CAPACITORS Part ICalendar of the WeekCapacitors Part ICapacitorFrom Before: A simple CapacitorINSIDE THE DEVICEWhat is STORED in the capacitor?Two Charged Plates (Neglect Fringing Fields)Where is the charge?One Way to Charge:Slide 11More on CapacitorsDEFINITION - CapacityUNITSIS THIS A CAPACITOR??Slide 16After the switch is closed, how much charge passed through the capacitor?NOTEContinuing…Units of e0Simple Capacitor CircuitsSize Matters!Small is better in the IC world!TWO Types of ConnectionsParallel ConnectionSeries ConnectionSeries Connection ContinuedMore GeneralExampleMore on the Big CSo….Not All Capacitors are Created EqualSpherical CapacitorCalculate Potential Difference VSlide 35CAPACITORS Part IFebruary 12, 2007Calendar of the WeekThis week – CapacitorsWatch for new WebAssignThere will be a quiz on FridayCapacitors Part ICapacitorComposed of two metal plates.Each plate is chargedone positiveone negativeStores ChargeSYMBOLFrom Before: A simple CapacitorTWO PLATESBatteryWIRESINSIDE THE DEVICEWhat is STORED in the capacitor?An Electric FieldEnergyChargeAll threeNone of theseTwo Charged Plates(Neglect Fringing Fields)dAir or VacuumArea A- Q +QEV=Potential DifferenceSymbolADDED CHARGEWhere is the charge?dAir or VacuumArea A- Q +QEV=Potential Difference------++++++AREA=A=Q/AOne Way to Charge:Start with two isolated uncharged plates.Take electrons and move them from the + to the – plate through the region between.As the charge builds up, an electric field forms between the plates.You therefore have to do work against the field as you continue to move charge from one plate to another.CapacitorMore on CapacitorsdAir or VacuumArea A- Q +QEV=Potential DifferenceGaussianSurface000000)/(0-AQAQEEAQQEAAEAqdGaussAESame result from other plate!DEFINITION - CapacityThe Potential Difference is APPLIED by a battery or a circuit.The charge q on the capacitor is found to be proportional to the applied voltage.The proportionality constant is C and is referred to as the CAPACITANCE of the device.CVqorVqCUNITSUNITSA capacitor which acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARADOne Farad is one Coulomb/VoltCVqorVqCIS THIS A CAPACITOR??YesNoYou gotta be kiddingThe two metal objects in the figure have net charges of +79 pC and -79 pC, which result in a 10 V potential difference between them. (a) What is the capacitance of the system? [7.9] pF(b) If the charges are changed to +222 pC and -222 pC, what does the capacitance become? [7.9] pF(c) What does the potential difference become?[28.1] VAfter the switch is closed, how much charge passed through the capacitor?C/VV/CCVC+VVNOTEWork to move a charge from one side of a capacitor to the other is qEd.Work to move a charge from one side of a capacitor to the other is qVThus qV=qEdE=V/d As beforeContinuing…dACsodAVEAAqVqC000The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates.C is dependent only on the geometry of the device!Units of 0 mpFmFandmFaradVoltmCoulombVoltCoulombmCoulombJoulemCoulombNmCoulomb/85.8/1085.812022220----picoSimple Capacitor CircuitsBatteriesApply potential differencesCapacitorsWiresWires are METALS.Continuous strands of wire are all at the same potential.Separate strands of wire connected to circuit elements may be at DIFFERENT potentials.Size Matters!A Random Access Memory stores information on small capacitors which are either charged (bit=1) or uncharged (bit=0).Voltage across one of these capacitors ie either zero or the power source voltage (5.3 volts in this example).Typical capacitance is 55 fF (femto=10-15)Question: How many electrons are stored on one of these capacitors in the +1 state?Small is better in the IC world!electronsCVFeCVeqn61915108.1106.1)3.5)(1055(--TWO Types of ConnectionsSERIESPARALLELParallel ConnectionVCEquivalent=CE32132132133221111)(CCCCthereforeCCCVQqqqQVCqVCqVCVCqEEESeries ConnectionVC1 C2q -q q -q The charge on eachcapacitor is the same !Series Connection Continued212121111CCCorCqCqCqVVVVC1 C2q -q q -qMore GeneraliiiiCCParallelCCSeries11ExampleC1 C2VC3C1=12.0 fC2= 5.3 fC3= 4.5 d(12+5.3)pfseries(12+5.3)pfMore on the Big CWe move a charge dq from the (-) plate to the (+) one.The (-) plate becomes more (-)The (+) plate becomes more (+).dW=Fd=dq x E x d+q-qE=0A/d+dqSo….22220202000002122)(12211CVCVCCQUordAqAdqqdqAdUWdqdAqdWAqEGaussEddqdWQNot All Capacitors are Created EqualParallel PlateCylindricalSphericalSpherical Capacitor???4)(402020surpriserqrEqErqdGauss-AECalculate Potential Difference VdrrqVEdsVabplatepositiveplatenegative20..14(-) sign because E and ds are in OPPOSITE directions.Continuing…ababVqCababqbaqVrqrdrqVba00002044114)1(44Lost (-) sign due to switch of
View Full Document
Unlocking...