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This 5 page Class Notes was uploaded by Vernice Schuster on Wednesday September 23, 2015. The Class Notes belongs to PHYS102 at Drexel University taught by LuisCruz in Fall. Since its upload, it has received 7 views. For similar materials see /class/212520/phys102-drexel-university in Physics 2 at Drexel University.
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Date Created: 09/23/15
Circuits Capacitors One such elements are capacitors Capacitors are devices that store electric charge Example electronic devices with capacitors Rad o rece vers F ters n power supp es Used to e m nate spark ng n car gn ton systems Energystor ng dev ces A circuit generally consists of a number of electrical components called circuit elements connected together by conducting wires forming one or more closed loops Definition of Capacitance More About Capacitance T e capac tance s a measure oft e capac tor s 39 capaCitance is de ned as QOSitiVe ab ty to store 0 arge The capacitance of a given capacitor is constant Capac tance C of a capac tor s def ned ast e The capacitance is a measure of the capacitor s rato oft e magn tude oft e c arge on at er ab ty to store charge conductor to t e potenta d fference between t e The Farad is a large unit typically you will see condUCtorS Cgt0 Q microfarads pF and picofarads pF The capacitance of a device depends on the AV geometric arrangement of the conductors T e 8 un t of capac tance s a farad F butt s s a arge un t Typ ca y you wl see m crofarads pF and p cofarads pF Makeup of a Capacitor A capac tor consists of two conductors A When the conductors are charged using a battery they carry charges of equal magnitude and opposite directions A potential difference exists between the conductors due to the char e g roA V The capacitor sto res charge Capacitance Isolated Sphere First example a spherical charged conductor Assume V 0 at infinity Q Q R 2 2 24 R AV kZQR quot60 Note this is independent of the charge and the potential difference Only depends on geometry Parallel Plate Capacitor Each plate is connected to a terminal of the battery If the capacitor is initially uncharged the battery establishes an electric field in the connecting wires Capacitance of a Cylindrical Capacitor From Gauss Law t e fe d betweente E2kthlr AV2ket T e capac tance becomes cz AV cy nders s n ba Capacitance Parallel Plates The charge density on the plates is o QA A is the area of each plate which are equal Q is the charge on each plate equal with opposite signs E is uniform between the plates and zero elsewhere Capacitance of a spherical 9 4Q conductor Potential difference ngt 4 Butwe know that Ezk r substituting Use other formula to obtain capacitance Q ab CAVkebea 1 Note that for b gtgt a we recover prevrous result 27 A d 1 1 VbTVaszeQJ39 r CzkeQE Z 1 Capacitance Parallel Plates cont The capacitance is proportional to the area of its plates and inversely proportional to the plate separation azi Q zeoA AV Ed QdeoA d Circuit Symbols Useful in circuit diagram 0 Lines are used to represent wires 0 The battery s pos tive terminal is indicated by the longer line Capaci tor symbol Battery symb 01 Sw39 Lch symbol HP ac Capacitors in Parallel Charge transfer from battery leave the left plate pos tively charged and the right plate negatively charged The flow of charges ceases when the voltage across the capacitors equals AV The total charge is equal to the sum of the charges on the capac tors T Q Q1 Q2 The potential difference across the capacitors is the same A And each is equal to the voltage of the battery Capacitors in Series 3 Charges are the same QQ1Q2 The potential differences add up to the battery voltage Capacitors in Parallel cont quot The capacitors can be replaced with one capacitor with a capacitance of Ceq Equivalent capacitor CM 2 C1 02 2H a 2 Energy in a Capacitor Overview Before the switch is closed the energy is stored as chemical energy in the battery When the switch is closed the energy is transformed from AVV1V2 Equivalentcapacitance 1 1 1 chemical to electric potential energy eq C1 C2 Capacitors in Series 0 AV transfers electrons from the left plate of C1 to the right plate of CZ an equivalent amount of negative charge is removed from the left plate of C2 leaving twth an excess pos tive charge Energy in a Capacitor Overview cont The electric potential energy is related to the separation of the positive and negative charges on the plates A capacitor can be described as a device that stores energy as well as charge Energy Stored in a Capacitor Assume the capacitor is being charged and Other expressions For a arallel late capacitor the energy at some point has a charge q on it Q2 1 1 can be expressed in terms of the field as U QAV Cmvf The work needed to transfer a charge from 20 2 2 1 2 U eAdE one plate to the other IS I d d t f t 2 1 39nemnenogwmgw Hanmmbemmahnmmmo m WV T AW T C dq Although UAV there IS a maxtmum voltage energy density epnergy per unit volume The total work requrred IS before breakdown Q q 02 The energy can be considered to be stored in the 1 e E2 W21 61qu electric field a 0 Energy cont Energy final LIE 2 Capacitors with dielectrics l Capacitors with Dielectrics Capacitors with Dielectrics Adielectric is an insulating material that when placed between the plates of a capacitor increases the capacitance With a dielectric C KC0 Dielectrics include rubber lastic or waxed a er r CampK Q r p r p p 039 AV AV 0 For a parallel plate capac tor this becomes Experiments show that if a dielectric is inserted inside a C K ea A parallel plate capacitor the voltage between the plates d decreases AVB K AV where K gt 1 Dielectrics cont In theory d could be made very small to create a very large capacitance In practice there is a limitto d d is limited by the electric discharge that could occur though the dielectric medium separating the plates For a given d the maximum voltage that can be applied to a capacitor without causing a discharge depends on the dielectric stren th of the material Dielectrics An Atomic View cont An external electric field is applied This produces a torque on the molecules The molecules partially align with the electric field Flil ll l Ij An external field can Dielectrics final Dielectrics provide the following advantages Increase in capacitance Increase the maximum operating voltage Possible mechanical support between the plates 0 This allows the plates to be close together without touching This decreases d and increases C Dielectrics An Atomic View cont polarize the dielectric whether the molecules are polar or nonpolar The charged edges of the dielectric act as a second pair of plates producing an induced electric field in the direction oppos te the original electric field EzEfEmd c Dielectrics An Atomic View The molecules that make up the dielectric are modeled as dipoles The molecules are randomly oriented in the absence of an electric field 333 Dielectrics An atomic View final The total electric field V inside is diminished EE04Emd From the exp finding of the potential the electric Eu field is correspondingly reduced Using Gauss39 Law we already know E the original field E 039 0 d combining EZEHAEdeE 4 To obtain 039 airHK1
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