FOWLER CHAPTER 1LECTURE 2 BASIC CONCEPTS

SCIENTIFIC NOTATION (powers of ten)SEE TABLE 2-1, P33

ANY NUMBER CAN BE EXPRESSED AS BASE x10 EXPONENT

(CAN BE POSITIVE OR NEGATIVE) + OR -

OTHER BASES AND EXPONENTS 32 53 8125

ANY NUMBER RAISED TO THE ZEROTH POWER IS EQUAL TO ZERO

EXAMPLES: 10 1100 11000,11,12 000

WRITE 1000 IN SCIENTIFIC NOTATION

33 100.1101000 1000 WRITE AS 1 FOLLOWED BY 3 ZERO’SANY NUMBER >0 CAN BE EXPRESSED THIS WAY.

EXAMPLE: 1,237 CAN BE EXPRESSED AS 1.237X10³

COUNT THE NUMBER OF DECIMAL PLACES TO THE RIGHT OF THE FIRST DIGITTHEN PLACE THE DECIMAL PT. AFTER THE FIRST DIGIT. 1.237

1.237 THE NUMBER OF DECIMAL PLACES TO THE RIGHT OF THE FIRST DIGIT IS THE EXPONENT EXPRESSED AS THE POWER OF TEN, IN THIS CASE IT IS 3

1,237 =1.237X10³

FOR NEGATIVE EXPONENTS(ANY NUMBER <0) FOLLOW THE PROCEDURE ON THE PRIOR SLIDE, BUT IN THE REVERSE DIRECTION.

EXAMPLES: 10 0.1 =¹־ 10 0.01 =²־ 10 0.001 =³־HERE WE COUNT DECEMICAL PLACES TO THE LEFT INSTEAD OF THE RIGHT.

EXAMPLE: 10 0.001 =³־

0.001= 10 ³־ COUNT 3 PLACE TO THE LEFT.

FROM OUR LAST EXAMPLE LET’S WRITE 0.001237 IN S. N.COUNT FROM THE FIRST DIGIT TO THE LEFT.

.001237 -3 IS THE EXPONENT FOR THIS POWER OF TEN.

SO .001237= 1.237X10 ³־

1,237 CAN ASLO BE EXPRESSED AS

12.37X10²=1,237

OR 123.7X10¹=1,237

DEPENDING ON WERE THE DECIMAL PT. IS PLACED, BOTH RESULTS GIVE THE NUMBER.

.001237 CAN ASLO BE EXPRESSED AS

1.237X10 001237= .³ ־

OR 0.1237X10 001237= .²־

DEPENDING ON WHERE THE DECIMAL PT. IS PLACED, BOTH RESULTS GIVE THE NUMBER.

ENGINEERING NOTATION

IN THIS SYSTEM POWERS OF TEN ARE ALWAYS MULTIPIES OF 3

963 10,10,10 …ETC.

963 10,10,10 OR

EXAMPLE: EXPRESS 27000 IN S.N. AND E.N. S.N. 4107.2

E.N. 31027

METRIC PREFIXES TABLE 2-2, P. 35

(ENGINEERING NOTATION)

POWER OF TEN

ELECTRICAL UNITS AND SYMBOLS TABLE 2-3 P.37

QUANTITY UNIT SYMBOL

CURRENT AMPERE(A) I

VOLTAGE VOLT(V) V

RESISTANCE OHM(Ω) R

FREQUENCY HERTZ(Hz) f

CAPACITANCE FARAD(F) C

INDUCTANCE HENERY(H) L

POWER WATTS(W) P

EXAMPLES : USES OF ENGINEERING NOTATION (E.N.)

1,000,000Ω = 6101 = 1MΩ

27,340Ω = 410734.2 =27.34X10³Ω =27.43KΩ IN E.N.OR .0274MΩOR O.OOO274GΩ

0.000546Ω =.546X10 ³־ Ω = .546mΩ =546uΩ =546000nΩ

QUICK MATH REVIEW

4 OPERATES IN ALL OF MATHEMATICS

ADDITIONSUBTRACTIONMULTIPICATIONDIVISION

DIVISION AND MULTIPICATION CAN BE DERIVATED FROM ADDITION AND SUBTRACTION.

MULTIPICATION IS A SERIES OF REPEATED ADDITIONS

EXAMPLE: 2X4=8 OR 2+2+2+2=8

DIVISION IS A SERIES OF REPEATED SUBTRACTIONS

EXAMPLE:

224

426

628

248

SIMPLE ALGEBRA

ANY QUANTITY ON BOTH SIDES OF AN EQUATION ARE EQUAL.

EXAMPLES V=V EXAMPLES I=I R=R

ADDITION V+V=2V 1+1=2SUBTRACTION V-V=0 1-1=0

2V-V=V

A+B=C

ANY QUANTITY CAN BE ADDED OR SUBTRACTED TO BOTH SIDES OF ANY EQUATION.

GIVEN A+B=C

SOLVE FOR ASINCE -B=- B, ADD THIS TO BOTH SIDES OF THE EQUATION.

A+B-B=C-B

SINCE B-B=0

A+0=C-B A=C-B

SOLVE FOR B A+B=C ADD –A TO BOTH SIDES. A+B-A=C-A B+A-A=C-A B+0=C-A B=C-A

LAWS OF EXPONENTS

V CAN ALSO BE EXPRESSED AS V¹, SO V=V¹

ANY QUANTITY DIVIDED BY ITSELF= 1

SINCE 1/V=1/V V=V V(1/V) =V(1/V) V(1/V) =V(1/V)

1=1

1/V CAN BE WRITTEN AS V ¹־

1/V=V ¹־

OR XVVX /1

V/V = 1 OR V¹/V¹ =V¹ ¹־ =Vº =1

EXAMPLE: V²/V =V²/V¹ = V² ¹־ =V¹ =V

OR VxV/V = VxV/V =V

YXYX VVV /

EXAMPLE: VVVVV /1/ 13232

XXX RVRV //

EXAMPLE: 222 // RVRV

OR 22 /// RVRVRV

422 VVVVVV

OR XYYX VV

EXAMPLE: 1642 222

YXY VV XV

51111111111

53232

VVVVVVVVV

VVVV

SQUARE ROOTS

WE CAN RAISE A BASE NUMBER TO ANY POWER

8² =64

LETS REVERSE THIS PROCESS

FIND 64

IS DEFINED AS A RADIAL SIGN

2 ANOTHER WAY OF SHOWING THE SAME THING

X2 64INDEX

INDEX: HOW MANY TIMES WAS THIS NUMBER X MULTILED BY ITSELF TO GET 64

864

64882

ANOTHER WAY TO EXPRESS THIS

222222228

8888886464

13/33/133 333

12/22/122/12/12 1

283

Y XYX VV /

VVVVV

VVOR

VV

12/22/122 2

2/12

2/1

)(EXAMPLE:

ASDEFINEDISMEANSSYMBOL

OHM’S LAW

IRV

RIV

RIV

RIV

IV

R IS A PROPORTIONIALITY CONSTANT

THE PRODUCT IR CAN BE WRITTEN SEVERAL WAYS IRRIRI

.INCREASINGISQUANTITYAMEANS

.DECREASINGISQUANTITYAMEANS

V=IR SOLVE FOR IMULTIPLIE BOTH SIDES BY 1/R

(1/R)V=IR(1/R)

V/R=IR/R

V/R=I R/R

V/R=I(1)

V/R=I

OR I=V/R

HOW CAN WE INCREASE I

RVI

VI

RTVI

RVI

/

/

/

ONE WAY IS TO INCREASE V

OR DECREASE R

I IS INVERSELY PROPORTIONAL

TO R. AS R ↓, I↑

IF WE WANT TO DECREASE I, ↑R

RVI /

I IS INVERSELY PROPORTIONAL

TO 1/R. AS R↑, I↓

.ALITYPROPORTIONFORSYMBOLAIS

OHM’S LAW CIRCLE AND TRIANGLE

TRIANGLE FOR THE POWER EQUATION

POWER,CURRENT, RESISTANCE, VOLTAGE WHEEL

ANY VARIABLE ON THE POWER WHEELCAN BE FOUND USING THE FOLLOWINGTWO EQUATIONS.

1. V=IR2. P=IV

EXAMPLE: P=V²/RWHERE DID THIS COME FROM?SOLVE EQ. 1. FOR I

V=IR

V/R=IR/R

I=V/R

SUBSITUTE I=V/R INTO EQ. 2

P=IV

P=(V/R)V =V²/R

P=V²/R

DERIVE P=I²R FROM EQUATIONS 1. AND 2.

P=IV SUB. FOR V=IR IN P=IV

P=I(IR)

P=I²R

ONE MORE TO TORTURE YOU!!!

PRV

PRV

PRV

RVPVVV

RVPV

IRV

PRV

2

2

)/(

)/(

SOLVE

SUB. FOR I=V/R

ANDRIOD APP APPLE APP

There are two types of energy: potential or stored energy, and kinetic or energy in motion.

Potential energy is stored, or latent. Energy can be stored in many ways

Kinetic energy is actual energy in motion. Moving water, wind, and solar radiation are examples of kinetic energy.

JOULE: UNIT OF ENERGY,TOO SMALL FOR PRACTICAL USE. WATTS ARE USED INSTEAD, MORE ON THIS LATER.

P-2

BARBELLS WITH P.E. UNTIL ITS DROPED

WRECKING BALL WITH HUGH AMOUNT OF K.E.

WORK IS FORCE MOVING THRU A DISTANCE

FOR 100%EFFICIENCY, Pout =Pin, NOT POSSIBLE!!VIOLATES THE LAWS OF THEMODYNAMICS

P-4

percentj

j

inpower

outpowerEFFICIENCY 101.

100

10

MIL= ONE THOUSANDTH OF AN INCHCIRCULAR MIL=TO THE AREA OF A CIRCLE WITH A DIAMETER OF ONE MIL.

http://www.youtube.com/watch?v=sSVI5l-MbMQ&list=UU2bkHVIDjXS7sgrgjFtzOXQ

Copper: The Miracle Metal

P-6

ATOMIC STRUCTURE OF ALUMINUM ATOMIC STRUCTURE OF COPPER

ATOMIC STRUCTURE OF SILVER ATOMIC STRUCTURE OF GOLD

ELECTRIC FIELD LINES AROUND POINT CHARGES

UNLIKE CHARGES ATTRACT LIKE CHARGES REPEL

P-8

CREATION OF SODIUM CHOLRIDE ION (SALT)

STATIC ELECTRICITY

ELECTROSTATIC PRECIPITATOR

DUST PARTICLES IN

NEGATIVE CHARGE PLACEDON DUST BY GRID

DUST REMOVED FROM AIRBY ELECTROSTATIC ATTRACTIONWITH THE POSITIVELY CHARGEDPLATES

Electrostatic Precipitator System Working.avi

http://www.youtube.com/watch?v=A0tDieiia_c