38061042 topic 20 capacitance

8/13/2019 38061042 Topic 20 Capacitance

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TOPIC 2

1 Four capacitors each of capacitance 2 are connected insuch a way tllat their total capacitan Ce is also 2 ~ F . Whichone of the following systems gives this value?

2 A 2 capacitor is charged to a potential of 200 V and thenisolated. When it is connected in parallel with a secondcapacitor which is initially uncharged, the common potentialbecomes 40 V. The capacitance of the s e c o n ~ capacitor isA 2 D S pFE 16

Capacitance6 A capacitor made from two thin, tlat metal sheets separated

by a small thickness of insulating material has a capaCitanceC. Each metal sheet is then cut into four smaller identicalsheets, which are used to make another capacitor as shownbelow (Fig. I). The same thickness of insulator is Usedbetween the interleaved sheets.

Fig. 1

Neglecting end-effects, the capacitance of the reconstructedcapacitor is approximatelyA C n 7C/4 e 7C D SC E 2SCJ80/Il/22

7 The electric field between the plates of an isolated air-spacedparallel-plate capacitor is E What is the field between the

l

n 4e 6 pF 177/11/22 plates after immersing the capacitor in a liquid of relativepermittivity 2?3 A photographic flash unit consists of a xenon-filled tubeenergised by the discharge of a capacitor previously charged

by a 1000 V source. The average power delivered to thenash tube is 2000 v'l and the t l a ~ h lasts 0.040 s; Thecapacitance of the capacitor can be estimated asA 40 X 10-6Fn 80 x 10-6 Fe 160x 10-6FD SO X 10-) FE 160 X 10-3 F 178/11/24

4 A capacitor of capacitance 160 pF is charged to a potentialdifference of 200 V and then connected across a dischargetube, which conducts until the potential difference across ithas fallen to 100 V. The energy dissipated in the tube isA 6.4 J D 2 4Jn 4.8 Je 3.2 J E O.S J N78/Tl/21,

5 A parallel-plate capacitor is charged in air. It is thenelectrically isolated and lowered into a liquid dielectric. As aresult,ABeDE

both the capacitance and the potential difference acrossthe plates decrease.the capacitance decreaSes and the potential differenceacross the pI ates increases.the capacitance increases and the potential differenceacross the plates decreases.both the capacitance and the charges on the platesdecrease.both the capacitance and the charges on the platesincrease. JS2/Il/22; N78IW23

A E/2n E {le 12ifD 2EE E JSllrTllS

8 A 10 IlF capacitor and a 20 capacitor, both initiallyuncharged, are connected in series with a 3 kV supply(Fig. 2 .

kV

C ; H ~ Fig. 21 0 ~ l F 2 ~ FThe charge on the 10 capacitor finally becomesA 4 S mel Om ee ISme

D 20 mCE 30 me JSI/II1249 A 3 W capacitor and a 6 IlF capacitor, both initially

uncharged, are connected in series with a 10 V battery. Whatcharges reside on the capacitors?3 Wcapacitor 6 capacitor

A 30 ~ l e 60 ~ l Cn IS 30 IlCe 20 20 ~ l eD 30 ~ l e IS pCE 60 30 NSI/Il/22

1 Two capacitors, of capacitance C and 2C are charged topotential differences V and 2 V respectively. If the tWOpositive plates are connected together and the two negativeplates are connected together, then this system of capacitors

20 Capacitance 226 A Physics Topical Paper

J1

Fb8c

eb

tO

l ~


2/8

y

:0

:f

ABCDE

gains charge but loses energy.gains energy but loses charge.loses both energy and charge.loses charge but energy remains constant.loses energy but charge remains constant. N83/1I122

11 A 20 llF capacitor is charged by a constant current of lamA.If the capacitor is initially uncharged, how long does ittake for the potential difference across the capacitor to reach300 V?A 6.0 X 10-4 S D 1.5xl04sB 0.60 s E 6.0 X 105 SC 15 s N8611/17

12An isolated parallel-plate capacitor of plate area A plateseparation d and capacitance C =EA/d) is found to losecharge slowly by conduction through the dielectric, whichhas resistivity p What is the resistance of the dielectric?A

pED

pC E

B pCE E pCEC CE 187/1/1 5

13 The circuit shown was used to discharge the 10 pF capacitorthrough the variable resistor R.

1 J lF.~ ~ I ~ ~ ~ ~ r ~

1 - - - - 4 lA } _ J

For a period of 40 s the current was kept constant at 20 ~ U \by cOlltinuous adjustment of R.By how much did the potential difference across thecapacitor fall during this time?A 1.3 x 10 2 VC 20Vn 14VD 80V N87/1/1 8; N971J117

4 A photographic flash unit consists of a xenon-filled tubeenergised by the discharge of a capacitor previously chargedby a 1000 V source. The average power delivered to thelash tube is '1000 Wand the flash lasts 0.040 s. Thecapacitance of the capacitor can be estimated asAncDE

40x10-6F80 x 10-6 F160 X 10-6 F80 X 10-3 F160 X 10-3 F J8811/1 6

5 A 2pF capacitor charged initially by a 30V source isdisconnected from the source and then connected to anuncharged I pF capacitor.What is the final potential difference across the capacitors?A 10V B ISV C 20V D 2SV E 30V

N911I1186 Four identical capacitors are connected as shown in the

diagrams.p

Q0 1 H J II t o

sR

Which of the following lists the arrangements in order ofincreasing capacitance?A PQRS B PRSQ C PSRQ D QRSP E QSRP

N92/11167 The energy stored in a capacitoro capacitance C carryingcharge Qwith potential difference V between its plates, maybe obtained by calculating the area under an appropriategraph.

Which graph shows the correct relationship between a pairof the quantities C Q and V and in addition shows a shadedarea which corresponds to the energy stored in the capacitor?

v cA i~

8

Q Q

C c ~ D Qt..~1 VV N92/1117; J96/1117

8 A thundercloud and the Earth's surface may be regarded as apair of charged pat'allel plates separated by a distance h asshown ih the diagram. The capacitance oUhe system is C.

I:hII

; ; ; ; ; ; ; 7 ; 7 7Earth20 Capacitance 227 A Physics Topical Paper


3/8

When a lightning l1ash of mean current I and time duration foccurs, the electric field strength between cloud and Earthis reduced byA If

h n ItC C If D It E ClfhJ93/I117

19 Three capacitors are arranged as shown.3 ~ F 6 ~ F

X----4---111--1 --+-1---t-t-II-------tl t-I t yWhat is the effective capacitance between X and Y?A I pF C ~ l F D II

N93/I115; N9811/l 820 Two capacitors are connected in series as shown in thediagram. c,

12 vO>------ifIlI---iIlI----.l1.0 .IF 2.0 ~ l F

What is the charge carried by each of these capacitors?charge on C1/ lC charge on C/ lC

A 4.0 4.0n 4.0 8.0C 8.0 4.0D 8.0 8.0 J94JTJI6

21 A capacitor which has a capacitance of I farad willA be fully charged in I second by a current of I ampere.n store I coulomb of charge at a potential difference of

I volt.C gain I joule of cnergy when I coulomb of charge is

stored on it.D discharge in I second when connected across a resistorof resistance I ohm. N9411118

22 Four identical capacitors are connected as shown.p

Qcr-IHHHI-o

Which of the following lists the arrangements in order ofdecreasing capacitance?A PQRS n PSRQ C QRSP D QSRP

N95/I118; J99 IJIB

23 In the circuit shown, a capacitor of capacitance 3 Iis charged from a battery of e.m.f. 6V wi th the switchconnected to terminal P. P Q

6V

1PF

T ~ ~ ~6pF

The switch is now connected to Q. This charges the 6 IFcapacitor from the 3 one.What is the new potential difference across the combination?A IV n 2V C 4V D 6V

N96/I/1724 A capacitor is charged to a voltage V and then dischargedthrough a small d.c. motor. As the capacitor discharges, themotor raises a mass through a height.h. The experiment is

repeated for several values of VA constant fraction of the capacitor energy is converted togain of gravitational potential energy.Which graph would be expected to give a straight line?A II against V 2 C II against IVn II against V D Ii against II[V J97/1118

25 An uncharged capacitor is connected between earth Z and aterminal W. A positively charged rod is brought close to W.w

f==:=J+ +

I ~_ Z

Which of the following describes the movement of charge?A Electrons move from W to X and from Y to Z.n Electrons move from W to X but not from Y to Z.C Electrons move from X to Wand from Z to Y.D Electrons move from X to W but not from Z to Y.J98/1/13


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26 The diagrams show two ways of connecting two identicalcapacitors of capacitance C in circuits each with a supply ofp.d. V.

circuit 1 circuit 2

~ J [,. e etWhat is the value oftotal electrical energy stored in the capacitors in circuit I ?total electrical energy stored in the capacitors in circuit 2 .An

412

CD

214 198/J1l7

27 A capacitor of capacitance C is charged to a potentialdifference of 100 V and then disconnected. When a seconduncharged capacitor of capacitance C2 is connected inparallel across it, the new p.d. is 60 V.What is the value of the ratio ?An

3523

CD

3253 N99/I117

28 Four students are asked to draw graphs to show how thep.d.V across a capacitor depends on its charge Q. They are alsoasked to shade the area that represents the increase in energystored in the capacitor when the charge is increased from QIto Q2Which graph is correct?

A Bv

c Dv

Q1 Q2 Q 12000/111829 When the potential difference V between the plates of a

capacitor is increased ti om VI to V2 the charge Q on theplates increases from QI to Q2

On the graphs, which shaded area represents the increase inthe energy stored in the capacitor?

A nV VV VVI VI00 QI Q2 Q Q

C DV VV V ~ ~ ~I VI

0 ~QI Q Q 0 QI Q QN2000/J/I730 An uncharged 0.1 IF' c a p ~ c i t o r is charged to a p.d. of 500 Vby a battery. Calculate

a) the energy stored in the capacitor,b) the charge circulated by the battery,c) the energy provided by the battery,d) the total heat dissipated in the resistance of the

connecting wires and of the battery. N76/I1731 The capacitance of a certain variable capacitor may be varied

between limits of I x 10- 10 F and x 10-10 F by turning aknob attached to the movable plates. The capacitor is set to5 x la-H) F, and is charged by connecting it to a battery ofe.m.f. 200 V.

32

a) What is the charge on the plates?The battery is then disconnected and the capacitancechanged to 1 x 10-10 F.b) Assuming that no charge is lost from the plates, what is

now the potential difference between them?c) How much mechanical work is done against electricalforces in changing the capacitance? 179/1/9

Fig. 3

In Fig. 3, C1 is a fixed capacitor of capacitance Co and C2 isa variable capacitor. The e.m.f. of the battery is Yoa) Initially, the switch is closed and C2 is adjusted so thatits capacitance is also Co . Find, in terms of Co and Vo,the total energy stored in the two capacitors.



5/8

---b) The switch is then opened and C2 is adjusted so that itscapacitance becomes Co14

(i) What is the resulting potential difference acrossthe capacitors?(ii) How much work is done against electrical forcesin reducing the capacitance of C2? J83/1/9

33 A rolled paper capacitor is made from strips of metalfoil of dimensions 2 cm x 40 cm separated by paper ofrelative permittivity 2 and thickness 0.002 cm. Estimate itscapacitance. N86/III/5

34 Given a number of capacitors each with a capacitance of2 and a maximum safe working potential difference oflOY. how would you construct capacitors ofa) I capacitance, suitable for use up to 20 V,b) 2 1F capacitance, suitabre for use up to 20 V?

J87/1I113

a) Calculate the magnitude of the charge transferred whenthe sphere touches the plate. [2]

b) The sphere in a) is now releascd and it is seen tooscillate between the two plates, touching each plate. inturn. The frequency of oscillation is 3.5 Hz.(i) Briefly explain why a current is detected in the

circuit. [4](ii) Calculate the magnitUde of this cUlTent. [3]

N92/II/4

37 A capacitor of capacitance C = 220 is charged by abattery which has an e.m.f. of 6.0Y.a) Calculate the charge on the capacitor when there is apotential difference of 6.0Y across it. [2]b) How much energy docs the capacitor store when the

potential difference across it is 6.0 Y? [2]N95/H/3 (part)

38 a) A capacitor is marked as having a capacitance of5 a) Define capacitance. [I] 100 -IF. It is also marked 20 Y.

b) A capacitor of capacitance 10 ).IF is fully charged froma 20 V d.c. supply.(i) Calculate the charge stored by the capacitor. [2](ii) Calculate the energy delivered by the 20V

supply. [1](iii) Calculate the energy stored by the capacitor. [2](iv) Account for the difference between the answers

for (ii) and (iii). [I]J92/I1/4 (part) b)

(i) Explain what is meant by a capacitance of100 ~ I F .

(ii) How much charge is stored by the capacitor whena p.d. of20 Y is applied across it?

(iii) Write down the Imlximum c l ~ \ r g e which maysafely be stored by the capacitor.

(iv) Calculate the energy stored by the capacitor whencharged as in (ii). [5]Suggest why the maximum voltagemarked on a capacitor.

to be lIsed is[I]

J96/II/3 (part)36 An initially uncharged conducting sphere of capacitance4.5 x 1O-12F is suspended by an insulating thread betweentwo metal plates as shown in Fig. 4. 39 a) An isolated capacitor of capacitance 200 ).IF has apotential difference across it of 30 Y. Calculate1

22 V+

Fig. 4. The plates are connected in series with a d.c. supply of e.mJ.220 Y and a microammeter. The sphere is moved to one sideso that it touches the positive plate.

20 Capacitance 230

(i) the charge stored on one plate of the capacitor,charge = ....................... C

(ii) the energy stored by the capacitorenergy = ....................... J [4]

b) An uncharged capacitor of capacitance 100 1F is thenconnected across the charged 200 ).IF capacitor in a).For this combination, state which electrical quantity(i) will have the same total value before and after

connection,(ij) will be the same for each of the capacitors afterconnection. [2]

c) Calculate the total energy stored by the two capacitorsin b) after they have been connected.

energy = ................. J [5]J99 I1/4A Physics Topical Paper

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I Long QuestionsI 40 Denne capacitance. Name the Sf units for all the quantitiesI involved. [4]How would you attempt to show that the capacitance of alarge conducting sphere is constant, whatever the p.d.applied? [6]

Fig.S

A large conducting sphere S is connected in the circuitshown in Fig. 5. CD is opened and AB is closed, then AB isopened and CD closed. Discuss what happens.N77/[If/4 (part)

41 Compare the energy stored in a fully charged 2.0 volt30 ampere hour accumulator with that stored in a Vandc Graafl machine of capacitance IQ-IO F charged to apotential of 2 x 106 V. Which would you consider the moredangerous? Give your reasons. N78/HI/6 (part)

42 What do you understand by the capacitance of a cOllductor?Explain, with reference to your definition, why a nearbyearthed metal plate increases the capacitarice of such a ..conductor.Describe an experiment which shows that the capacitance of, : a conductor may also be increased by increasing its exposedsurface area.Two capacitors of capacitances C I and C2 are charged topotentials VI and V2 respectively. They are then connected soas to provide a larger capacitance C. Derive an expressionfor the potential V of this larger capacitor in terms of CI C2VI and V2. Explain clearly the steps in your argument.Calculate the energy loss when the capacitors are soconnected if CI =C2 =2 ~ l F and VI =200 V and V2 =0 V.Comment on this loss in relation to the principle ofconservation of energy. N80/1H/4

43 Define capacitance and name its unit. Write down anexpression for the potential at the surface of a conductingsphere carrying charge Q. Hence show that the capacitanceof an isolated conducting sphere is proportional to its radius.

J821f11/S (part)44 The cap of a negatively charged electroscope is irradiated

with a-particles in a vacuum. The potential differencebetween the electroscope and earth is initially 2.5 kV and the. capacitance of the electroscope is 1.2 x 10- 2 F. Calculatei) the initial charge on the electroscope,

*(ii) the time for the leaves to collapse completely if the rateof arrival of the a-particles is 1.1 x 107 S I.In air, much shorter times of leaf collapse are observed.Explain this. N82/rrrlS (part)

45 What do you understand by capacitance and afarad?Describe in terms of electron tlow what happens when anisolated positively charged conducting sphere is connected toeartha) by a large resistance,b) by a parallel-plate capacitor of capacitance equal to that

of the sphere.Calculate the time for the charge on the sphere in a) to fallto half its initial value if its capacitance is I x JO-II F andthe resistance is 1 x 109 n

183/1f1/S (part)46 What do you understand by the capacitance of an isolatedconductor? Explain why the concept would be inappropriatefor an insulator.

Explain why the capacitance of a metal plate is increased ifanother earthed metal plate is brought near.

xFig. 6

A parallel plate capacitor is shown in Fig 6. Copy thediagram and show the distribution of charges and the electrict1eld pattern established when a negative charge is given toplate X. Indicate the direction of conventional current flowin the wire connecting plate Y to earth while X is beingcharged. Show also the direction of the electrostatic force onXX is disconnected from the charging system. Explain whythe force Oil X is independent of its diStance from Yneglecting edge effects. Write down expressions fora) the capacitance of a parallel plate capacitor of plate

area A.and separation db) the energy of a parallel plate capacitor in terms of platearea A, separation d and charge q

By considering energy changes when the plate X is moved,with q remaining constant, deduce an expression for theforce on the plates. Calculate this force for plates of area100 cm 2 carrying charge of I ~ l C in vacuum.

47 Explain what is meant by the capacitance oa) an isolated conductor,b) a parallel-plate capacitor.

N83/II1/3

Derive an expression for the capacitance of two capacitors ofcapacitance CI and C2 connected in series.



7/8

Explain, in terms of electron fiow, how a capacitor canc) offer inlinite resistance to direct current, butd) allow alternating current to pass when an alternating

e.m.f. is applied. 184 1Il 4 (part)48 Derive a formula for the capacitance of a parallel plate

capacitor. Explain why the presence of a dielectric betweenthe plates of a pmallel plate capacitor increases thecapacitance.What is meant by relative permittivity? Describe a methodby which it may be measured.A parallel plate capacitor has a capacitance of 120 pF whenthe space between the plates is completely filled with aninsulator of relative permittivity 6.0. The capacitor ischarged to a potential difference of 100 V. What isa) the charge on the plates of the capacitor,b) the energy stored in the capacitor?

a i r ~ ~ Fig. 7The capacitor is now isolated and the insulator is withclrawn so that only half of the space between the platesis filled (see Fig. 7). If the air-tIlled and insulator-filledsections may be considered as two separate capacitors,calculate

c) the new value of the total capacitance,d) the energy now stored.

Comment on the difference between your answers in b) ancld). N8S/I111 12

9 a) What clo you understand by (i) the capacitance C of acapacitor,

b) Two capacitors of capacitances C I and C2 are chargedto potentials V and V2 respectively. The capacitorsare then connected by connecting the positi velycharged plates and by connecting the negativelycharged plates. Derive an expression for the finalpotential difference V across this combination. Explainyour working carefully. [S]

188/111/12 (part)50 a) An isolated, positively charged conducting sphere issituated above a large fiat metal plate which is earthecl

(see Fig. 8). -0Fig. 8

.

i) Copy the diagram of Fig. 8 and show the patternof electric field lines in the region surrounding thesphere. [3]

(ii) Describe, in terms of electron tlow, what happenswhen the sphere is connected to the pI ate bymeans of a parallel plate capacitor of capacitanceapproximately equal to that of the sphere. [4)

51 a)N88/l11/ I I (part) \ _

An uncharged capacitor is connected in series with a .battery of e.mJ. E and a switch. When the SWitch isclosed, a charge Q flows through the battery. Writeclown expressions in terms of E and Q fori) the energy supplied by the battery,ii) the energy stored in the capacitor.

Comment on your answers with reference to the law ofconservation of energy. [S]189 IHII I (part)

52 a) Draw a simple circuit diagram in which a capacitor isused. Explain the function of the capacitor in the circuityou have drawn. [4]

b) A capacitor of capacitance 64 JlF, which is initiallyuncharged, is connected to a supply which gives aconstant current of 0.16 mA. Calculate(i) the time taken for the potential difference across

the capacitor to become 30 V,Cii) the energy stored by the capacitor when the

potential difference aCross it is 30 V. [S]c) Two capacitors of capacitances 22 JlF and 47 JlF are

connected in series with a constant 24 V supply. Thecapacitors are initially ullcharged. Calculate(i) the total circuit capacitance,(ii) the charge delivered by the supply,(iii) the charge on each capacitor,(iv) the potential difference across the capacitor of

capacitance 47 flF [7]d) (ii) Explain why it is that some items of electronic

equipment have the warning message DANGER:EVEN WHEN SWITCHED OFF, IT MAYBEDANGEROUS TO REMOVE THE BACK OFTHIS EQUIPMENT . [4]N96 rrr 4 (part)

53 a) i) Sketch a graph to show the variation withpotential of the charge on an isolated conductor .

(ii) By reference to your graph in i),l. define what is meant by capacitance,2. derive an expression for the energy E stored

in a capacitor of capacitance C charged to apotential V [6]

1l -I

20 Capacitance 232 A Physics Topical Paper 20


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IIb) Four capacitors, each of capacitance 50 ~ l F are

connected as shown in Fig. 9 to a high-voltagesupply, a resistor and a switch S.

high-voltage

' P.' ---

38061042 topic 20 capacitance

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