Inductor Combinations

Series inductors combine like series resistors

Lser = L1 + L2 + L3 + · · ·

Parallel inductors combine like parallel resistors

1/Lpar = 1/L1 + 1/L2 + 1/L3 + · · ·


142

Active and Passive Elements

Active elements can generate energyBatteriesVoltage and current sources

Passive elements cannot generate energyResistorsCapacitors and Inductors (but CAN store energy)

intended learning outcomes - lnx01lnx01.ee.polyu.edu.hk/~eewlchan/ee1d01/ee1d01_1a.pdf ·...

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