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ECE 102Engineering Computation

Chapter 4SI Terms and Formulae

Dr. Herbert G. Mayer, PSUDr. Herbert G. Mayer, PSUStatus 9/2/2015Status 9/2/2015

For use at CCUT Fall 2015For use at CCUT Fall 2015

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Syllabus

SISI What Is?What Is? Passive Sign ConventionPassive Sign Convention Electric SourcesElectric Sources BibliographyBibliography

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SI SI is the abbreviation fSI is the abbreviation from the French name: rom the French name: Le Le

SSystème ystème IInternational d'Unitésnternational d'Unités

Standards, published in 1960 as the result of an Standards, published in 1960 as the result of an initiative started in 1948; they are based on the initiative started in 1948; they are based on the meter-kilogram-second (MKS) systemmeter-kilogram-second (MKS) system

SI is formally declared to be SI is formally declared to be evolvingevolving

Some of the SI units will change, but is so, then per Some of the SI units will change, but is so, then per international agreementsinternational agreements

Main reason for change is technological evolution, Main reason for change is technological evolution, allowing more and more precise definitionsallowing more and more precise definitions

The corresponding American organization is NIST:The corresponding American organization is NIST:

NIST stands for: National Institute for Standard and NIST stands for: National Institute for Standard and TechnologyTechnology

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SI 7 Base Units

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SI Units

m: meter – is length of light traveled in m: meter – is length of light traveled in 1/299,792,4581/299,792,458thth of a second of a second

kg: kilogram – equal reference prototype; will likely kg: kilogram – equal reference prototype; will likely changechange

s: second – duration of 9,192,631,770 periods of s: second – duration of 9,192,631,770 periods of radiation corresponding to the transition between radiation corresponding to the transition between the two hyperfine levels of the ground state of the two hyperfine levels of the ground state of cesium 133 atom cesium 133 atom

A: ampere – current which in 2 parallel conductors 1 A: ampere – current which in 2 parallel conductors 1 meter apart in vacuum produces a force of 2 * 10meter apart in vacuum produces a force of 2 * 10-7-7 newton per meter of conductornewton per meter of conductor

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SI Units K: Kelvin – thermodynamic temperature unit that is K: Kelvin – thermodynamic temperature unit that is

the 1/273.16 fraction of water temperature at triple the 1/273.16 fraction of water temperature at triple pointpoint

mol: mole – is amount of substance of a system mol: mole – is amount of substance of a system which contains as many elementary entities as there which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; entities are atoms in 0.012 kilogram of carbon 12; entities can be atoms, molecules, electronscan be atoms, molecules, electrons

Old definition: the mole is the amount of substance Old definition: the mole is the amount of substance that contains 6.022,141,79 x 10that contains 6.022,141,79 x 102323 specified specified elementary entitieselementary entities

cd: candela – is luminous intensity of a source that cd: candela – is luminous intensity of a source that emits monochromatic radiation of frequency 540 * emits monochromatic radiation of frequency 540 * 10101212 hertz and further constraints hertz and further constraints

More on SI units later in the term . . .More on SI units later in the term . . .

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Changes Coming

Per 2011 declaration, the Per 2011 declaration, the kilogramkilogram, the , the ampereampere, , the degree the degree kelvinkelvin and the and the molemole, , will be will be redefined in terms of invariants of natureredefined in terms of invariants of nature

New definitions will be based on fixed New definitions will be based on fixed numerical values of the Planck constant (h), the numerical values of the Planck constant (h), the elementary charge (e), the Boltzmann constant elementary charge (e), the Boltzmann constant (k), and the Avogadro constant (N(k), and the Avogadro constant (NAA), ), respectivelyrespectively

See [4]See [4]

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What Is?

An An electronelectron? Subatomic particle with electric ? Subatomic particle with electric charge; we call that charge charge; we call that charge negativenegative; part of lepton ; part of lepton familyfamily

Called an Called an elementary particleelementary particle, since it seems to have , since it seems to have no sub-particlesno sub-particles

Has mass of approx. 1/1836 of a protonHas mass of approx. 1/1836 of a proton

Yet electrons have properties of Yet electrons have properties of particlesparticles AND AND waveswaves

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What Is?

A A coulombcoulomb? Is a fundamental unit of electrical ? Is a fundamental unit of electrical chargecharge, and is also the SI , and is also the SI derived unit derived unit of electric of electric charge; the symbol Coulomb is C; the symbol for charge; the symbol Coulomb is C; the symbol for charge flowing, creating a current, is: Q or qcharge flowing, creating a current, is: Q or q

A A coulomb coulomb is equal to a charge of approximately is equal to a charge of approximately 6.241×106.241×101818 electrons electrons

Now what a charge really is, we don’t understand, Now what a charge really is, we don’t understand, but we do know some key properties, and we can but we do know some key properties, and we can measure it quite accuratelymeasure it quite accurately

Similar to Similar to gravitygravity: we can measure and use it, but : we can measure and use it, but we don’t fundamentally understand what it is; we we don’t fundamentally understand what it is; we only observe how it worksonly observe how it works

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What is? An An ampereampere? Unit of current. One of the base units of ? Unit of current. One of the base units of

the SIthe SI

Named after André Marie Named after André Marie AmpèreAmpère, French physicist , French physicist 1775 – 18361775 – 1836

Compare that definition with the SI definition of Compare that definition with the SI definition of AAmpèrmpère!e!

When about 6.241 * 10When about 6.241 * 101818 electrons stream though a electrons stream though a conductor in a second, the amount of charge moved conductor in a second, the amount of charge moved was 1 C and the current was was 1 C and the current was 1 A1 A; AKA “amp”.; AKA “amp”.

i = dq / dti = dq / dt

1 A = 1 C / s1 A = 1 C / s

C here: Coulomb! Not capacitanceC here: Coulomb! Not capacitance

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What is?

A A VoltVolt? The electric potential difference between 2 ? The electric potential difference between 2 points of a conductor when a current dissipates one points of a conductor when a current dissipates one wattwatt

A A VoltVolt is AKA the potential difference between 2 is AKA the potential difference between 2 planes that are 1 m apart with an electric field of 1 planes that are 1 m apart with an electric field of 1 newton / coulombnewton / coulomb

AKA potential difference between 2 points that AKA potential difference between 2 points that deliver 1 Joule of energy per coulomb of charge deliver 1 Joule of energy per coulomb of charge passing throughpassing through

In In mksmks the dimension is: the dimension is:

V = kg * mV = kg * m22 / ( A * s / ( A * s33 ) )

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What is?

A A Volt Volt is named named in honor of the Italian is named named in honor of the Italian physicist physicist Alessandro Volta Alessandro Volta (1745-1827), inventor of (1745-1827), inventor of the first voltaic pile (chemical battery)the first voltaic pile (chemical battery)

A A VoltVolt is Amperes times Ohm, Watts per Ampere, or is Amperes times Ohm, Watts per Ampere, or Joules per Coulomb:Joules per Coulomb:

V = A * ΩV = A * Ω

V = W / AV = W / A

V = J / C V = J / C

V = dw / dqV = dw / dq

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What is?

Electrical Electrical powerpower, like its mechanical equivalent, is , like its mechanical equivalent, is the ability to do workthe ability to do work

Is measured in Watt, unit dimension shown as W, in Is measured in Watt, unit dimension shown as W, in equations denoted by letter pequations denoted by letter p

It is the ability to do work of a 1 Coulomb charge It is the ability to do work of a 1 Coulomb charge every second, when passing through a field of one every second, when passing through a field of one VoltVolt

p = v * q / t = v * ip = v * q / t = v * i

p = dW / dt = ( dW / dq ) * ( dq / dt ) = v * ip = dW / dt = ( dW / dq ) * ( dq / dt ) = v * i

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What is? Electrical Electrical resistanceresistance? A material’s opposition to the ? A material’s opposition to the

free flow of electronsfree flow of electrons

In an insulator, such as vacuum or porcelain, In an insulator, such as vacuum or porcelain, resistivity is very large, typically >> 1 MΩ (Mega resistivity is very large, typically >> 1 MΩ (Mega Ohm)Ohm)

R ~ kR ~ kii * length / Area * length / Area

A

I

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What is? ResistanceResistance Continued: In a conductor, such as Continued: In a conductor, such as

silver, carbon (graphene) or copper or gold, silver, carbon (graphene) or copper or gold, resistivity is very smallresistivity is very small

Resistance is expressed in units of Ohm Resistance is expressed in units of Ohm ΩΩ

Resistance grows proportional to the length Resistance grows proportional to the length ll of of conducting material, and decreases inversely conducting material, and decreases inversely proportional to the diameter proportional to the diameter AA of the conductor of the conductor; k; kii is is a material constant!a material constant!

R = ~ kR = ~ kii * l / A * l / A

kkii being a constant depending on materialbeing a constant depending on material

ll being the length being the length

AA being the diameter of the conducting material --not ampere! being the diameter of the conducting material --not ampere!

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What is?

Electrical Electrical inductanceinductance? A charge in motion (a ? A charge in motion (a current) creates a magnetic field around its current) creates a magnetic field around its conductorconductor

If the current remains constant, so does the fieldIf the current remains constant, so does the field

If current If current ii varies over time, the magnetic field also varies over time, the magnetic field also changes as a direct function. A time-varying changes as a direct function. A time-varying magnetic field induces a voltage in any conductor magnetic field induces a voltage in any conductor linked to the field; linked meaning: “close-by”linked to the field; linked meaning: “close-by”

v ~ di / dtv ~ di / dtv = L * di / dtv = L * di / dt

vv measured in Volt V measured in Volt V

LL inductance in Henry H inductance in Henry H

didi the change in current A the change in current A

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What is?

Electrical Electrical inductanceinductance and related power and energy? and related power and energy?

p = i * vp = i * v

p = i * L * di / dt p = i * L * di / dt

w = ( L / 2 ) * i w = ( L / 2 ) * i 22

w w the energy in Joule the energy in Joule

pp the power measured in Watt the power measured in Watt

LL the inductance in Henry H the inductance in Henry H

ii the current in A the current in A

didi the change of current over time, in A the change of current over time, in A

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What is? Electrical Electrical capacitancecapacitance? Circuit parameter capacitance ? Circuit parameter capacitance

is represented by the letter C, measured in farad F. A is represented by the letter C, measured in farad F. A capacitor does not directly conduct current, since an capacitor does not directly conduct current, since an insulator separates its 2 platesinsulator separates its 2 plates

But a charge placed onto one plate repels similarly But a charge placed onto one plate repels similarly charged particles on the other plate, and so can charged particles on the other plate, and so can cause a charge to move; known as cause a charge to move; known as displacement displacement currentcurrent. The current so created is proportional to the . The current so created is proportional to the rate at which the voltage across the plates varies rate at which the voltage across the plates varies over time. Note: farad is a very large unit; thus in over time. Note: farad is a very large unit; thus in diagrams we see smaller units, such as μF or nF. diagrams we see smaller units, such as μF or nF.

i ~ dv / dti ~ dv / dt

i = C * dv / dt i = C * dv / dt i i the resulting current in A, caused by the changing voltagethe resulting current in A, caused by the changing voltageCC the capacitor’s capacitance, measured in farad the capacitor’s capacitance, measured in faraddvdv the change in voltage across the 2 plates the change in voltage across the 2 plates

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What is? A A capacitor’s capacitor’s power and energy?power and energy?

p = v * ip = v * i

p = C * v * dv / dt p = C * v * dv / dt

w = C * vw = C * v22 / 2 / 2

ww energy in Joule energy in Joule

pp power v measured in Watt power v measured in Watt

i i the displacement current, in Athe displacement current, in A

CC is the capacitor’s capacitance, measured in farad is the capacitor’s capacitance, measured in farad

dvdv the change in voltage across the 2 plates the change in voltage across the 2 plates

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Passive Sign Convention

Assigning a reference direction for current or Assigning a reference direction for current or voltage in a circuit is arbitraryvoltage in a circuit is arbitrary

Used consistently, any method works out fineUsed consistently, any method works out fine

The most widely used method is the The most widely used method is the Passive Sign Passive Sign ConventionConvention::

When the reference direction for the current in a When the reference direction for the current in a passive element is in the direction of the voltage passive element is in the direction of the voltage drop across that element, use a + sign in any drop across that element, use a + sign in any expression that relates current to voltage; else use expression that relates current to voltage; else use the – sign. That convention we call the the – sign. That convention we call the Passive Passive Sign ConventionSign Convention

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Electric Sources

We We use 4 types of electric sources:use 4 types of electric sources:

1.1.Constant voltage sourcesConstant voltage sources

2.2.Constant current sourcesConstant current sources

3.3.Dependent voltage sources, andDependent voltage sources, and Can depend on separate voltage Other kinds depend on separate current

4.4.Dependent current sourcesDependent current sources Can depend on separate voltage Other kinds depend on separate current

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Bibliography

1. Electric Circuits, 10nd edition, Nilsson and Riedel, Pearsons Publishers

2. SI Units from NIST: http://physics.nist.gov/cuu/Units/units.html

3. NIST Special Publication 330, © 2008 Edition, by Taylor and Thompson, lists the SI units

4. Peter Mohr, NIST “Redefining the SI Base Units,” Redefining the SI Base Units,” http://www.nist.gov/pml/newsletter/siredef.cfmitshttp://www.nist.gov/pml/newsletter/siredef.cfmits