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International System of Units (SI) Table 1. SI base units SI base unit Name Symbol meter m Base quantity Length Mass Time Electric current Thermodynamic temperature Amount of substance Luminous intensity kilogram second ampere kg s A kelvin K mole mol candela cd Table 5. SI prefixes Factor Name 1024 yotta 1021 zetta 1018 exa 1015 peta 1012 tera 109 giga 6 10 mega 103 kilo 2 10 hecto 1 10 deka Symbol Y Z E P T G M k h da Factor Name 10-1 deci -2 10 centi 10-3 milli -6 10 micro -9 10 nano -12 10 pico -15 10 femto 10-18 atto 10-21 zepto 10-24 yocto Symbol d c m µ n p f a z y Force, Work, and Power □ Work is done by a force on an object if the force acts on the object in it moves through a distance parallel to the force. □ Work = Force times Distance moved □ W=Fd □ The unit for work is the Joule (J) which is equivalent to Newton-meter □ 1 J = 1N m = 1 Kg m2 / s2 □ Energy □ Things have energy if they are able to do work. A human body has energy; so does a tank of gas and a falling stone. □ Energy is the capacity to do work. □ Energy exists in a variety of forms: □ Chemical Energy, Potential Energy, Nuclear Energy, Thermal (Heat) Energy etc… □ Work □ Work is done whenever energy is changed from one form into another. □ The amount of energy changed from one form to another is known as the energy transferred: □ work done = energy transferred □ Power □ Power is equal to the amount of work done per unit time. □ The unit for power in Standard Units is the Watt (W) which is equivalent to Joule/second □ 1 W = 1J / s □ Another unit for power is horsepower (hp) □ 1 hp = 746 W Derived SI Units □ The derived units follow the mathematical expressions which relate the quantities. □ From “force equals mass times acceleration,” the newton (N) is defined as the unbalanced force that imparts an acceleration of 1 meter per second squared to a 1-kilogram mass. Thus, □ Quantity Symbol SI Unit Abbreviation electric charge Q, q coulomb C electric potential V, v volt V resistance R ohm conductance G siemens S inductance L henry H capacitance C farad F frequency f hertz Hz force F,f newton N energy, work W, w joule J power P, p watt W weber Wb B tesla T magnetic flux magnetic flux density Constant Acceleration Motion: Let us consider the case where a particle accelerates from rest at a constant acceleration a: The initial velocity is v0 V0 The final velocity is v f V0 at The average velocity is v (v0 v f ) / 2 V0 at / 2 Thus the displacement is d vt V0t at 2 / 2 Kinetic Energy KE mv 2 / 2 EXAMPLE In simple rectilinear motion a 10-kg mass is given a constant acceleration of 2m / s 2 (a) Find the acting force F. (b) If the body was at rest at t 0, x 0 find the position, kinetic energy, and power for t = 4s. F ma 10kg 2m/s 2 20kg m/s 2 20 N (b) At t 4s, x at 2 2m/s 2 (4s) 2 16m v f V0 at 0 2m/s 2 4s 8m/s KE mv 2 / 2 10kg (8m/s) 2 (320kg m/s 2 ) m 320J It can be shown: P Fv f 20N 8m/s 160W Resistive Circuits □ This are circuits in which there are not energy storing components other than the voltage or current sources they do not contain capacitors or inductors. □ The definitions of Work, Energy and Power do not change but the nature of the Involved forces does. □ An Electric Circuit is a model that approximates the behavior of an actual Electric System □ Electric Effects Happen Instantaneously Throughout a System □ The net charge on every component of the system is always zero □ There is no magnetic coupling between any two different components in a system □ Circuit theory provides simple solutions to problems that would be otherwise extremely complicated Electric Charge The unit of electric charge is the coulomb. Ordinary matter is made up of atoms which have positively charged nuclei and negatively charged electrons surrounding them. Charge is quantized as a multiple of the electron or proton charge: m 9.11 10 31 kg # e in 1C 6.24E+18 Mass of 1C 5.69E-12 □ Like charges repel, unlike charges attract. The electric force acting on a point charge q1 as a result of the presence of a second point charge q2 is given by Coulomb's Law: 0 is the permitivit y of space r 1m q1 q 2 1C F 9 10 9 N 9 10 9 / 9.8 9.18 kgf 1000 tons □ The electric field of a point charge can be obtained from Coulomb's law: Gravitational Force F G Mm Mm ; U G G= 2 r r □ Potential energy can be defined as the capacity for doing work which arises from position or configuration. PE mgh □ If a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge q in the vicinity of this source charge will be: □ Voltage is electric potential energy per unit charge, measured in joules per coulomb ( = volts). It is often referred to as "electric potential", which then must be distinguished from electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. □ □ The unit of current, the ampere (A), is defined as the constant current in two parallel conductors of infinite length and negligible cross section, 1 meter apart in vacuum, which produces a force between the conductors of 2.0 x10 7 newtons per meter length. A more useful concept, however, is that current results from charges in motion, and 1 ampere is equivalent to 1 coulomb of charge moving across a fixed surface in 1 second. w q w q w ;i ; v i ; hence, q t q t t p v i v The Ideal Basic Circuit Element □ Has Only two terminal □ It is described mathematically in terms of current and/or voltage □ It cannot be subdivided into other elements Passive Sign Convention Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element, use a positive sign in any expression relating voltage and current Notation □ Time varying quantities - lower case e.g. v(t), i(t) □ sometimes assume time - v(t) = v □ Time invariant quantities - upper case e.g. V, R, □ Remember to include units of measure e.g. 15 Volts Voltage & Current Sources □ An ideal voltage source maintains its stated voltage regardless of the load attached □ An ideal current source supplies its stated current regardless of the load attached □ Short Circuit. □ Basic Circuit element whose voltage is always 0. (Resistance =0) □ Symbol □ Open Circuit □ Basic Circuit element whose current is always 0. (Resistance = infinity) □ Symbol