DOCSLIB.ORG

26-Summary of Equations to Accompany.Pdf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
26-Summary of Equations to Accompany.Pdf boy30444_formulacard.qxd 3/24/06 2:04 PM Page 1 Summary of Equations to Accompany INTRODUCTORY CIRCUIT ANALYSIS, Eleventh Edition, by Robert L. Boylestad © Copyright 2007 by Prentice Hall. All Rights Reserved. dc Introduction Capacitors Ϫ12 Conversions 1 meter ϭ 100 cm ϭ 39.37 in., 1 in. ϭ 2.54 cm, Capacitance C ϭ Q/V ϭ eA/d ϭ 8.85 ϫ 10 er A/d farads (F), 1 yd ϭ 0.914 m ϭ 3 ft, 1 mile ϭ 5280 ft, °F ϭ 9/5°C ϩ 32, °C ϭ C ϭ erCo Electric field strength Ᏹ ϭ V/d ϭ Q/eA (volts/meter) 12 Ϫt/t Ϫt/t 5/9(°F Ϫ 32), K ϭ 273.15 ϩ °C Scientific notation 10 ϭ Transients (charging) iC ϭ (E/R)e , t ϭ RC, uC ϭ E(1 Ϫ e ), ϭ 9 ϭ ϭ 6 ϭ ϭ 3 ϭ ϭ Ϫ3 ϭ ϭ Ϫt/t ϭ Ϫt/RC ϭ tera T, 10 giga G, 10 mega M, 10 kilo k, 10 (discharge) uC Ee , iC (E/R)e iC iCav C(DuC /Dt) Ϫ6 Ϫ9 Ϫ12 milli ϭ m, 10 ϭ micro ϭ m, 10 ϭ nano ϭ n, 10 ϭ pico ϭ p Series QT ϭ Q1 ϭ Q2 ϭ Q3, 1/CT ϭ (1/C1) ϩ (1/C2) ϩ (1/C3) ϩ иии ϩ n Ϫn Ϫn n n m nϩm Powers of ten 1/10 ϭ 10 , 1/10 ϭ 10 , (10 )(10 ) ϭ 10 , (1/CN), CT ϭ C1C2/(C1 ϩ C2) Parallel QT ϭ Q1 ϩ Q2 ϩ Q3, n m nϪm n m nm 2 10 /10 ϭ 10 , (10 ) ϭ 10 CT ϭ C1 ϩ C2 ϩ C3 Energy WC ϭ (1/2)CV Voltage and Current Inductors 2 9 2 2 2 Coulomb’s law F ϭ kQ1Q2/r , k ϭ 9 ϫ 10 Nиm /C , Self-inductance L ϭ N mA/l (henries), L ϭ mr Lo ϭ ϭ ϭ ϭ ϭ Q coulombs (C), r meters (m) Current I Q/t (amperes), Induced voltage eLav L(Di/Dt) Transients (storage) iL Ϫ19 Ϫt/t Ϫt/t t ϭ seconds (s), Qe ϭ 1.6 ϫ 10 C Voltage V ϭ W/Q (volts), Im(1 Ϫ e ), Im ϭ E/R, t ϭ L/R, uL ϭ Ee (decay), uL ϭ Ϫt/t ′ Ϫt/t ′ W ϭ joules (J) [1 ϩ (R2/R1)]Ee , t′ ϭ L/(R1 ϩ R2), iL ϭ Ime , Im ϭ E/R1 Series LT ϭ L1 ϩ L2 ϩ L3 ϩ иии ϩ LN Parallel 1/LT ϭ (1/L1) ϩ Resistance (1/L2) ϩ (1/L3) ϩ иии ϩ (1/LN), LT ϭ L1L2/(L1 ϩ L2) ϭ 2 Circular wire R ϭ rl/A (ohms), r ϭ resistivity, l ϭ feet, Energy WL 1/2(LI ) 2 2 ACM ϭ (dmils) , r(Cu) ϭ 10.37 Metric units l ϭ cm, A ϭ cm , Ϫ6 Magnetic Circuits r(Cu) ϭ 1.724 ϫ 10 ohm-cm Temperature (ͿTͿ ϩ T1)/R1 ϭ Ϳ Ϳ ϩ ϭ ϩ Ϫ ϭ 2 ( T T2)/R2, R1 R20[1 a20(T1 20°C)], a20(Cu) 0.00393 Flux density B ϭ F/A (webers/m ) Permeability m ϭ mrmo Color code Bands 1–3: 0 ϭ black, 1 ϭ brown, 2 ϭ red, 3 ϭ orange, (Wb/Aиm) Reluctance ᏾ ϭ l/mA (rels) Ohm’s law F ϭ Ᏺ/᏾ ϭ ϭ ϭ ϭ ϭ ϭ 4 yellow, 5 green, 6 blue, 7 violet, 8 gray, 9 white, (webers) Band 3: 0.1 ϭ gold, 0.01 ϭ silver, Band 4: 5% ϭ gold, 10% ϭ silver, Ᏺ ϭ ϭ ϭ ϭ ϭ Magnetomotive force NI (ampere-turns) Magnetizing 20% no band, Band 5: 1% brown, 0.1% red, 0.01% orange, ϭ Ᏺ ϭ ⌺ Ᏺ ϭ ϭ ϭ force H /l NI/l Ampère’s circuital law 0 0.001% yellow Conductance G 1/R siemens (S) 5 Flux ⌺ Fentering ϭ ⌺ Fleaving Air gap Hg ϭ 7.96 ϫ 10 Bg Ohm’s Law, Power, and Energy Ohm’s law I ϭ E/R, E ϭ IR, R ϭ E/I Power P ϭ W/t ϭ VI ϭ I 2R ϭ V 2/R (watts), 1 hp ϭ 746 W Greek Alphabet Efficiency h% ϭ (Po /Pi) ϫ 100%, hT ϭ h1 и h2 и h3 hn Energy W ϭ Pt, W (kWh) ϭ [P(W) t(h)]/1000 Letter Capital Lowercase Letter Capital Lowercase Series Circuits Alpha AaNu Nn RT ϭ R1 ϩ R2 ϩ R3 ϩ иии ϩ RN, RT ϭ NR, I ϭ E/RT, V ϭ IR Beta BbXi Yy Kirchhoff’s voltage law ⌺ V ϭ 0, ⌺ Vrises ϭ ⌺ Vdrops Gamma GgOmicron Oo ϭ Voltage divider rule Vx RxE/RT Delta DdPi Pp Parallel dc Circuits Epsilon EeRho Rr Zeta ZzSigma ⌺ j ϭ ϩ ϩ ϩ иии ϩ ϭ RT 1/(1/R1 1/R2 1/R3 1/RN), RT R/N, Eta HhTau Tt R ϭ R R R ϩ R I ϭ EG ϭ E/R T 1 2/( 1 2), T T Theta VvUpsilon Uu Kirchhoff’s current law ⌺ I ϭ ⌺ I entering leaving Iota IiPhi Ff Current divider rule I ϭ (R /R )I, (Two parallel elements): x T x Kappa KkChi Xx I1 ϭ R2I/(R1 ϩ R2), I2 ϭ R1I/(R1 ϩ R2) Lambda LlPsi Ww Series-Parallel Circuits Mu M m Omega ⍀ q Potentiometer loading RL >> RT Ammeter Rshunt ϭ RmICS /(Imax ICS) ϭ Ϫ Voltmeter Rseries (Vmax VVS)/ICS Prefixes Ohmmeter Rs (E/ICS) Rm zero-adjust/2 Methods of Analysis and Selected Topics (dc) Multiplication SI SI Factors Prefix Symbol Source conversions E ϭ IRp, Rs ϭ Rp, I ϭ E/Rs a b 18 exa E 10 ؍ Determinants D ϭ 1 1 ϭ a b Ϫ a b 1 000 000 000 000 000 000 ⏐⏐a b 1 2 2 1 peta P 1015 ؍ 000 000 000 000 000 1 2 2 ϭ ⌬ ′ ϭ tera T 1012 ؍ Bridge networks R1/R3 R2/R4 -Y conversions R 1 000 000 000 000 R ϩ R ϩ R , R ϭ R R /R′, R ϭ R R /R′, R ϭ R R /R′, R ϭ R /3 giga G 109 ؍ A B C 3 A B 2 A C 1 B C Y D 1 000 000 000 Y-⌬ conversions R″ ϭ R R ϩ R R ϩ R R , R ϭ R″/R , R ϭ R″/R , mega M 106 ؍ C 3 B 2 1 000 000 3 2 3 1 2 1 RA ϭ R″/R1, RD ϭ 3RY kilo k 103 ؍ 000 1 10؊3 milli m ؍ Network Theorems 0.001 ؊6 micro M 10 ؍ Superposition Voltage sources (short-circuit equivalent), current 0.000 001 ؊ nano n 9 10 ؍ sources (open-circuit equivalent) 0.000 000 001 ؊12 pico p 10 ؍ Thévenin’s Theorem RTh: (all sources to zero), ETh: (open-circuit 0.000 000 000 001 10؊15 femto f ؍ terminal voltage) 0.000 000 000 000 001 ؊18 ؍ Maximum power transfer theorem RL ϭ RTh ϭ RN, Pmax ϭ 2 2 0.000 000 000 000 000 001 10 atto a E Th /4RTh ϭ IN RN /4 boy30444_formulacard.qxd 3/24/06 2:04 PM Page 2 Summary of Equations to Accompany INTRODUCTORY CIRCUIT ANALYSIS, Eleventh Edition, by Robert L. Boylestad © Copyright 2007 by Prentice Hall. All Rights Reserved. ac 2 2 Sinusoidal Alternating Waveforms R-C filters (high-pass) fc ϭ 1/(2pRC), Vo /Vi ϭ R/͙RෆෆϩෆෆXෆC ЄtanϪ1(X /R) (low-pass) f ϭ 1/(2pRC), V /V ϭ X /͙Rෆෆ2 ϩෆෆXෆ2 Sine wave u ϭ Vm sin a, a ϭ qt ϭ 2pft, f ϭ 1/T, 1 radian ϭ 57.3°, C c o i C C ϭ ϫ ϭ ϫ Ϫ R radians (p/180°) (degrees), degrees (180°/p) (radians) ЄϪtan 1 Identities sin(qt ϩ 90°) ϭ cos qt, sin qt ϭ cos[qt Ϫ (p/2)], XC sin(Ϫa) ϭϪsin a, cos(Ϫa) ϭ cos a Average value G ϭ Octave 2 1, 6 dB/octave Decade 10 1, 20 dB/decade algebraic sum of areas/length of curve Transformers Effective (rms) value Irms ϭ 0.707Im, Im ϭ ͙2ෆIrms, 2 ϭ ͙ෆෆෆ ϭ Irms ϭ ͙arෆeaෆෆ[iෆ(tෆ)]ෆ/ෆT Mutual inductance M k LpLs Iron-core Ep 4.44fNpFm, Es ϭ 4.44fNsFm, Ep /Es ϭ Np /Ns, a ϭ Np /Ns, Ip /Is ϭ Ns/Np, The Basic Elements and Phasors 2 Zp ϭ a ZL, Ep Ip ϭ Es Is, Pi ϭ Po(ideal) ϭ ϩ 2 ϩ R: Im ϭ Vm /R, in phase L: XL ϭ qL, uL leads iL by 90° Air-core Zi Zp [qM) /(Zs ZL)] ϭ ϭ ϭ C: XC 1/qC, iC leads uC by 90° Power P (Vm Im /2) cos v Polyphase Systems V I cos v R: P ϭ V I ϭ I2 R ϭ V 2 /R Power rms rms rms rms rms rms ϭ ϭ ϭ ϭ ͙ෆ factor F ϭ cos v ϭ P/V I Rectangular form C ϭ A Ϯ jB Y-Y system Ifg IL IfL, Vf Ef, EL 3 Vf Y-D system p rms rms ϭ ϭ ͙ෆ ϭ ϭ ϭ ͙ෆ Polar form C ϭ CЄv Conversions C ϭ ͙Aෆෆ2 ϩෆෆBෆ2, v ϭ Vf EL, IL 3If D-D system Vf EL Ef, IL 3If Ϫ1 ϭ ͙ෆ ϭ ϭ ϭ tan (B/A), A ϭ C cos v, B ϭ C sin v Operations j ϭ ͙Ϫෆ1ෆ, D-Y system EL 3Vf, If IL, EL Ef Power PT 3Pf, 2 ϭ ϭ ϭ ͙ෆ ϭ j ϭϪ1, 1/j ϭϪj, C1 Ϯ C2 ϭ (ϮA1 Ϯ A2) ϩ j(ϮB1 Ϯ B2), QT 3Qf, ST 3Sf 3ELIL, Fp PT /ST и ϭ Є ϩ ϭ Є Ϫ C1 C2 C1C2 (v1 v2), C1/C2 (C1/C2) (v1 v2) Pulse Waveforms and the R-C Response Series and Parallel ac Circuits % tilt ϭ [(V1 Ϫ V2)/V] ϫ 100% with V ϭ (V1 ϩ V2)/2 ϭ Elements RЄ X Є X ЄϪ Pulse repetition frequency (prf) 1/T 0°, L 90°, C 90° ϭ ϫ ϭ ϩ ϩ ϩ иии ϩ ϭ ϭ Duty cycle (tp/T) 100% Series ZT Z1 Z2 Z3 ZN, Is E/ZT, Fp R/ZT ϭ ϩ Ϫ ϫ ϭ ϭ ϩ ϩ Vav (duty cycle)(peak value) (1 duty cycle) (Vb) Voltage divider rule Vx ZxE/ZT Parallel YT Y1 Y2 ϭ ϩ Ϫ Ϫ Ϫt/RC ϩ иии ϩ ϭ ϩ Є ЄϪ R-C circuits uC Vi (Vf Vi)(1 e ) Y3 YN, ZT Z1Z2/(Z1 Z2), G 0°, BL 90°, ϭ Є ϭ ϭ ϭ Compensated attenuator RpCp RsCs BC 90°, Fp cos vT G/YT Current divider rule I1 Z2IT/(Z1 ϩ Z2), I2 ϭ Z1IT /(Z1 ϩ Z2) Equivalent circuits Rs ϭ Nonsinusoidal Circuits 2 2 ϩ 2 ϭ 2 2 ϩ 2 ϭ 2 ϩ 2 Rp Xp /(Xp Rp ), Xs Rp Xp/(Xp Rp ), Rp (Rs Xs )/Rs, Fourier series f(a) ϭ A0 ϩ A1 sin qt ϩ A2 sin 2qt ϩ иии ϩ ϭ 2 ϩ 2 Xp (Rs Xs )/Xs An sin nqt ϩ B1 cos qt ϩ B2 cos 2qt ϩ иии ϩ Bn cos nqt Even function f(a) ϭ f(Ϫa), no B terms Odd function f(a) ϭ Series-Parallel ac Networks: n Ϫf(Ϫa), no An terms, no odd harmonics if f(t) ϭ f [(T/2) ϩ t], no even Employ block impedances and obtain general solution for reduced harmonics if f(t) ϭϪf [(T/2) ϩ t] network.
Load more

Recommended publications
  • Ch Pter 1 Electricity and Magnetism Fundamentals
    CH PTER 1 ELECTRICITY AND MAGNETISM FUNDAMENTALS PART ONE 1. Who discovered the relationship between magnetism and electricity that serves as the foundation for the theory of electromagnetism? A. Luigi Galvani B. Hans Christian Oersted C.Andre Ampere D. Charles Coulomb 2. Who demonstrated the theory of electromagnetic induction in 1831? A. Michael Faraday B.Andre Ampere C.James Clerk Maxwell D. Charles Coulomb 3. Who developed the electromagnetic theory of light in 1862? A. Heinrich Rudolf Hertz B. Wilhelm Rontgen C. James Clerk Maxwell D. Andre Ampere 4. Who discovered that a current-carrying conductor would move when placed in a magnetic field? A. Michael Faraday B.Andre Ampere C.Hans Christian Oersted D. Gustav Robert Kirchhoff 5. Who discovered the most important electrical effects which is the magnetic effect? A. Hans Christian Oersted B. Sir Charles Wheatstone C.Georg Ohm D. James Clerk Maxwell 6. Who demonstrated that there are magnetic effects around every current-carrying conductor and that current-carrying conductors can attract and repel each other just like magnets? A. Luigi Galvani B.Hans Christian Oersted C. Charles Coulomb D. Andre Ampere 7. Who discovered superconductivity in 1911? A. Kamerlingh Onnes B.Alex Muller C.Geory Bednorz D. Charles Coulomb 8. The magnitude of the induced emf in a coil is directly proportional to the rate of change of flux linkages. This is known as A. Joule¶s Law B. Faraday¶s second law of electromagnetic induction C.Faraday¶s first law of electromagnetic induction D. Coulomb¶s Law 9. Whenever a flux inking a coil or current changes, an emf is induced in it.
    [Show full text]
  • Advanced Magnetism and Electromagnetism
    ELECTRONIC TECHNOLOGY SERIES ADVANCED MAGNETISM AND ELECTROMAGNETISM i/•. •, / .• ;· ... , -~-> . .... ,•.,'. ·' ,,. • _ , . ,·; . .:~ ~:\ :· ..~: '.· • ' ~. 1. .. • '. ~:;·. · ·!.. ., l• a publication $2 50 ADVANCED MAGNETISM AND ELECTROMAGNETISM Edited by Alexander Schure, Ph.D., Ed. D. - JOHN F. RIDER PUBLISHER, INC., NEW YORK London: CHAPMAN & HALL, LTD. Copyright December, 1959 by JOHN F. RIDER PUBLISHER, INC. All rights reserved. This book or parts thereof may not be reproduced in any form or in any language without permission of the publisher. Library of Congress Catalog Card No. 59-15913 Printed in the United States of America PREFACE The concepts of magnetism and electromagnetism form such an essential part of the study of electronic theory that the serious student of this field must have a complete understanding of these principles. The considerations relating to magnetic theory touch almost every aspect of electronic development. This book is the second of a two-volume treatment of the subject and continues the attention given to the major theoretical con­ siderations of magnetism, magnetic circuits and electromagnetism presented in the first volume of the series.• The mathematical techniques used in this volume remain rela­ tively simple but are sufficiently detailed and numerous to permit the interested student or technician extensive experience in typical computations. Greater weight is given to problem solutions. To ensure further a relatively complete coverage of the subject matter, attention is given to the presentation of sufficient information to outline the broad concepts adequately. Rather than attempting to cover a large body of less important material, the selected major topics are treated thoroughly. Attention is given to the typical practical situations and problems which relate to the subject matter being presented, so as to afford the reader an understanding of the applications of the principles he has learned.
    [Show full text]
  • Chapter 7 Magnetism and Electromagnetism
    Chapter 7 Magnetism and Electromagnetism Objectives • Explain the principles of the magnetic field • Explain the principles of electromagnetism • Describe the principle of operation for several types of electromagnetic devices • Explain magnetic hysteresis • Discuss the principle of electromagnetic induction • Describe some applications of electromagnetic induction 1 The Magnetic Field • A permanent magnet has a magnetic field surrounding it • A magnetic field is envisioned to consist of lines of force that radiate from the north pole to the south pole and back to the north pole through the magnetic material Attraction and Repulsion • Unlike magnetic poles have an attractive force between them • Two like poles repel each other 2 Altering a Magnetic Field • When nonmagnetic materials such as paper, glass, wood or plastic are placed in a magnetic field, the lines of force are unaltered • When a magnetic material such as iron is placed in a magnetic field, the lines of force tend to be altered to pass through the magnetic material Magnetic Flux • The force lines going from the north pole to the south pole of a magnet are called magnetic flux (φ); units: weber (Wb) •The magnetic flux density (B) is the amount of flux per unit area perpendicular to the magnetic field; units: tesla (T) 3 Magnetizing Materials • Ferromagnetic materials such as iron, nickel and cobalt have randomly oriented magnetic domains, which become aligned when placed in a magnetic field, thus they effectively become magnets Electromagnetism • Electromagnetism is the production
    [Show full text]
  • Phasor Analysis of Circuits
    Phasor Analysis of Circuits Concepts Frequency-domain analysis of a circuit is useful in understanding how a single-frequency wave undergoes an amplitude change and phase shift upon passage through the circuit. The concept of impedance or reactance is central to frequency-domain analysis. For a resistor, the impedance is Z ω = R , a real quantity independent of frequency. For capacitors and R ( ) inductors, the impedances are Z ω = − i ωC and Z ω = iω L. In the complex plane C ( ) L ( ) these impedances are represented as the phasors shown below. Im ivL R Re -i/vC These phasors are useful because the voltage across each circuit element is related to the current through the equation V = I Z . For a series circuit where the same current flows through each element, the voltages across each element are proportional to the impedance across that element. Phasor Analysis of the RC Circuit R V V in Z in Vout R C V ZC out The behavior of this RC circuit can be analyzed by treating it as the voltage divider shown at right. The output voltage is then V Z −i ωC out = C = . V Z Z i C R in C + R − ω + The amplitude is then V −i 1 1 out = = = , V −i +ω RC 1+ iω ω 2 in c 1+ ω ω ( c ) 1 where we have defined the corner, or 3dB, frequency as 1 ω = . c RC The phasor picture is useful to determine the phase shift and also to verify low and high frequency behavior. The input voltage is across both the resistor and the capacitor, so it is equal to the vector sum of the resistor and capacitor voltages, while the output voltage is only the voltage across capacitor.
    [Show full text]
  • Network Analysis
    LECTURE NOTES ON NETWORK ANALYSIS B. Tech III Semester (IARE-R18) Ms. S Swathi Asistant professor ELECTRICAL AND ELECTRONICS ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) DUNDIGAL, HYDERABAD - 50043 1 SYLLABUS MODULE-I NETWORK THEOREMS (DC AND AC) Network Theorems: Tellegen‘s, superposition, reciprocity, Thevenin‘s, Norton‘s, maximum power transfer, Milliman‘s and compensation theorems for DC and AC excitations, numerical problems. MODULE-II SOLUTION OF FIRST AND SECOND ORDER NETWORKS Transient response: Initial conditions, transient response of RL, RC and RLC series and parallel circuits with DC and AC excitations, differential equation and Laplace transform approach. MODULE-III LOCUS DIAGRAMS AND NETWORKS FUNCTIONS Locus diagrams: Locus diagrams of RL, RC, RLC circuits. Network Functions: The concept of complex frequency, physical interpretation, transform impedance, series and parallel combination of elements, terminal ports, network functions for one port and two port networks, poles and zeros of network functions, significance of poles and zeros, properties of driving point functions and transfer functions, necessary conditions for driving point functions and transfer functions, time domain response from pole-zero plot. MODULE-IV TWO PORTNETWORK PARAMETERS Two port network parameters: Z, Y, ABCD, hybrid and inverse hybrid parameters, conditions for symmetry and reciprocity, inter relationships of different parameters, interconnection (series, parallel and cascade) of two port networks, image parameters. MODULE-V FILTERS Filters: Classification of filters, filter networks, classification of pass band and stop band, characteristic impedance in the pass and stop bands, constant-k low pass filter, high pass filter, m- derived T-section, band pass filter and band elimination filter. Text Books: 1.
    [Show full text]
  • 33. RLC Parallel Circuit. Resonant Ac Circuits
    University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II -- Lecture Notes PHY 204: Elementary Physics II (2021) 12-4-2020 33. RLC parallel circuit. Resonant ac circuits Gerhard Müller University of Rhode Island, [email protected] Robert Coyne University of Rhode Island, [email protected] Follow this and additional works at: https://digitalcommons.uri.edu/phy204-lecturenotes Recommended Citation Müller, Gerhard and Coyne, Robert, "33. RLC parallel circuit. Resonant ac circuits" (2020). PHY 204: Elementary Physics II -- Lecture Notes. Paper 33. https://digitalcommons.uri.edu/phy204-lecturenotes/33https://digitalcommons.uri.edu/ phy204-lecturenotes/33 This Course Material is brought to you for free and open access by the PHY 204: Elementary Physics II (2021) at DigitalCommons@URI. It has been accepted for inclusion in PHY 204: Elementary Physics II -- Lecture Notes by an authorized administrator of DigitalCommons@URI. For more information, please contact [email protected]. PHY204 Lecture 33 [rln33] AC Circuit Application (2) In this RLC circuit, we know the voltage amplitudes VR, VC, VL across each device, the current amplitude Imax = 5A, and the angular frequency ω = 2rad/s. • Find the device properties R, C, L and the voltage amplitude of the ac source. Emax ~ εmax A R C L V V V 50V 25V 25V tsl305 We pick up the thread from the previous lecture with the quantitative anal- ysis of another RLC series circuit. Here our reasoning must be in reverse direction compared to that on the last page of lecture 32. Given the
    [Show full text]
  • Lecture 8: Magnets and Magnetism Magnets
    Lecture 8: Magnets and Magnetism Magnets •Materials that attract other metals •Three classes: natural, artificial and electromagnets •Permanent or Temporary •CRITICAL to electric systems: – Generation of electricity – Operation of motors – Operation of relays Magnets •Laws of magnetic attraction and repulsion –Like magnetic poles repel each other –Unlike magnetic poles attract each other –Closer together, greater the force Magnetic Fields and Forces •Magnetic lines of force – Lines indicating magnetic field – Direction from N to S – Density indicates strength •Magnetic field is region where force exists Magnetic Theories Molecular theory of magnetism Magnets can be split into two magnets Magnetic Theories Molecular theory of magnetism Split down to molecular level When unmagnetized, randomness, fields cancel When magnetized, order, fields combine Magnetic Theories Electron theory of magnetism •Electrons spin as they orbit (similar to earth) •Spin produces magnetic field •Magnetic direction depends on direction of rotation •Non-magnets → equal number of electrons spinning in opposite direction •Magnets → more spin one way than other Electromagnetism •Movement of electric charge induces magnetic field •Strength of magnetic field increases as current increases and vice versa Right Hand Rule (Conductor) •Determines direction of magnetic field •Imagine grasping conductor with right hand •Thumb in direction of current flow (not electron flow) •Fingers curl in the direction of magnetic field DO NOT USE LEFT HAND RULE IN BOOK Example Draw magnetic field lines around conduction path E (V) R Another Example •Draw magnetic field lines around conductors Conductor Conductor current into page current out of page Conductor coils •Single conductor not very useful •Multiple winds of a conductor required for most applications, – e.g.
    [Show full text]
  • Magnetic Induction
    Online Continuing Education for Professional Engineers Since 2009 Basic Electric Theory PDH Credits: 6 PDH Course No.: BET101 Publication Source: US Dept. of Energy “Fundamentals Handbook: Electrical Science – Vol. 1 of 4, Module 1, Basic Electrical Theory” Pub. # DOE-HDBK-1011/1-92 Release Date: June 1992 DISCLAIMER: All course materials available on this website are not to be construed as a representation or warranty on the part of Online-PDH, or other persons and/or organizations named herein. All course literature is for reference purposes only, and should not be used as a substitute for competent, professional engineering council. Use or application of any information herein, should be done so at the discretion of a licensed professional engineer in that given field of expertise. Any person(s) making use of this information, herein, does so at their own risk and assumes any and all liabilities arising therefrom. Copyright © 2009 Online-PDH - All Rights Reserved 1265 San Juan Dr. - Merritt Island, FL 32952 Phone: 321-501-5601 DOE-HDBK-1011/1-92 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 1 of 4 U.S. Department of Energy FSC-6910 Washington, D.C. 20585 Distribution Statement A. Approved for public release; distribution is unlimited. Department of Energy Fundamentals Handbook ELECTRICAL SCIENCE Module 1 Basic Electrical Theory Basic Electrical Theory TABLE OF CONTENTS TABLE OF CONTENTS LIST OF FIGURES .................................................. iv LIST OF TABLES ..................................................
    [Show full text]
  • ELECTRICAL CIRCUIT ANALYSIS Lecture Notes
    ELECTRICAL CIRCUIT ANALYSIS Lecture Notes (2020-21) Prepared By S.RAKESH Assistant Professor, Department of EEE Department of Electrical & Electronics Engineering Malla Reddy College of Engineering & Technology Maisammaguda, Dhullapally, Secunderabad-500100 B.Tech (EEE) R-18 MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY II Year B.Tech EEE-I Sem L T/P/D C 3 -/-/- 3 (R18A0206) ELECTRICAL CIRCUIT ANALYSIS COURSE OBJECTIVES: This course introduces the analysis of transients in electrical systems, to understand three phase circuits, to evaluate network parameters of given electrical network, to draw the locus diagrams and to know about the networkfunctions To prepare the students to have a basic knowledge in the analysis of ElectricNetworks UNIT-I D.C TRANSIENT ANALYSIS: Transient response of R-L, R-C, R-L-C circuits (Series and parallel combinations) for D.C. excitations, Initial conditions, Solution using differential equation and Laplace transform method. UNIT - II A.C TRANSIENT ANALYSIS: Transient response of R-L, R-C, R-L-C Series circuits for sinusoidal excitations, Initial conditions, Solution using differential equation and Laplace transform method. UNIT - III THREE PHASE CIRCUITS: Phase sequence, Star and delta connection, Relation between line and phase voltages and currents in balanced systems, Analysis of balanced and Unbalanced three phase circuits UNIT – IV LOCUS DIAGRAMS & RESONANCE: Series and Parallel combination of R-L, R-C and R-L-C circuits with variation of various parameters.Resonance for series and parallel circuits, concept of band width and Q factor. UNIT - V NETWORK PARAMETERS:Two port network parameters – Z,Y, ABCD and hybrid parameters.Condition for reciprocity and symmetry.Conversion of one parameter to other, Interconnection of Two port networks in series, parallel and cascaded configuration and image parameters.
    [Show full text]
  • How to Design Analog Filter Circuits.Pdf
    a b FIG. 1-TWO LOWPASS FILTERS. Even though the filters use different components, they perform in a similiar fashion. MANNlE HOROWITZ Because almost every analog circuit contains some filters, understandinghow to work with them is important. Here we'll discuss the basics of both active and passive types. THE MAIN PURPOSE OF AN ANALOG FILTER In addition to bandpass and band- age (because inductors can be expensive circuit is to either pass or reject signals rejection filters, circuits can be designed and hard to find); they are generally easier based on their frequency. There are many to only pass frequencies that are either to tune; they can provide gain (and thus types of frequency-selective filter cir- above or below a certain cutoff frequency. they do not necessarily have any insertion cuits; their action can usually be de- If the circuit passes only frequencies that loss); they have a high input impedance, termined from their names. For example, are below the cutoff, the circuit is called a and have a low output impedance. a band-rejection filter will pass all fre- lo~~passfilter, while a circuit that passes A filter can be in a circuit with active quencies except those in a specific band. those frequencies above the cutoff is a devices and still not be an active filter. Consider what happens if a parallel re- higlzpass filter. For example, if a resonant circuit is con- sonant circuit is connected in series with a All of the different filters fall into one . nected in series with two active devices signal source.
    [Show full text]
  • AC Power • Resonant Circuits • Phasors (2-Dim Vectors, Amplitude and Phase) What Is Reactance ? You Can Think of It As a Frequency-Dependent Resistance
    Physics-272 Lecture 20 • AC Power • Resonant Circuits • Phasors (2-dim vectors, amplitude and phase) What is reactance ? You can think of it as a frequency-dependent resistance. 1 For high ω, χ ~0 X = C C ωC - Capacitor looks like a wire (“short”) For low ω, χC∞ - Capacitor looks like a break For low ω, χL~0 - Inductor looks like a wire (“short”) XL = ω L For high ω, χL∞ - Inductor looks like a break (inductors resist change in current) ("XR "= R ) An RL circuit is driven by an AC generator as shown in the figure. For what driving frequency ω of the generator, will the current through the resistor be largest a) ω large b) ω small c) independent of driving freq. The current amplitude is inversely proportional to the frequency of the ω generator. (X L= L) Alternating Currents: LRC circuit Figure (b) has XL>X C and (c) has XL<X C . Using Phasors, we can construct the phasor diagram for an LRC Circuit. This is similar to 2-D vector addition. We add the phasors of the resistor, the inductor, and the capacitor. The inductor phasor is +90 and the capacitor phasor is -90 relative to the resistor phasor. Adding the three phasors vectorially, yields the voltage sum of the resistor, inductor, and capacitor, which must be the same as the voltage of the AC source. Kirchoff’s voltage law holds for AC circuits. Also V R and I are in phase. Phasors R ε ω Problem : Given Vdrive = m sin( t), C L find VR, VL, VC, IR, IL, IC ε ∼ Strategy : We will use Kirchhoff’s voltage law that the (phasor) sum of the voltages VR, VC, and VL must equal Vdrive .
    [Show full text]
  • Chapter 14 Frequency Response
    CHAPTER 14 FREQUENCYRESPONSE One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man. — Elbert G. Hubbard Enhancing Your Career Career in Control Systems Control systems are another area of electrical engineering where circuit analysis is used. A control system is designed to regulate the behavior of one or more variables in some desired manner. Control systems play major roles in our everyday life. Household appliances such as heating and air-conditioning systems, switch-controlled thermostats, washers and dryers, cruise controllers in automobiles, elevators, traffic lights, manu- facturing plants, navigation systems—all utilize control sys- tems. In the aerospace field, precision guidance of space probes, the wide range of operational modes of the space shuttle, and the ability to maneuver space vehicles remotely from earth all require knowledge of control systems. In the manufacturing sector, repetitive production line opera- tions are increasingly performed by robots, which are pro- grammable control systems designed to operate for many hours without fatigue. Control engineering integrates circuit theory and communication theory. It is not limited to any specific engi- neering discipline but may involve environmental, chemical, aeronautical, mechanical, civil, and electrical engineering. For example, a typical task for a control system engineer might be to design a speed regulator for a disk drive head. A thorough understanding of control systems tech- niques is essential to the electrical engineer and is of great value for designing control systems to perform the desired task. A welding robot. (Courtesy of Shela Terry/Science Photo Library.) 583 584 PART 2 AC Circuits 14.1 INTRODUCTION In our sinusoidal circuit analysis, we have learned how to find voltages and currents in a circuit with a constant frequency source.
    [Show full text]