1. 1 ECE 221 Electric Circuit Analysis I Chapter 2 Terms and Formulae Herbert G. Mayer, PSU & CCUT Status 1/8/2015

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

3. 3 SI SI is the abbreviation from the French name: Le Système International d'Unités 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 Standard published in 1960 as the result of initiative started in 1948 Based on the meter-kilogram-second (MKS) system Based on the meter-kilogram-second (MKS) system SI is declared to be evolving, as newer technologies enable higher accuracies in the future 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 SI units will change in the near future per international agreements The corresponding American organization is NIST: The corresponding American organization is NIST: NIST stands for: National Institute for Standards and Technology NIST stands for: National Institute for Standards and Technology

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

5. 5 SI Units m: meter – is length of light traveled in 1/299,792,458 th of a second m: meter – is length of light traveled in 1/299,792,458 th of a second kg: kilogram – equal reference prototype; will likely change 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 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 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. 6 SI Units K: Kelvin – thermodynamic temperature unit that is the 1/273.16 fraction of water temperature at triple point 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 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 10 23 specified elementary entities Old definition: the mole is the amount of substance that contains 6.022,141,79 x 10 23 specified elementary entities cd: candela – is luminous intensity of a source that emits monochromatic radiation of frequency 540 * 10 12 hertz and further constraints cd: candela – is luminous intensity of a source that emits monochromatic radiation of frequency 540 * 10 12 hertz and further constraints More on SI units later in the term... More on SI units later in the term...

7. 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 (N A ), respectively

8. 8 What Is? An electron? Subatomic particle with electric charge; we call that charge negative An electron? Subatomic particle with electric charge; we call that charge negative Electron is part of lepton family Electron is part of lepton family Called an elementary particle, since it seems to have no sub-particles Called an elementary particle, since it seems to have no sub-particles Has mass of approx. 1/1836 of a proton Has mass of approx. 1/1836 of a proton Yet electrons have some properties of particles AND waves Yet electrons have some properties of particles AND waves

9. 9 What Is? A coulomb? Is a fundamental unit of electrical charge, and is also the SI derived unit of electric charge 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 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 × 10 18 electrons A coulomb is equal to a charge of 6.241 × 10 18 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 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 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. 10 What is? An ampere? Unit of current. One of the base units of the SI An ampere? Unit of current. One of the base units of the SI Named after André Marie Ampère, French physicist 1775 – 1836 Named after André Marie Ampère, French physicist 1775 – 1836 When about 6.241 × 10 18 electrons stream though a conductor in a second, the amount of charge moved is 1 C and the current is 1 A; ACA “amp”. When about 6.241 × 10 18 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. 11 What is? A Volt? Is a derived unit in the SI 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 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 / s 2 Reminder: Newton being the force to accelerate 1 kg of mass at a rate of 1 m / s 2 AKA the electric potential difference between 2 points of a conductor when a current dissipates one watt 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: 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 * m 2 / ( A * s 3 )

12. 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 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: 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. 13 What is? Electrical power, like its mechanical equivalent, is the ability to do work 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 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. 14 What is? Electrical resistance? A material’s opposition to the free flow of electrons 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) In an insulator, such as vacuum or porcelain, resistivity is very large, typically >> 1 MΩ (Mega Ohm) R ~ length / Area A I

15. 15 What is? Resistance Continued: In a conductor, such as silver, carbon (graphene) or copper or gold, resistivity is very small 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 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; k i is a material constant! Resistance grows proportional to the length l of conducting material, and decreases inversely proportional to the diameter A of the conductor; k i is a material constant! R = k i * l / A k i being a constant depending on material l being the length A being the diameter of the conducting material

16. 16 What is? Electrical inductance? A charge in motion (a current) creates a magnetic field around its conductor 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 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” 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. 17 What is? Electrical inductance and related power and energy? 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. 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 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. 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; symbol F dv the voltage change across the 2 plates

19. 19 What is? A capacitor’s power and energy? A capacitor’s power and energy? p = v * i = C * v * dv / dt w = C * v 2 / 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. 20 Passive Sign Convention Assigning a reference direction for current or voltage in a circuit is arbitrary 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 Used consistently, any method of computing voltages and currents works out fine A widely used method is the Passive Sign Convention: 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 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 Else use the – sign. That convention we call the Passive Sign Convention

21. 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 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 + x iα -

22. 22 References 1. 1.Electric Circuits, 10 nd edition, Nilsson and Riedel, Pearsons Publishers 2. 2.SI Units from NIST: http://physics.nist.gov/cuu/Units/units.html 3. 3.NIST Special Publication 330, © 2008 Edition, by Taylor and Thompson, lists the SI units 4.Redefining the SI Base Units 4.Peter Mohr, NIST Publication “Redefining the SI Base Units”, November 2. 2011