Download PHY112 – Chapter 16 – Problems – Electrical Energy and

PHY112–Chapter16–Problems–ElectricalEnergyandCapacitance
1. A uniform electric field of magnitude 375 N/C pointing in the positive x-direction acts on an electron, which is
initiallyatrest.Aftertheelectronhasmoved3.20cm,whatis(a)theworkdonebythefieldontheelectron,(b)the
changeinpotentialenergyassociatedwiththeelectron,and(c)thevelocityoftheelectron?
2.Aprotonisreleasedfromrestinauniformelectricfieldofmagnitude385N/C.Find(a)theelectricforceonthe
proton,(b)theaccelerationoftheproton,and(c)thedistanceittravelsin2.00μs.
3.Apotentialdifferenceof90mVexistsbetweentheinnerandoutersurfacesofacellmembrane.Theinnersurface
isnegativerelativetotheoutersurface.Howmuchworkisrequiredtoejectapositivesodiumion(Na+)fromthe
interiorofthecell?
5.ThepotentialdifferencebetweentheacceleratingplatesofaTVsetisabout25kV.Ifthedistancebetweenthe
platesis1.5cm,findthemagnitudeoftheuniformelectricfieldintheregionbetweentheplates.
7.Oppositelychargedparallelplatesareseparatedby5.33mm.Apotentialdifferenceof600Vexistsbetweenthe
plates.(a)Whatisthemagnitudeoftheelectricfieldbetweentheplates?(b)Whatisthemagnitudeoftheforceon
anelectronbetweentheplates?(c)Howmuchworkmustbedoneontheelectrontomoveittothenegativeplateif
itisinitiallypositioned2.90mmfromthepositiveplate?
11. An electron is at the origin. (a) Calculate the electric potential VA at point A, x = 0.250 cm. (b) Calculate the
electric potential VB at point B, x = 0.750 cm. What is the potential difference VB – VA? (c) Would a negatively
charged particle placed at point A necessarily go through this same potential difference upon reaching point B?
Explain.
13.(a)Findtheelectricpotential,takingzeroatinfinity,attheupperrightcorner(thecornerwithoutacharge)of
therectangleinthefigurebelow.(b)Repeatifthe2.00-μCchargeisreplacedwithachargeof–2.00μC.
14. Three charges are situated at corners of a rectangle, as in the figure below. How much energy would be
expendedinmovingthe8.00-μCchargetoinfinity?
15.TwopointchargesQ1=+5.00nCandQ2=–3.00nCareseparatedby35.0cm.(a)Whatistheelectricpotentialat
a point midway between the charges? (b) What is the potential energy of the pair of charges? What is the
significanceofthealgebraicsignofyouranswer?
17.Thethreechargesinthefigurebelowareattheverticesofanisoscelestriangle.Letq=7.00nCandcalculatethe
electricpotentialatthemidpointofthebase.
23. In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles
(havingchargesof+2eandmassesof6.64x10-27kg)werefiredtowardagoldnucleuswithcharge+79e.Analpha
particle,initiallyveryfarfromthegoldnucleusisfiredat2.00x107m/sdirectlytowardthenucleus,asinthefigure
below.Howclosedoesthealphaparticlegettothegoldnucleusbeforeturningaround?Assumethegoldnucleus
remainsstationary.
24.FourpointchargeseachhavingchargeQarelocatedatthecornersofasquarehavingsidesoflength a.Find
symbolicexpressionsfor(a)thetotalelectricpotentialatthecenterofthesquareduetothefourchargesand(b)the
workrequiredtobringafifthchargeqfrominfinitytothecenterofthesquare.
25.ConsidertheEarthandacloudlayer800mabovetheplanettobetheplatesofaparallel-platecapacitor.(a)If
thecloudlayerhasanareaof1.0km2=1.0x105m2,whatisthecapacitance?(b)Ifanelectricfieldstrengthgreater
than 3.0 x 105 N/C causes the air to break down and conduct charge (lightning), what is the maximum charge the
cloudcanhold?
26. (a) When a 9.00-V battery is connected to the plates of a capacitor, it stores a charge of 27.0 μC. What is the
valueofthecapacitance?(b)Ifthesamecapacitorisconnectedtoa12.0-Vbattery,whatchargeisstored?
27.Anair-filledparallel-platecapacitorhasplatesofarea2.30cm2separatedby1.0mm.Thecapacitorisconnected
toa12.0-Vbattery.(a)Findthevalueofitscapacitance.(b)Whatisthechargeonthecapacitor?(c)Whatisthe
magnitudeoftheuniformelectricfieldbetweentheplates?
29.Anair-filledcapacitorconsistsoftwoparallelplates,eachwithanareaof7.60cm2andseparatedbyadistanceof
1.80mm.Ifa20.0-Vpotentialdifferenceisappliedtotheseplates,calculate(a)theelectricfieldbetweentheplates,
(b)thecapacitance,and(c)thechargeoneachplate.
31.Aparallel-platecapacitorwitharea0.200m2andplateseparationof3.00mmisconnectedtoa6.00-Vbattery.
(a)Whatisthecapacitance?(b)Howmuchchargeisstoredontheplates?(c)Whatistheelectricfieldbetweenthe
plates?(d)Findthemagnitudeofthechargedensityoneachplate.(e)Withoutdisconnectingthebattery,theplates
aremovedfartherapart.Qualitatively,whathappenstoeachofthepreviousanswers?
33. Given a 2.50-μF capacitor, a 6.25-μF capacitor, and a 6.00-V battery, find the charge on each capacitor if you
connectthem(a)inseriesacrossthebatteryand(b)inparallelacrossthebattery.
34. Two capacitors, C1 = 5.00 μF and C2 = 12.0 μF, are connected in parallel, and the resulting combination is
connectedtoa9.00-Vbattery.Find(a)theequivalentcapacitanceofthecombination,(b)thepotentialdifference
acrosseachcapacitor,and(c)thechargestoredoneachcapacitor.
35.Find(a)theequivalentcapacitanceofthecapacitorsinthefigurebelow,(b)thechargeoneachcapacitor,and(c)
thepotentialdifferenceacrosseachcapacitor.
36. Two capacitors give an equivalent capacitance of 9.00 pF when connected in parallel and an equivalent
capacitanceof2.00pFwhenconnectedinseries.Whatisthecapacitanceofeachcapacitor?
37.Forthesystemofcapacitorsshownbelow,find(a)theequivalentcapacitanceofthesystem,(b)thechargeon
eachcapacitor,and(c)thepotentialdifferenceacrosseachcapacitor.
38.Considerthecombinationofcapacitorsshowninthefigurebelow.(a)Findtheequivalentsinglecapacitanceof
the two capacitors in series and redraw the diagram (called diagram 1) with this equivalent capacitance. (b) In
diagram 1, find the equivalent capacitance of the three capacitors in parallel and redraw the diagram as a single
batteryandsinglecapacitorinaloop(c)Computethechargeonthesingleequivalentcapacitor.(d)Returningto
diagram1,computethechargeoneachindividualcapacitor.Doesthesumagreewiththevaluefoundinpart(c)?
(e)Whatisthechargeonthe2.40-μFcapacitorandonthe8.00-μFcapacitor?Computethevoltagedropacross(f)
the24.0-μFcapacitorand(g)the8.00-μFcapacitor.
39.Findthechargeoneachofthecapacitorsinthefigurebelow.
40.Threecapacitorsareconnectedtoabattery,asshowninthefigurebelow.TheircapacitancesareC1=3C,C2=C,
andC3=5C.(a)Whatistheequivalentcapacitanceofthissetofcapacitors?(b)Statetherankingofthecapacitors
according to the charge they store from largest to smallest. (c) Rank the capacitors according to the potential
differencesacrossthemfromlargesttosmallest.(d)AssumeC3isincreased.Explainwhathappenstothecharge
storedbyeachcapacitor.
41.A25.0-μFcapacitoranda40.0-μFcapacitorarechargedbybeingconnectedacrossseparate50.0-Vbatteries.(a)
Determinetheresultingchargeoneachcapacitor.(b)Thecapacitorsarethendisconnectedfromtheirbatteriesand
connectedtoeachother,witheachnegativeplateconnectedtotheotherpositiveplate.Whatisthefinalchargeof
eachcapacitor?(c)Whatisthefinalpotentialdifferenceacrossthe40.0-μFcapacitor?
42. (a) Find the equivalent capacitance between points a and b for the group of capacitors connected, as shown
below,ifC1=5.00μF,C2=10.00μF,andC3=2.00μF.(b)Ifthepotentialbetweenpointsaandbis60.0V,what
chargeisstoredinC3?
43. A 1.00-μF capacitor is charged by being connected across a 10.0-V battery. It is then disconnected from the
batteryandconnectedacrossanuncharged2.00-μFcapacitor.Determinetheresultingchargeoneachcapacitor.
44.Fourcapacitorsareconnectedasshowninthefigurebelow.(a)Findtheequivalentcapacitancebetweenpoints
aandb.(b)Calculatethechargeoneachcapacitor,takingΔVab=15.0V.
45.A12.0-Vbatteryisconnectedtoa4.50-μFcapacitor.Howmuchenergyisstoredinthecapacitor?
46.Twocapacitors,C1=18.0μFandC2=36.0μF,areconnectedinseries,anda12.0-Vbatteryisconnectedacross
them.(a)Findtheequivalentcapacitance,andtheenergycontainedinthisequivalentcapacitor.(b)Findtheenergy
storedineachindividualcapacitor.Showthatthesumofthesetwoenergiesisthesameastheenergyfoundinpart
(a).Willthisequalityalwaysbetrue,ordoesitdependonthenumberofcapacitorsandtheircapacitances?(c)If
thesamecapacitorswereconnectedinparallel,whatpotentialdifferencewouldberequiredacrossthemsothatthe
combinationstoresthesameenergyasinpart(a)?Whichcapacitorstoresmoreenergyinthissituation,C1orC2?
47. A parallel-plate capacitor has capacitance 3.00 μF. (a) How much energy is stored in the capacitor if it is
connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates
doubled, what is the energy stored? (c) The battery is subsequently reattached to the capacitor, but the plate
separationremainsasinpart(b).Howmuchenergyisstored?(Answereachpartinunitsofmicro-Joules.)
48.Acertainstormcloudhasapotentialdifferenceof1.00x108Vrelativetoatree.If,duringalightningstorm,50.0
C of charge is transferred through this potential difference, and 1.00% of the energy is absorbed by the tree, how
much water (sap in the tree) initially at 30.00C can be boiled away? (Water has a specific heat of 4,186 J/kg 0C, a
boilingpointof1000C,andaheatofvaporizationof2.26x106J/kg.)
56.Forthesystemoffourcapacitorsshownbelow,find(a)thetotalenergystoredinthesystemand(b)theenergy
storedbyeachcapacitor.(c)Comparethesumoftheanswersinpart(b)withyourresulttopart(a)andexplain
yourobservation.
61.Findtheequivalentcapacitanceofthegroupofcapacitorsshownbelow.
65. Capacitors C1 = 6.0 μF and C2 = 2.0 μF are charged as a parallel combination across a 250-V battery. The
capacitors are disconnected from the battery and from each other. They are then connected positive plate to
negativeplateandnegativeplatetopositiveplate.Calculatetheresultingchargeoneachcapacitor.