Capacitors

capacitanceCapacitance–capacitorsinseriesandinparallelEnergyincapacitorsCharginganddischargingcapacitorsThecoefficientiscalledthe“capacitance”Dthechargeontheplate(s)isproportionaltothevoltage

Forparallel-plates,Theratiodependsonthegeometryoftheplates,relativepositionanddielectricbutnotonthechargeq.Differentshapesofcapacitorsunits–farad(F)

Electrolyticcapacitorssolidnon-solid(wet)CeramiccapacitorsConnectingcapacitors“inseries”Whatisthe“equivalent”capacitance?Chargehastobethesame(withoppositesign)Thetotaldifferenceinvoltageis:Theequivalentcapacitanceis:+Q-QA+QAD-QADForparallel-platecapacitorsD2DCC/2

+Q-QA+QA-QAHowwillthecapacitancechangeaftertheinsertionofapieceofmetal?d1d2

Connectingcapacitors“inparallel”Thepotentialdifferenceisthesame-QA+QAD+Q-QADA2AC2C

Capacitorwithcharge

Q=ne(nchargesoneachside)+-------++++++e=elementarychargeEnergyisrequiredtobringachargefromoneplatetotheother,duetotheelectricforcedoing(negative)workTheenergystoredisthesumoftheenergyrequiredtomoveallofthechargesMoreenergyisrequiredwhenvoltageishigher-Asyouaddcharges,youneedmoreandmoreenergytomoveachargeAnenergyofeVtot

isneeded!+--+++++----chargeEaddedvoltageacrossplatesenergyrequiredchargenumber1n32TotalenergyaddednTotalenergystoredinacapacitor:Theenergyneededtoaddachargedq

is:Thetotalenergyaddedis:

ItisalsotheelectricenergyofacapacitordielectricHowwilltheenergystoredinthecapacitorchangeafterthedielectricbeingremoved?

dielectricHowwilltheenergystoredinthecapacitorchangeafterthedielectricbeingremoved?

TheRCcircuit&charging/dischargingacapacitorVBRCTheRCcircuitWhathappenswhenweclosetheswitch?0V=0VC=0V=0IQ=0V=VBVBRCV=0VB

>0

Atthebeginning

t=0later

t>0++++V>0

----Thecurrentdecreasesfromthebeginning!solution:differentialequation!voltageofbattery(constant)voltageofcapacitor(afunctionoftime)increaseofthechargeonthecapacitorafunctionoftimeTimeconstantofRCcircuitBaseforthenaturallogarithm

ChargingacapacitortForsmallt:VBRC0V=0VC=0V=0V=VBIWhatisthecurrentinR?I(t)ExponentialdecayAtthet

=timeconstant,thefunctiondecaysto1/e

=

37%ofitsoriginalvalueRC0VCIQnegativesignbecausethecurrentgo