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ECE 221Electric Circuit Analysis I

Chapter 2Terms and Formulae

Herbert G. Mayer, PSU & CCUTStatus 10/2/2015

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Syllabus

SI What Is? Passive Sign Convention Electric Sources References

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SI

SI is the abbreviation from the French name: Le Système International d'Unités

Standard published in 1960 as the result of initiative started in 1948

Based on the meter-kilogram-second (MKS) system

SI is declared to be evolving, as newer technologies enable higher accuracies in the future

The SI units will change in the near future per international agreements

The corresponding American organization is NIST:

NIST stands for: National Institute for Standards and Technology

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SI 7 Base Units --Note: V missing!

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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 12 grams 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 and further constraints

More on SI units later in the term . . .

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Changes Coming

Per 2011 declaration, the kilogram, the ampère, 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

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What Is?

An electron? Subatomic particle with electric charge; we call that charge negative

Electron is 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 some 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

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 6.241 × 1018 electrons

What exactly a charge really is, we don’t understand, but we do know some key properties, and we can measure such properties quite accurately

Similar to gravity: we can measure and use it, even fly to the moon with rockets overcoming gravity, but don’t fundamentally understand how gravity works; theories exist

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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 is 1 A; ACA “amp”.

i = dq / dt

1 A = 1 C / s

assumes even flow of current during one second s

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What is? A Volt? Is a derived unit in the SI

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

Reminder: Newton being the force to accelerate 1 kg of mass at a rate of 1 m / s2

AKA the electric potential difference between 2 points of a conductor when a current dissipates one watt

AKA potential difference between 2 points that deliver 1 Joule of energy per coulomb of charge passing through. In mks the dimension it:

V = kg * m2 / ( A * s3 )

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What is?

A Volt is 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, denoted by letter p. It is the ability to do work by a 1 Coulomb charge every second, passing through a field of one Volt

p = v * q / t

p = v * i

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What is?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, resistivityresistivity is very large, typically >> 1 MΩ (Mega is very large, typically >> 1 MΩ (Mega Ohm)Ohm)

R ~ length / AreaR ~ length / Area

AA

II

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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

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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 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 = “close-by”

v = L * di / dt

v measured in Volt

L inductance in Henry

di the change in the current over time, measured in A

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What is?

Electrical inductance and related power and energy?

p = i * L di / dt

w = L * i 2 / 2

w energy in Joule

p power measured in Watt

L inductance in Henry; symbol H

i 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 = C * dv / dt

i: resulting current in A, caused by changing voltageC: capacitor’s capacitance, measured in farad; symbol F

dv: voltage change across two plates

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

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

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

w energy in Joule w energy in Joule

p power v measured in Wattp power v measured in Watt

i the displacement current, in Ampère Ai the displacement current, in Ampère A

C is the capacitor’s capacitance, measured in Farad FC is the capacitor’s capacitance, measured in Farad F

dv the change in voltage across the 2 platesdv 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 of computing voltages and currents works out fine

A 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 SourcesElectric 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 some separate voltageCan depend on some separate voltage Other kinds depend on some separate currentOther kinds depend on some separate current

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

++ x ix iαα --

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References1. 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 Redefining the SI Base UnitsUnits”