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ELEC130 Electrical Engineering 1 Week 4 Module 2 DC Circuit Tools 1 Administration Laboratory This Week in ES 210 - Using Electronic Workbench Practical Laboratories - Do Not Come Late Quiz Quiz 1 - results (marks, to be returned) Missed the quiz? Survey Web site (Access site & PowerPoint viewer) Textbook availability 2 Review Week 3 Thevenin & Norton Laboratory 2 Example from last weeks lecture will be covered in the laboratory Tutorial 1 - Questions 26 to 30 Tutorial problems are for you to do at home 3 Capacitors The capacitor is a device which can store electrical charge, thereby creating an electric field that in turn, stores energy. The measure of the energy storing ability of a capacitor is its capacitance. Your Research: to investigate the relationship between force, charge, distance between the plates, capacitance, voltage and energy stored. Floyd chapter 13 Dorf chapter 7 Hambley chapter 3 4 Basic Construction - Capacitor Consider two parallel conductive plates of area A, separated by an insulting material called a dielectric by a distance d. d dielectric plates (plate area A) C OH Slide - Floyd Figure 13-2 A d A voltage source connected to the plates transfers charge. That is, electrons are removed from one of the plates and an equal number are deposited on the opposite plate, creating a potential difference. Electrons only flow through the conductors and voltage source (the dielectric is an insulator) This transfer will stop when the voltage difference between the plates = the voltage sources 5 Types of Capacitors Normally classified according to the type of dielectric material Most common material types used are: mica, ceramic, plastic-film [non-polarised] electrolytic (aluminium oxide & tantalum oxide) [polarised] and [bi-polar] Show using Matrix - Parts Gallery 6 Properties - Capacitance The amount of charge that a capacitor can store per unit voltage across its plates is its capacitance Notation: C Unit: Farads (F) Symbol: C = Q/V 1 Farad is the amount of capacitance when 1 Coulomb of charge is stored with one volt across the plates Common size units are F to pF Voltage rating - maximum DC voltage that can be applied without risk of damage to the device. (breakdown voltage) Energy Stored: W = ½ CV2 Show in Matrix - Circuits & Components 7 Series Capacitors Capacitors in series effectively lower the total capacitance as the effective plate separation increases. VT = V1 + V2 +.....+ Vn QT/CT = Q1/C1 + ..…+ Qn/Cn Since charges on all the capacitors are equal, the Q term can be factored and cancelled resulting in 1/CT = 1/C1 + 1/C2 ...… +1/Cn A series connection of charged capacitors acts as a voltage divider 8 Parallel Capacitors Capacitors connected in parallel give a total capacitance of the sum of the individual capacitance's as the effective plate area increases QT = Q1 + Q2 + ...+ Qn CTVT = C1V1 + C2V2 +.....+ CnVn CT= C1 + C2 +......+ Cn 9 The Formula d i( t ) q( t ) dt dvc ( t ) ic ( t ) C dt vc(t) constant means ic (t) = 0 vc(t) cannot change instantaneously (else ic (t) ) vc(t) changing quickly means ic (t) is large 10 Rules (Floyd, pg 511) Voltage across a capacitor cannot change instantaneously Current in a capacitive circuit can ideally change instantaneously A fully charged capacitor appears as an open circuit to non changing current An uncharged capacitor appears as a short to an instantaneous change in current 11 Characteristics of Capacitors in DC Circuits Charging a Capacitor When a capacitor is fully charged, there is no current A capacitor blocks constant DC When a charged capacitor is disconnected from the source it will remain charged (except for leakage resistance) Discharging a Capacitor the energy stored by a capacitor is dissipated in the closed circuit the charge is neutralised on each plate, at this time the voltage across the capacitor is zero Use diagram from Matrix 12 RC Circuits / Transients Derivation of general formula ….. t Charging and discharging exponential curves foran RC v V ( V V ) e F i F circuit. General Formula: [where: F - Final value & i - initial value] (v = steady state + transient) Response is made up of transient & steady state t Special Case Charging from zero (Vi = 0) Discharging to Zero (VF = 0) v V F (1 e v Vi e RC ) t RC 13 Time Constant Resistance is unavoidable in circuits, whether it be the wires or designed resistance This resistance introduces the element of time into charging and discharging of a capacitor The voltage across a capacitor cannot change instantaneously because it takes finite time to move charge from one point to another. The rate at which the capacitor charges or discharges is determined by the time constant = RC seconds During one time constant interval, the charge on a capacitor changes approx. 63% Five (5) time constant intervals, is accepted as the time to fully charge or discharge a capacitor and is called the transient time Show OH 14 Capacitor Applications Electrical Storage backup voltage source Power supply filtering computer memories DC blocking and AC coupling Power Line decoupling decouple voltage transients or spikes Bypassing bypassing an ac voltage around a resistor without affecting the dc voltage across the resistor Signal Filters selecting specific frequencies Timing Circuits 15 RC Example Assume switch is in position A for a long time The switch is moved to position B at t = 0 sec. At t = 6 milli sec the switch is again placed in position A [A] 16 Inductors The inductor, which is basically a coil of wire, is based on the principle of electromagnetic induction. An electromagnetic field surrounds any conductor when there is a current through it. Inductance is the property of a coil of wire that opposes a change in current. Your Research: to investigate the relationship between flux, number of turns, cross section al area, length of core, inductance, current, voltage and energy stored. Floyd chapter 14 Dorf chapter 7 Hambley chapter 3 17 Basic Construction A coil of wire forms an inductor. N i + VL - dN di VL dt dt di VL L dt When current flows through it a electromagnetic field is created. When current changes, the electromagnetic field changes. A changing electromagnetic field causes an induced voltage in a direction to oppose the current. This property is referred to as inductance. 18 Types of Inductors Two general categories fixed variable Classified by type of core air iron ferrite Losses winding resistance winding capacitance Show using Matrix - Parts Gallery 19 Properties Inductance Inductor and capacitor have similar but opposite properties. (refer Table 7.9 Dorf pg 301) Induced voltage is determined by the time rate of change of the current and the inductance of the coil Notation: L Unit: Henry (H) di VL L dt Symbol: 1 Henry = 1 volt sec / ampere Common size units are H to H Energy Stored: W = ½ LI2 Show in Matrix - Circuits & Components 20 Series & Parallel Inductors Series: LT=L1+ L2+ …….+ Ln Parallel: 1/LT = 1/L1+ 1/L2 +….+ 1/Ln 21 The Formula di VL L dt iL(t) constant means vL 0 iL(t) cannot change instantaneously (else vL (t) ) iL(t) changing quickly means vL (t) is large t Derivation similar to that of C’s: 1 iL (t ) iL (t0 ) vL dt L to 22 Characteristics of Inductor in DC Circuits Charging a Inductor When an inductor is fully charged, there is no voltage A inductor acts like a short circuit When a charged inductor is disconnected from the source it will remain charged (except for winding leakage's) Discharging a Inductor the energy stored by an inductor is dissipated in the closed circuit the electromagnetic field collapses, at this time the current through the inductor is zero Use diagram from Matrix 23 RL Circuits / Transients Time Constant: General Formula: = L/R sec [where: F - Final value & i - initial value] i I F ( I i I F )e t (i = steady state + transient) Response is made up of transient & steady state Rt Special Case Charging from zero (Ii = 0) Discharging to Zero (IF = 0) i I F (1 e i Iie L ) Rt L 24 Inductor Applications Power Supply Filter RF Choke Tuned Circuit 25