ECE 101 Exploring Electrical Engineering Chapter 2 Terms and Formulae Herbert G. Mayer, PSU Status 2/2/2016 1 Syllabus SI What is . . . ? Passive Sign Convention Electric Sources References 2 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, so some will change, but if so, then per international agreement change: kilogram, Ampere, Kelvin, mole Replace by specifying via: Planck-, Boltzman-, and Avogadro-constants 3 SI Replace by specifying via constants that can be reproduced in a good lab No need to measure temperature, gravity, air pressure, etc. at some location, which might make measurement location-dependent; i.e.: Reason for change is technological evolution, allowing more and more precise definitions The corresponding American organization is NIST: National Institute for Standard and Technology 4 SI 7 Base Units 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 * 10-7 newton per meter of conductor 6 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 7 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] 8 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 9 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 10 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 1A=1C/s C here: Coulomb! Not capacitance 11 What is? A Volt is the SI unit of electrical force to push one ampere of current against a one Ω resistance Or 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 It is NOT one of the 7 base units on page 4! In the mks system, the dimension is: V = kg * m2 / ( A * s3 ) 12 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 13 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 sometimes denoted by letter p Is the ability to do the work of a 1 Coulomb charge every second, when passing through a field of 1 V p=v*q/t=v*i p = dW / dt = ( dW / dq ) * ( dq / dt ) = 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 ~ ki * 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, symbol: Ω Resistance grows proportional to the length l of conducting material, and decreases inversely proportional to the diameter A of the conductor; ki being a material constant! R~l/A R = ki * l / A ki l A being a constant depending on material being the length being the diameter of the conducting material --not ampere! 16 What is? Electrical inductance? A charge in motion (e.g. some 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 it is close-by v ~ di / dt v = L * di / dt v L di measured in Volt V inductance in Henry H the change in current A 17 What is? Electrical inductance and related power and energy? p=i*v p = i * L * di / dt w=(L/2)*i2 w p L i di the energy in Joule the power measured in Watt the inductance in Henry H the current in A 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 ~ dv / dt 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 change in voltage across the 2 plates 19 What is? A capacitor’s power p and energy w? p=v*i p = C * v * dv / dt w = C * v2 / 2 w p i C dv energy in Joule power v measured in Watt the displacement current, in A is the capacitor’s capacitance, measured in farad 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 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 21 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 22 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 23