Transcript Elementary Terms and Formulae

ECE 221
Electric Circuit Analysis I
Chapter 2
Terms and Formulae
Herbert G. Mayer, PSU & CCUT
Status 11/2/2014
For use at Changchun University of Technology CCUT
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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 an
initiative started in 1948, are based on the meterkilogram-second (MKS) system
 SI is declared to be “evolving”
 The SI units will change in the near future per
international agreements
 The corresponding American organization is NIST:
 NIST stands for: 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 and further constraints
 More on SI units later in the term . . .
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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 the 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; the symbol 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
 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 it 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
 Compare that definition with the SI definition of
Ampère!
 When about 6.241 × 1018 electrons stream though a
conductor in a second, the amount of charge moved
was 1 C and the current was 1 A; ACA “amp”.
i = dq / dt
1A=1C/s
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What is?
 A Volt? The electric potential difference between 2
points of a conductor when a current dissipates one
watt
 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 it:
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, 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=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
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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*i2/2
w energy in Joule
p power measured in Watt
L inductance in Henry
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 the resulting current in A, caused by the changing voltage
C the capacitor’s capacitance, measured in farad
dv the voltage change across the 2 plates
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What is?
 A capacitor’s power and energy?
p = v * i = 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 some separate voltage
Other kinds depend on some separate current
4. Dependent current sources


Can depend on some separate voltage
Other kinds depend on some 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
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