Chapter 6 Inductance, Capacitance, and Mutual Inductance

Total Page:16

File Type:pdf, Size:1020Kb

Chapter 6 Inductance, Capacitance, and Mutual Inductance Chapter 6 Inductance, Capacitance, and Mutual Inductance 6.1 The inductor 6.2 The capacitor 6.3 Series-parallel combinations of inductance and capacitance 6.4 Mutual inductance 6.5 Closer look at mutual inductance 1 Overview In addition to voltage sources, current sources, resistors, here we will discuss the remaining 2 types of basic elements: inductors, capacitors. Inductors and capacitors cannot generate nor dissipate but store energy. Their current-voltage (i-v) relations involve with integral and derivative of time, thus more complicated than resistors. 2 Key points di Why the i-v relation of an inductor isv L ? dt dv Why the i-v relation of a capacitor isi C ? dt Why the energies stored in an inductor and a capacitor are: 1 1 w Li, 2 , 2 Cv respectively? 2 2 3 Section 6.1 The Inductor 1. Physics 2. i-v relation and behaviors 3. Power and energy 4 Fundamentals An inductor of inductance L is symbolized by a solenoidal coil. Typical inductance L ranges from 10 H to 10 mH. The i-v relation of an inductor (under the passive sign convention) is: di v L , dt 5 Physics of self-inductance (1) Consider an N1 -turn coil C1 carrying current I1 . The resulting magnetic fieldB 1() r 1 N 1(Biot- I will pass through Savart law) C1 itself, causing a flux linkage 1 , where B1() r 1 N 1 , 1 B1 r1() d s1 P 1, 1 N I S 1 P1 is the permeance. 2 1 PNI 1 11. 6 Physics of self-inductance (2) The ratio of flux linkage to the driving current is defined as the self inductance of the loop: 1 2 L1NP 1 1, I1 which describes how easy a coil current can introduce magnetic flux over the coil itself. 7 Examples Solenoidal & toroidal coils: ~2 cm L = 270 H L = 36 H RG59/U coaxial cable: L = 351 nH/m. 8 The i-v relation Faraday’s law states that the electromotive force v (emf, in units of volt) induced on a loop equals the time derivative of the magnetic flux linkage : d d d v , v Li L i. dt dt dt Note: The emf of a loop is a non-conservative force that can drive current flowing along the loop. In contrast, the current-driving force due to electric charges is conservative. 9 Behaviors of inductors di v L dt DC-current: inductor behaves as a short circuit. Current cannot change instantaneously in an inductor, otherwise, infinite voltage will arise. Change of inductor current is the integral of voltage during the same time interval: 1 t i()() t i0 t v(). d L t0 10 Inductive effect is everywhere! Nearly all electric circuits have currents flowing through conducting wires. Since it’s difficult to shield magnetic fields, inductive effect occurs even we do not purposely add an inductor into the circuit. 11 Example 6.1: Inductor driven by a current pulse 0 , t 0 i() t 5t 10 te , t 0 The inductor voltage is: Inductor voltage can Memory-less di 0 , t 0 v() t L in steady 5t jump! dt (e 1 5 t ), t 0 state. 12 Power & energy (1) Consider an inductor of inductance L. The instantaneous power in the inductor is: di p vi Li. dt Assume there is no initial current (i.e. no initial energy), i(t =0)=0, w(t =0)=0. We are interested in the energy W when the current increases from zero to I with arbitrary i(t). 13 Power & energy (2) dw di W I p dwLi , Li di, dw, L idi dt dt 0 0 I i2 1 1 WL LI 2 , i.e.w Li2 2 2 0 2 How the current changes with time doesn’t matter. It’s the final current I determining the final energy. Inductor stores magnetic energy when there is nonzero current. 14 Example 6.3: Inductor driven by a current pulse t <0.2, p>0, w, charging. t >0.2, p<0, w, discharging. In steady state (t ), i 0, v0, p0, w0 (no energy). 15 Example 6.3: Inductor driven by a voltage pulse 1 t i() t (v ) d ( i 0 ) L 0 p>0, w, always charging. In steady state (t), i 2 A, v0, p0, w200 mJ (sustained current and With memory in steady state. constant energy). 16 Section 6.2 The Capacitor 1. Physics 2. i-v relation and behaviors 3. Power and energy 17 Fundamentals A capacitor of capacitance C is symbolized by a parallel-plate . Typical capacitance C ranges from 10 pF to 470 F. The i-v relation of an capacitor (under the passive sign convention) is: dv i C . dt 18 Physics of capacitance (1) If we apply a voltage V12 between two isolated conductors, charge Q will be properly distributed over the conducting surfaces such that the resulting electric field E() r satisfies: 2 E() r 1 1 B1 E(), r d l 12 V 2 which is valid for any integral path linking the two conducting E surfaces. 19 Physics of capacitance (2) IfVV 12 12 , QQ while the spatial distribution of charge remains such that 1 E r( ) E ( r ), V 12 E ( r ) d12 l . V 2 The ratio of the deposited charge to the bias voltage is defined as the capacitance of the conducting pair: Q C , V describing how easy a bias voltage can deposit charge on the conducting pair. 20 Examples Ceramic disc & electrolytic: RG59/U coaxial cable: C = 53 pF/m. 21 The i-v relation From the definition of capacitance: Q d d d C, q ( t ) Cv ( ),q t Cv, i C v . V dt dt dt Note: Charge cannot flow through the dielectric between the conductors. However, a time-varying voltage causes a time-varying electric field that can slightly displace the dielectric bound charge. It is the time-varying bound charge contributing to the “displacement current”. 22 Polarization charge 23 Behaviors of capacitors dv i C dt DC-voltage: capacitor behaves as an open circuit. Voltage cannot change instantaneously in an capacitor, otherwise, infinite current will arise. Change of capacitor voltage is the integral of current during the same time interval: 1 t v()() t v0 t i(). d C t0 24 Capacitive effect is everywhere! A Metal-Oxide-Semiconductor (MOS) transistor has three conducting terminals (Gate, Source, Drain) separated by a dielectric layer with one another. Capacitive effect occurs even we do not purposely add a capacitor into the circuit. (info.tuwien.ac.at) charges 25 Power & energy (1) Consider a capacitor of capacitance C. The instantaneous power in the capacitor is: dv p vi Cv . dt Assume there is no initial voltage (i.e. no initial energy), v(t =0)=0, w(t =0)=0. We are interested in the energy W when the voltage increases from zero to V with arbitrary v(t). 26 Power & energy (2) dw dv W V p dwCv , Cv dv, dw C , vdv dt dt 0 0 2 V v 1 2 1 WC CV , i.e.w Cv2 2 0 2 2 How the voltage increases with time doesn’t matter. It’s the final voltage V determining the final energy. Capacitor stores electric energy when there is nonzero voltage. 27 Example 6.4: Capacitor driven by a voltage pulse Capacitor current can jump! t <1, p>0, w, charging. t >1, p<0, w, discharging. In steady state (t), i 0, v Memory-less in 0, p0, w0 (no energy). steady state. 28 Section 6.3 Series-Parallel Combinations 1. Inductors in series-parallel 2. Capacitors in series-parallel 29 Inductors in series i1 i 2i , i3 v v1 v2 , 3 v di v L j , j j dt di di di v L L L 1 dt 2 dt 3 dt di L , eq dt n LLeq j j1 30 Inductors in parallel 1 t v v 1 v 2 v, 3 i1 i 2 , i 3 j iv i( ) d j i (0 t ), t 0 L j 3 t 3 t 3 1 1 i v()() d j i0 t v() d ()j i0 t t0 t0 j1 L j j1 L j j1 n 1 t 1 1 (v ) d ( i0 ),t t 0 Leq LLeq j1 j 31 Capacitors in series = v v1 v 2 3 v, i 1 i 2 i, 3 i n 1 1 1 t 1 t v j id( vj 0 ), t v id ( v0 ), t t0 t0 CCeq j1 j C j Ceq 32 Capacitors in parallel = v v v v, i i i, i 1 2 3 1 2 3 n dv dv CCeq j i C ,i C , j1 j j dt eq dt 33 Section 6.4, 6.5 Mutual Inductance 1. Physics 2. i-v relation and dot convention 3. Energy 34 Fundamentals Mutual inductance M is a circuit parameter between two magnetically coupled coils. The value of M satisfiesM k 1 L 2 , where L 0 k 1is the magnetic coupling coefficient. The emf induced in Coil 2 due to time-varying current in Coil 1 is proportionalM to di1 . dt 35 The i-v relation (1) Coil 1 of N1 turns is driven by a time-varying current i1 , while Coil 2 of N2 turns is open. The flux components linking (1) only Coil 1, (2) both coils, and (3) total flux linking Coil 1 are: B11 r1() d s11 P 1, 1 N B 21 I r1() d s21 P 1.
Recommended publications
  • Electric Circuit • Basic Laws – Ohm’S Law – Kirchhoff's Voltage Law – Kirchhoff's Current Law • Power and Energy
    Basic Definitions & Basic Laws Dr. Mohamed Refky Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University [email protected] http://scholar.cu.edu.eg/refky/ Outline of this Lecture • Course Contents, References, Course Plan • Basic Definitions • Topology of Electric Circuit • Basic Laws – Ohm’s Law – Kirchhoff's Voltage Law – Kirchhoff's Current Law • Power and Energy Dr. Mohamed Refky 2 References • Textbook: – “Fundamentals of Electric Circuits”, Alexander and Sadiku, 5th edition • References: – J. W. Nilsson and S. Riedel, Electric Circuits. 8th Edition, Prentice Hall, 2008. – Syed A. Nasar, “Electric Circuits,” Schaum’s Solved Problems Series, Mcgraw-Hill, New York, 1988. – Cunningham Stuller, “Circuit Analysis,” John Wiley & Sons Inc., New York, 1995. Dr. Mohamed Refky 3 Course Plan • Instructor: Prof. Mohamed Fathy Dr. Mohamed Refky • TA: TBA • Grading: – 40% Activity • Quizzers • Assignments • Attendance – 20 % Midterm – 40% Final Exam • Office Hours: TBA Dr. Mohamed Refky 4 Course Contents Week Topic 1 Basic Definitions & Basic Laws 2 3 Methods of solution of DC circuits 4 8 Network Theorems 6 Midterm 7 Introduction to Capacitors and Inductors 8 Sinusoids and phasors 9 10 Sinusoidal steady state analysis 11 12 Three Phase Circuits Dr. Mohamed Refky 5 Introduction Importance of this Course For an electrical engineering student, basic electric circuit theory is an essential to understand several other courses. Many branches of electrical engineering, such as power, electric machines, electronics, and instrumentation, are based on electric circuit theory. Dr. Mohamed Refky 6 Outline of this Lecture • Course Contents, References, Course Plan • Basic Definitions • Topology of Electric Circuit • Basic Laws – Ohm’s Law – Kirchhoff's Voltage Law – Kirchhoff's Current Law • Power and Energy Dr.
    [Show full text]
  • Determination of the Magnetic Permeability, Electrical Conductivity
    This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE Transactions on Industrial Informatics TII-18-2870 1 Determination of the magnetic permeability, electrical conductivity, and thickness of ferrite metallic plates using a multi-frequency electromagnetic sensing system Mingyang Lu, Yuedong Xie, Wenqian Zhu, Anthony Peyton, and Wuliang Yin, Senior Member, IEEE Abstract—In this paper, an inverse method was developed by the sensor are not only dependent on the magnetic which can, in principle, reconstruct arbitrary permeability, permeability of the strip but is also an unwanted function of the conductivity, thickness, and lift-off with a multi-frequency electrical conductivity and thickness of the strip and the electromagnetic sensor from inductance spectroscopic distance between the strip steel and the sensor (lift-off). The measurements. confounding cross-sensitivities to these parameters need to be Both the finite element method and the Dodd & Deeds rejected by the processing algorithms applied to inductance formulation are used to solve the forward problem during the spectra. inversion process. For the inverse solution, a modified Newton– Raphson method was used to adjust each set of parameters In recent years, the eddy current technique (ECT) [2-5] and (permeability, conductivity, thickness, and lift-off) to fit the alternating current potential drop (ACPD) technique [6-8] inductances (measured or simulated) in a least-squared sense were the two primary electromagnetic non-destructive testing because of its known convergence properties. The approximate techniques (NDT) [9-21] on metals’ permeability Jacobian matrix (sensitivity matrix) for each set of the parameter measurements.
    [Show full text]
  • Units in Electromagnetism (PDF)
    Units in electromagnetism Almost all textbooks on electricity and magnetism (including Griffiths’s book) use the same set of units | the so-called rationalized or Giorgi units. These have the advantage of common use. On the other hand there are all sorts of \0"s and \µ0"s to memorize. Could anyone think of a system that doesn't have all this junk to memorize? Yes, Carl Friedrich Gauss could. This problem describes the Gaussian system of units. [In working this problem, keep in mind the distinction between \dimensions" (like length, time, and charge) and \units" (like meters, seconds, and coulombs).] a. In the Gaussian system, the measure of charge is q q~ = p : 4π0 Write down Coulomb's law in the Gaussian system. Show that in this system, the dimensions ofq ~ are [length]3=2[mass]1=2[time]−1: There is no need, in this system, for a unit of charge like the coulomb, which is independent of the units of mass, length, and time. b. The electric field in the Gaussian system is given by F~ E~~ = : q~ How is this measure of electric field (E~~) related to the standard (Giorgi) field (E~ )? What are the dimensions of E~~? c. The magnetic field in the Gaussian system is given by r4π B~~ = B~ : µ0 What are the dimensions of B~~ and how do they compare to the dimensions of E~~? d. In the Giorgi system, the Lorentz force law is F~ = q(E~ + ~v × B~ ): p What is the Lorentz force law expressed in the Gaussian system? Recall that c = 1= 0µ0.
    [Show full text]
  • On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
    Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics.
    [Show full text]
  • SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for Sensitive Magnetometry in Moderate Background Magnetic Fields
    SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields Cite as: Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 Submitted: 24 July 2018 . Accepted: 10 October 2018 . Published Online: 25 October 2018 A. T. Asfaw , E. I. Kleinbaum, T. M. Hazard , A. Gyenis, A. A. Houck, and S. A. Lyon ARTICLES YOU MAY BE INTERESTED IN Multi-frequency spin manipulation using rapidly tunable superconducting coplanar waveguide microresonators Applied Physics Letters 111, 032601 (2017); https://doi.org/10.1063/1.4993930 Publisher's Note: “Anomalous Nernst effect in Ir22Mn78/Co20Fe60B20/MgO layers with perpendicular magnetic anisotropy” [Appl. Phys. Lett. 111, 222401 (2017)] Applied Physics Letters 113, 179901 (2018); https://doi.org/10.1063/1.5018606 Tunneling anomalous Hall effect in a ferroelectric tunnel junction Applied Physics Letters 113, 172405 (2018); https://doi.org/10.1063/1.5051629 Appl. Phys. Lett. 113, 172601 (2018); https://doi.org/10.1063/1.5049615 113, 172601 © 2018 Author(s). APPLIED PHYSICS LETTERS 113, 172601 (2018) SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for sensitive magnetometry in moderate background magnetic fields A. T. Asfaw,a) E. I. Kleinbaum, T. M. Hazard, A. Gyenis, A. A. Houck, and S. A. Lyon Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA (Received 24 July 2018; accepted 10 October 2018; published online 25 October 2018) We describe sensitive magnetometry using lumped-element resonators fabricated from a supercon- ducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconduc- tor, we demonstrate a continuous resonance frequency shift of 27 MHz for a change in the magnetic field of 1.8 lT within a perpendicular background field of 60 mT.
    [Show full text]
  • Chapter 32 Inductance and Magnetic Materials
    Chapter 32 Inductance and Magnetic Materials The appearance of an induced emf in one circuit due to changes in the magnetic field produced by a nearby circuit is called mutual induction. The response of the circuit is characterized by their mutual inductance. Can we find an induced emf due to its own magnetic field changes? Yes! The appearance of an induced emf in a circuit associated with changes in its own magnet field is called self-induction. The corresponding property is called self-inductance. A circuit element, such as a coil, that is designed specifically to have self-inductance is called an inductor. 1 32.1 Inductance Close: As the flux through the coil changes, there is an induced emf that opposites this change. The self induced emf try to prevent the rise in the current. As a result, the current does not reach its final value instantly, but instead rises gradually as in right figure. Open: When the switch is opened, the flux rapidly decreases. This time the self- induced emf tries to maintain the flux. When the current in the windings of an electromagnet is shut off, the self-induced emf can be large enough to produce a spark across the switch contacts. 2 32.1 Inductance (II) Since the self-induction and mutual induction occur simultaneously, both contribute to the flux and to the induced emf in each coil. The flux through coil 1 is the sum of two terms: N1Φ1 = N1(Φ11 + Φ12 ) The net emf induced in coil 1 due to changes in I1 and I2 is d V = −N (Φ + Φ ) emf 1 dt 11 12 3 Self-Inductance It is convenient to express the induced emf in terms of a current rather than the magnetic flux through it.
    [Show full text]
  • Introduction to Electrical and Computer Engineering International
    Introduction to Electrical and Computer Engineering Basic Circuits and Simulation Electrical & Computer Engineering Basic Circuits and Simulation (1 of 22) International System of Units (SI) • Length: meter (m) • SI Prefixes (power of 10) • Mass: kilogram (kg) – 1012 Tera (T) • Time: second (s) – 109 Giga (G) – 106 Mega (M) • Current: Ampere (A) – 103 kilo (k) • Voltage: Volt (V) – 10-3 milli (m) • Temperature: Degrees – 10-6 micro (µ) Kelvin (ºK) – 10-9 nano (n) – 10-12 pico (p) Electrical & Computer Engineering Basic Circuits and Simulation (2 of 22) 1 SI Examples • A few examples: • 1 Gbit = 109 bits, or 103106 bits, or one thousand million bits – 10-5 s = 0.00001 s; use closest SI prefix • 1×10-5 s = 10 × 10-6 s or 10 μs or • 1×10-5 s = 0.01 × 10-3 s or 0.01 ms Electrical & Computer Engineering Basic Circuits and Simulation (3 of 22) Typical Ranges Voltage (V) Current (A) • 10-8 Antenna of radio • 10-12 Nerve cell in brain receiver (10 nV) • 10-7 Integrated circuit • 10-3 EKG – voltage memory cell (0.1 µA) produced by heart • 10×10-3 Threshold of • 1.5 Flashlight battery sensation in humans • 12 Car battery • 100×10-3 Fatal to humans • 110 House wiring (US) • 1-2 Typical Household • 220 House wiring (Europe) appliance • 107 Lightning bolt (10 MV) • 103 Large industrial appliance • 104 Lightning bolt Electrical & Computer Engineering Basic Circuits and Simulation (4 of 22) 2 Electrical Quantities • Electric Charge (positive or negative) – (Coulombs, C) - q – Electron: 1.602 x 10 • Current (Ampere or Amp, A) – i or I – Rate of charge flow, – 1 1 Electrical & Computer Engineering Basic Circuits and Simulation (5 of 22) Electrical Quantities (continued) • Voltage (Volts, V) – w=energy required to move a given charge between two points (Joule, J) – – 1 1 1 Joule is the work done by a constant 1 N force applied through a 1 m distance.
    [Show full text]
  • Relative Permeability Measurements for Metal-Detector Research
    NATL INST. OF STAND & TECH MIST 1""""""""" PUBUCATI0N8 National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Technical Note 1532 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic James Baker-Jarvis /oo NIST Technical Note 1532 Relative Permeability Measurements For Metal-Detector Research Michael D. Janezic James Baker-Jarvis Radio-Frequency Technology Division Electronics and Electrical Engineering Laboratory National Institute of Standards and Technology Boulder, CO 80305 April 2004 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary for Technology National Institute of Standards and Technology Arden L. Bement, Jr., Director National Institute of Standards U.S. Government Printing Office For sale by the and Technology Washington: 2004 Superintendent of Documents Technical Note 1532 U.S. Government Printing Office Natl. Inst. Stand. Technol. Stop SSOP Tech. Note 1532 Washington, DC 20402-0001 1 6 Pages (April 2004) Phone: (202) 512-1 800 CODEN: NTNOEF Fax: (202) 512-2250 Internet: bookstore.gpo.gov Contents 1 Introduction 1 2 Overview and Definitions 2 3 Toroid Meeisurement Technique 4 3.0.1 Relative Permeability Model Excluding Toroid Conductivity 4 3.0.2 Relative Permittivity Model Including Toroid Conductivity 5 4 Measurements of Relative Permeability 7 5 Conclusions 11 6 References 12 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic and James Baker- Jarvis Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305 We examine a measurement method for characterizing the low-frequency relative per- meability of ferromagnetic metals commonly used in the manufacture of weapons.
    [Show full text]
  • Chapter 5 Capacitance and Dielectrics
    Chapter 5 Capacitance and Dielectrics 5.1 Introduction...........................................................................................................5-3 5.2 Calculation of Capacitance ...................................................................................5-4 Example 5.1: Parallel-Plate Capacitor ....................................................................5-4 Interactive Simulation 5.1: Parallel-Plate Capacitor ...........................................5-6 Example 5.2: Cylindrical Capacitor........................................................................5-6 Example 5.3: Spherical Capacitor...........................................................................5-8 5.3 Capacitors in Electric Circuits ..............................................................................5-9 5.3.1 Parallel Connection......................................................................................5-10 5.3.2 Series Connection ........................................................................................5-11 Example 5.4: Equivalent Capacitance ..................................................................5-12 5.4 Storing Energy in a Capacitor.............................................................................5-13 5.4.1 Energy Density of the Electric Field............................................................5-14 Interactive Simulation 5.2: Charge Placed between Capacitor Plates..............5-14 Example 5.5: Electric Energy Density of Dry Air................................................5-15
    [Show full text]
  • Power-Invariant Magnetic System Modeling
    POWER-INVARIANT MAGNETIC SYSTEM MODELING A Dissertation by GUADALUPE GISELLE GONZALEZ DOMINGUEZ Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 2011 Major Subject: Electrical Engineering Power-Invariant Magnetic System Modeling Copyright 2011 Guadalupe Giselle González Domínguez POWER-INVARIANT MAGNETIC SYSTEM MODELING A Dissertation by GUADALUPE GISELLE GONZALEZ DOMINGUEZ Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Chair of Committee, Mehrdad Ehsani Committee Members, Karen Butler-Purry Shankar Bhattacharyya Reza Langari Head of Department, Costas Georghiades August 2011 Major Subject: Electrical Engineering iii ABSTRACT Power-Invariant Magnetic System Modeling. (August 2011) Guadalupe Giselle González Domínguez, B.S., Universidad Tecnológica de Panamá Chair of Advisory Committee: Dr. Mehrdad Ehsani In all energy systems, the parameters necessary to calculate power are the same in functionality: an effort or force needed to create a movement in an object and a flow or rate at which the object moves. Therefore, the power equation can generalized as a function of these two parameters: effort and flow, P = effort × flow. Analyzing various power transfer media this is true for at least three regimes: electrical, mechanical and hydraulic but not for magnetic. This implies that the conventional magnetic system model (the reluctance model) requires modifications in order to be consistent with other energy system models. Even further, performing a comprehensive comparison among the systems, each system’s model includes an effort quantity, a flow quantity and three passive elements used to establish the amount of energy that is stored or dissipated as heat.
    [Show full text]
  • Tunable Synthesis of Hollow Co3o4 Nanoboxes and Their Application in Supercapacitors
    applied sciences Article Tunable Synthesis of Hollow Co3O4 Nanoboxes and Their Application in Supercapacitors Xiao Fan, Per Ohlckers * and Xuyuan Chen * Department of Microsystems, Faculty of Technology, Natural Sciences and Maritime Sciences, University of South-Eastern Norway, Campus Vestfold, Raveien 215, 3184 Borre, Norway; [email protected] * Correspondence: [email protected] (P.O.); [email protected] (X.C.); Tel.: +47-310-09-315 (P.O.); +47-310-09-028 (X.C.) Received: 17 January 2020; Accepted: 7 February 2020; Published: 11 February 2020 Abstract: Hollow Co3O4 nanoboxes constructed by numerous nanoparticles were prepared by using a facile method consisting of precipitation, solvothermal and annealing reactions. The desirable hollow structure as well as a highly porous morphology led to synergistically determined and enhanced supercapacitor performances. In particular, the hollow Co3O4 nanoboxes were comprehensively investigated to achieve further optimization by tuning the sizes of the nanoboxes, which were well controlled by initial precipitation reaction. The systematical electrochemical measurements show that the optimized Co3O4 electrode delivers large specific capacitances of 1832.7 and 1324.5 F/g at current densities of 1 and 20 A/g, and only 14.1% capacitance decay after 5000 cycles. The tunable synthesis paves a new pathway to get the utmost out of Co3O4 with a hollow architecture for supercapacitors application. Keywords: Co3O4; hollow nanoboxes; supercapacitors; tunable synthesis 1. Introduction Nowadays, the growing energy crisis has enormously accelerated the demand for efficient, safe and cost-effective energy storage devices [1,2]. Because of unparalleled advantages such as superior power density, strong temperature adaptation, a fast charge/discharge rate and an ultralong service life, supercapacitors have significantly covered the shortage of conventional physical capacitors and batteries, and sparked considerable interest in the last decade [3–5].
    [Show full text]
  • Physics 1B Electricity & Magnetism
    Physics 1B! Electricity & Magnetism Frank Wuerthwein (Prof) Edward Ronan (TA) UCSD Quiz 1 • Quiz 1A and it’s answer key is online at course web site. • http://hepuser.ucsd.edu/twiki2/bin/view/ UCSDTier2/Physics1BWinter2012 • Grades are now online Outline of today • Continue Chapter 20. • Capacitance • Circuits Capacitors • Capacitance, C, is a measure of how much charge can be stored for a capacitor with a given electric potential difference. " ! Where Q is the amount of charge on each plate (+Q on one, –Q on the other). " ! Capacitance is measured in Farads. " ! [Farad] = [Coulomb]/[Volt] " ! A Farad is a very large unit. Most things that you see are measured in μF or nF. Capacitors •! Inside a parallel-plate capacitor, the capacitance is: " ! where A is the area of one of the plates and d is the separation distance between the plates. " ! When you connect a battery up to a capacitor, charge is pulled from one plate and transferred to the other plate. Capacitors " ! The transfer of charge will stop when the potential drop across the capacitor equals the potential difference of the battery. " ! Capacitance is a physical fact of the capacitor, the only way to change it is to change the geometry of the capacitor. " ! Thus, to increase capacitance, increase A or decrease d or some other physical change to the capacitor. •! ExampleCapacitance •! A parallel-plate capacitor is connected to a 3V battery. The capacitor plates are 20m2 and are separated by a distance of 1.0mm. What is the amount of charge that can be stored on a plate? •! Answer •! Usually no coordinate system needs to be defined for a capacitor (unless a charge moves in between the plates).
    [Show full text]