EE215ClassProblems,Week7
Solutions
Allquestionsareinitiallylistedinblack.Afterclass,thosethatwerecoveredinclassusingTopHat
(asclassactivities)willbehighlightedinblue.Questionsremaininginblack(afterclass)maybe
usedforadditionalreview.Solutionsarenotedinitalics.
Week7,Q1
PartA
Inthefollowingcircuitfindthevoltageacrossthecapacitoratt=0-(rightbeforetheswitch
changesposition).
Solution:
Priortotheswitchmovingfrompositionbtopositiona,thevoltageacrossthecapacitoris0(thereis
nopowerappliedtotherighthandsideofthecircuit.
PartB
InthecircuitinPartA,findthevoltageacrossthecapacitoratt=0+(rightbeforetheswitch
changesposition).
Solution:
Thevoltageacrossthecapacitorcannotchangeinstantaneously,sothevoltageremains0att=0+.
PartC
Inthefollowingcircuitfindthevoltageacrossthecapacitoratt=infinity.
Solution:
Aseriesofsourcetransformationstransformstheleftsideofthecircuitintoa11mAsource(pointing
upwaEd)inparallelwitha6,000ohmresistor.Atinfinity,thecapacitorbehavesasanopencircuit
andthevoltageacrossitisinparallelwiththe6,000ohmresistor=11mA*6,000ohms=66V
PartD
Whatisthetimeconstantofthiscircuitatt>0?
Solution:
ThetimeconstantisRC=6,000ohms*0.25µF=1.5msec
PartE
Whatisthevalueofthecapacitorvoltageatt=1msec
v(t)=66-66e-t/.0015
v(.001)=32.1V
PartF
Supposetheswitchnowmovesfrompositionatopositionbatt=1.5msec.Whatistheinitialvalue
ofthecapacitorvoltageatt=1.5msec+?
Solution:
1.5msecisonetimeconstantaftertheswitchwasoriginallymoved.Thevoltageatthattimewillbe
63.2%ofitsfinalvalueof66Vor41.7V
PartG
Supposetheswitchnowmovesfrompositionatopositionbatt=1.5msec.Whatisthe"new"final
valueofthecapacitorvoltageatt=infinity?
Solution:
Thefinalvalueofcapacitorvoltageis0V.
PartH
Giventhisnewswitchingevent,whatisthetimeconstantofthecircuitaftert=1.5msec
Solution:
ThenewR=(2k+4k)||6k=3,000ohms
RC=0.75msec
PartI
Giventhisnewswitchingevent,whatisthevalueofthecapacitorvoltageatt=2msec
Solution
Thevoltageacrossthecapacitoraftert=1.5msecis:
v(t)=41.7e-(t-.0015)/.00075
att=2msec,thisgivesavoltageof:21.4V