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ECE 101Exploring Electrical Engineering

Chapter 2Terms and Formulae

Herbert G. Mayer, PSUStatus 12/13/2015

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Syllabus

SIWhat is . . . ?Passive Sign ConventionElectric SourcesReferences

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SI SI is the abbreviation from French name: Le Système

International d'Unités

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

SI is formally declared to be evolving

Some of the SI units will change, but if so, then per international agreement

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

The corresponding American organization is NIST:

National Institute for Standard and Technology

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SI 7 Base Units

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SI Units

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

kg: kilogram – equal reference prototype; will likely change

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

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

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SI Units K: Kelvin – thermodynamic temperature unit that is

the 1/273.16 fraction of water temperature at triple point

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

Old definition: the mole is the amount of substance that contains 6.022,141,79 x 1023 specified elementary entities

cd: candela – is luminous intensity of a source that emits monochromatic radiation of frequency 540 * 1012 hertz, plus some further constraints

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Changes Coming

Per 2011 declaration, the kilogram, the ampere, the degree kelvin, and the mole, will be redefined in terms of invariants of nature

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

See [4]

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What is . . . ?

An electron? Subatomic particle with electric charge; we call that charge negative; part of lepton family

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

Has mass of approx. 1/1836 of a proton

Yet electrons have properties of particles AND waves

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What Is?

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

A coulomb is equal to a charge of approximately 6.241×1018 electrons

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

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

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

the SI

Named after André Marie Ampère, French physicist 1775 – 1836

When about 6.241 * 1018 electrons stream though a conductor in a second, the amount of charge moved is 1 C and the current 1 A; AKA “amp”.

i = dq / dt

1 A = 1 C / s

C here: Coulomb! Not capacitance

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What is?

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

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

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

In mks the dimension is:

V = kg * m2 / ( A * s3 )

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What is?

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

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

V = A * Ω

V = W / A

V = J / C

V = dw / dq

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What is?

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

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

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

p = v * q / t = v * i

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

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

free flow of electrons

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

R ~ ki * length / Area

A

I

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What is? Resistance Continued: In a conductor, such as silver,

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

Resistance is expressed in units of Ohm Ω

Resistance grows proportional to the length l of conducting material, and decreases inversely proportional to the diameter A of the conductor; ki is a material constant!

R = ~ ki * l / A

ki being a constant depending on material

l being the length

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

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What is?

Electrical inductance? A charge in motion (a current) creates a magnetic field around its conductor

If the current remains constant, so does the field

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

v ~ di / dtv = L * di / dt

v measured in Volt V

L inductance in Henry H

di the change in current A

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What is?

Electrical inductance and related power and energy?

p = i * v

p = i * L * di / dt

w = ( L / 2 ) * i 2

w the energy in Joule

p the power measured in Watt

L the inductance in Henry H

i the current in A

di the change of current over time, in A

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What is? Electrical capacitance? Circuit parameter capacitance

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

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

i ~ dv / dt

i = C * dv / dt i the resulting current in A, caused by the

changing voltageC the capacitor’s capacitance, measured in faraddv the change in voltage across the 2 plates

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What is? A capacitor’s power and energy?

p = v * i

p = C * v * dv / dt

w = C * v2 / 2

w energy in Joule

p power v measured in Watt

i the displacement current, in A

C is the capacitor’s capacitance, measured in farad

dv the change in voltage across the 2 plates

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Passive Sign Convention

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

Used consistently, any method works out fine

The most widely used method is the Passive Sign Convention:

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

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Electric Sources

We use 4 types of electric sources:1. Constant voltage sources

2. Constant current sources

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

4. Dependent current sources Can depend on separate voltage Other kinds depend on separate current

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References

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 Publication “Redefining the SI Base Units”, November 2., 2011