1. ECE 221 Electric Circuit Analysis I Chapter 2 Terms and Formulae
Herbert G. Mayer, PSU & CCUT
Status 10/2/2015

2. Syllabus SI What Is? Passive Sign Convention Electric Sources
References

3. 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

4. SI 7 Base Units --Note: V missing!

5. 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 * newton per meter of conductor

6. SI Units
K: Kelvin – thermodynamic temperature unit that is the 1/ 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 * hertz and further constraints
More on SI units later in the term . . .

7. 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

8. 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

9. 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 × 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

10. assumes even flow of current during one second s
What is?
An ampere? Unit of current. One of the base units of the SI
Named after André Marie Ampère, French physicist – 1836
When about × 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

11. 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 )

12. What is?
A Volt is named in honor of the Italian physicist Alessandro Volta ( ), 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

13. 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

14. 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 ~ length / Area A I

15. 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

16. 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

17. 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

18. 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 voltage
C: capacitor’s capacitance, measured in farad; symbol F
dv: voltage change across two plates

19. 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 Ampère A
C is the capacitor’s capacitance, measured in Farad F
dv the change in voltage across the 2 plates

20. 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

21. Electric Sources We use 4 types of electric sources:
Constant voltage sources
Constant current sources
Dependent voltage sources, and
Can depend on some separate voltage
Other kinds depend on some separate current
Dependent current sources +
x iα -

22. References
Electric Circuits, 10nd edition, Nilsson and Riedel, Pearsons Publishers
SI Units from NIST:
NIST Special Publication 330, © 2008 Edition, by Taylor and Thompson, lists the SI units
Peter Mohr, NIST Publication “Redefining the SI Base Units”