capacitance jee assignment

1. QUESTION BANK ON
CAPACITANCE
PHYSICS

2. QUESTION FOR SHORT ANSWER
Q.1 Theelectricstrengthof airisabout 30, 000 V/cm.Bythis we meanthat when the electricfield intensity
exceeds this value, a spark will jump through the air.We saythat “electric breakdown” has occurred.
Usingthis value, estimate the potential difference between two objects where a spark jumps.Atypical
situation might be the spark that jumps between your body and a metal door handle after you have
walked on a deep carpet or slid across a plastic car seat in very dryweather.
Q.2 Ifyougraspthetwowiresleadingfrom thetwoplates of achargedcapacitor, you mayfeelashock.The
effect is much greater for a 2–F capacitor than for a 0.02F capacitor, even though both are are
charged to thesame potential difference. Why?
Q.3 Threeinfinitenonconductingsheets,withuniformsurfacechargedensities
,2and3arearrangedtobeparallellikethetwosheetsinFig.What
is their order, from left toright, if the electricfield

E produced bythe
arrangementhasmagnitudeE=0inoneregionandE=2/0
inanother
region?
Q.4 As shown in the figure plots of charge versus potential difference for three parallel plate capacitors,
which havetheplateareas andseparations given inthetable. Which oftheplots goes with which ofthe
capacitors?
Capacitor Area Separation
1 A d
2 2A d
3 A 2d
Q.5 Initially, a single capacitance C1
is wiredto a battery.Then capacitance C2
is added in parallel.Are (a)
the potential difference across C1
and (b) the charge q1
on C1
now more than, less than, or the same as
previously? (c) Is the equivalent capacitance C12
of C1
and C2
more than, less than, or equal to C1
? (d)
Is the total charge stored on C1
and C2
together more than, less than, or equal to the charge stored
previouslyonC1
?
Q.6 Asshowninthefigurethreecircuits,each consistingof
a switch and two capacitors, initially charged as
indicated.Aftertheswitcheshavebeenclosed,inwhich
circuit(ifany)willthechargeontheleft–handcapacitor
(a) increase, (b) decrease and (c) remain the same?
Q.7 Cap-monster maze. In the Figure all the capacitors have a capacitance
of 6.0 F, and all the batteries have an emf of 10V. What is the charge
oncapacitorC? (Ifyou canfindtheproper loop throughthis maze, you
can answerthe question with a few seconds of mental calculation.)
Q.8 An oil filled capacitor has been designed to have a capacitance C and to operate safely at or below a
certain maximumpotential differenceVm
withoutarcingover.However, thedesignerdid not doagood
job and the capacitor occasionally arcs over.What can be done to redesign the capacitor, keeping C
andVm
unchangedandusingthesamedielectric?
Q.9 One of the plates of a capacitor connected to batteryis earthed. Will the potential diffrence between
the plates change if the earthing wire is removed?

3. ONLY ONE OPTION IS CORRECT.
Take approx. 2 minutes for answering each question.
Q.1 The distance between plates of aparallel plate capacitor is 5d. Let the
positively charged plate is at x=0 and negatively charged plate is at
x=5d. Two slabs one of conductor and other of a dielectric of equal
thickness d areinserted between the plates as shown in figure.
Potentialversusdistancegraphwill looklike:
(A) (B) (C) (D)
Q.2 Aparallelplatecapacitorhastwolayersofdielectricasshowninfigure.
Thiscapacitorisconnectedacrossabattery.Thegraphwhichshows
thevariationof electricfield(E)anddistance(x)fromleftplate.
(A) (B) (C) (D)
Q.3 Thedistance betweentheplates ofacharged parallel platecapacitor is 5 cm and electricfield inside the
plates is 200Vcm–1.An uncharged metal bar of width 2 cm is fullyimmersed into the capacitor. The
length of the metal bar is same as that of plate of capacitor. The voltage across capacitor after the
immersionofthebaris
(A) zero (B) 400 V (C) 600 V (D) 100 V
Q.4 Threelargeplates are arrangedasshown. Howmuch chargewill flow through
the keyk if it is closed?
(A)
6
Q5
(B)
3
Q4
(C)
2
Q3
(D) none
Q.5 FiveconductingparallelplateshavingareaAandseparationbetweenthemd,areplaced
as shownin the figure. Plate number 2 and 4 are connected wire and between pointA
and B,a cell of emfE is connected. Thecharge flown through thecell is
(A)
d
AE
4
3 0
(B)
d
AE
3
2 0
(C)
d
AE4 0
(D)
d2
AE0
Q.6 Ifchargeonleftplaneofthe5Fcapacitorinthecircuitsegmentshown
in the figure is –20C, thecharge on the right plate of 3Fcapacitor is
(A) +8.57 C (B) –8.57 C (C) +11.42 C (D) –11.42 C
Q.7 Five identical capacitorplates are arranged such that theymake capacitors each of
2 F. The plates are connected to a source of emf 10V. The charge on plate C is
(A) + 20 C (B) + 40 C (C) + 60 C (D) + 80 C

4. Q.8 A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected
from it.Acharge +Q is now given to its positive plate.The potential difference across the capacitor is
now
(A) V (B) V +
C
Q
(C) V +
C2
Q
(D) V –
C
Q
, if V < CV
Q.9 In the circuitshown infigure chargestored in thecapacitor
of capacity5 f is
(A) 60 C (B) 20 C
(C) 30 C (D) zero
Q.10 Aconductingbody1has someinitialchargeQ, anditscapacitanceisC. Therearetwo otherconducting
bodies, 2 and 3, having capacitances : C2 = 2C and C3  . Bodies 2 and 3 are initially uncharged.
"Body2 is touched with body1. Then, body 2 is removed from body1 and touched with body3, and
then removed." This process is repeated N times. Then, the charge on body1 at the end must be
(A) Q/3N (B) Q/3N–1 (C) Q/N3 (D) None
Q.11 CondenserAhas acapacityof 15 F when it is filledwith amediumofdielectricconstant15.Another
condenser B has a capacity1 F with air between the plates. Both are charged separatelybya battery
of 100V.After charging, both are connected in parallel without the batteryand the dielectric material
beingremoved.Thecommonpotential nowis
(A) 400V (B) 800V (C) 1200V (D) 1600V
Q.12 Intheadjoiningfigure,capacitor(1)and(2)haveacapacitance‘C’each.Whenthedielectricofdielectric
consatntKisinsertedbetweentheplatesofoneofthecapacitor,thetotalchargeflowingthroughbatteryis
(A)
1K
KCE

from B to C (B)
1K
KCE

from C to B
(C)
)1K(2
CE)1K(


from B to C (D)
)1K(2
CE)1K(


from C to B
Q.13 Twoidenticalcapacitors1and2areconnectedinseriestoabatteryasshownin
figure.Capacitor2containsadielectricslabofdielectricconstantkasshown.Q1
andQ2 arethechargesstoredinthecapacitors.Nowthedielectric
slabisremovedandthecorrespondingchargesareQ’1 andQ’2.Then
(A)
k
1k
Q
Q
1
1 


(B)
2
1k
Q
Q
2
2 


(C) k2
1k
Q
Q
2
2 


(D)
2
k
Q
Q
1
1


Q.14 The area ofthe plates of aparallel plate capacitor isAand the gap between them is d.The gap is filled
withanon-homogeneousdielectric whosedielectricconstantvaries withthedistance‘y’from oneplate
as : K = sec(y/2d), where  is a dimensionless constant. The capacitance of this capacitor is
(A) 0A / 2d (B) 0A /d (C) 20A /d (D) none
Q.15 Acapacitor stores 60C charge when connected across a battery.When the gap between the plates is
filled with a dielectric , a charge of 120C flows through the battery. The dielectric constant of the
materialinsertedis:
(A) 1 (B) 2 (C) 3 (D) none

5. Q.16 In the abovequestion, iftheinitial capacitanceof thecapacitor was 2F, theamount of heat produced
whenthedielectricis inserted.
(A) 3600J (B) 2700J (C) 1800J (D) none
Q.17 AcapacitorofcapacitanceC is initiallycharged toapotential differenceofVvolt. Nowit is connected
to a batteryof 2V with opposite polarity. The ratio of heat generated to the final energy stored in the
capacitorwill be
(A) 1.75 (B) 2.25 (C) 2.5 (D) 1/2
Q.18 Three plates A, B and C each of area 0.1 m2 are separated by 0.885
mm from each other as shownin the figure.A10 V batteryis used to
charge the system. The energystored inthe system is
(A) 1 J (B) 10–1 J (C) 10–2 J (D) 10–3 J
Q.19 A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential
differenceV.Anothercapacitor ofcapacitance2C is similarlychargedto apotential difference2V.The
charging batteryis now disconnected and the capacitors are connect in parallel to each other in such a
waythat thepositiveterminal ofone is connected tothe negativeterminal of theother.Thefinal energy
oftheconfigurationis
(A) zero (B)
2
3
CV2 (C)
6
25
CV2 (D)
2
9
CV2
Q.20 A 2 F capacitor is charged to a potential = 10V. Another 4 F capacitor is charged to a
potential = 20V.The two capacitors are then connected in a singleloop, with the positive plate of one
connected with negativeplate oftheother.What heat is evolved in thecircuit?
(A) 300 J (B) 600 J (C) 900 J (D) 450 J
Q.21 The plates S andTof an uncharged parallel plate capacitor are connected across a battery.The battery
is then disconnected and the charged plates are now connected in asystem as shown inthe figure. The
system shownis inequilibrium.All thestrings areinsulatingand massless.The magnitudeof chargeon
one of the capacitor plates is: [Area of plates =A]
(A) 0
mgA2  (B)
k
mgA4 0
(C) 0
mgA  (D)
k
mgA2 0
Q.22 In the circuit shown,the energystored in 1Fcapacitor is
(A) 40 J (B) 64 J
(C) 32 J (D) none
Q.23 Fourmetallicplatesarearrangedasshowninthefigure.Ifthedistancebetweeneachplatethencapacitance
of the givensystem between pointsAand B is (Given d <<A)
(A)
d
A0
(B)
d
A2 0
(C)
d
A3 0
(D)
d
A4 0

6. Q.24 What is the equivalent capacitance of the system of capacitors
between A& B
(A)
7
6
C (B) 1.6 C (C) C (D) None
Q.25 From a supplyofidentical capacitors rated 8 F, 250V,theminimum number ofcapacitors required to
form a composite 16 F, 1000 V is :
(A) 2 (B) 4 (C) 16 (D) 32
Q.26 Theminimumnumberofcapacitorseachof3Frequiredtomakeacircuitwithanequivalentcapacitance
2.25 F is
(A) 3 (B) 4 (C) 5 (D) 6
Q.27 The capacitance (C) for an isolated conductingsphere of radius (a) is given by 40a. If the sphere is
enclosed with anearthed concentric sphere. The ratioof the radii of thespheres being
)1n(
n

then the
capacitance of such a sphere will be increased bya factor
(A) n (B)
)1n(
n

(C)
n
)1n( 
(D) a . n
Q.28 Two capacitor having capacitances 8 F and 16 F have breaking voltages 20 V and 80 V. They are
combinedinseries.Themaximumchargetheycanstoreindividuallyinthecombinationis
(A) 160 C (B) 200 C (C) 1280 C (D) none of these
Q.29 A capacitor of capacitance 1 F withstands the maximum voltage 6 kV while a capacitor of 2 F
withstands themaximum voltage4 kV.What maximum voltagewill the system ofthesetwo capacitor
withstands iftheyare connected inseries?
(A) 10 kV (B)12 kV (C) 8 kV (D) 9 kV
Q.30 Four identical plates 1, 2, 3 and 4 are placed parallel to each other at equal distance as shown in the
figure. Plates 1 and 4 are joined together and the space between 2 and 3 is filled with a dielectric of
dielectric constant k = 2. The capacitance of the system between 1 and 3 & 2 and 4 are C1 and C2
respectively.The ratio
2
1
C
C
is :
(A)
3
5
(B) 1 (C)
5
3
(D)
7
5
Q.31 Inthecircuitshowninfigure,theratioofchargeson5F
and 4F capacitoris :
(A) 4/5 (B) 3/5
(C) 3/8 (D) 1/2
Q.32 In the circuit shown, a potential difference of 60V is applied acrossAB.
The potential differencebetween the point M and N is
(A) 10 V (B) 15 V
(C) 20 V (D) 30 V

7. Q.33 Find theequivalent capacitance acrossA& B
(A)
3
28
f (B)
2
15
F
(C) 15 F (D) none
Q.34 Acapacitorofcapacitance1Fwithstandsthemaximumvoltages6KVwhileacapacitorofcapacitance
2.0 F with stands the maximum voltage =4KV. if the twocapacitors are connected in series, then the
twocapacitors combinedcantake up amaximum voltage of
(A) 2.4 KV (B) 5 KV (C) 9 KV (D) 10 KV
Q.35 Thediagram showsfourcapacitors withcapacitances andbreakdown voltages
as mentioned. What should be the maximum value of the external emf source
such that no capacitor breaks down?[Hint: First of all find out the break down
voltages ofeach branch.After that compare them.]
(A) 2.5 kV (B) 10 / 3kV (C) 3 kV (D) 1 kV
Q.36 Three capacitors 2 F, 3 F and 5 F can withstand voltages to 3V, 2V and 1V respectively. Their
seriescombinationcanwithstandamaximumvoltageequalto
(A) 5 Volts (B) (31/6)Volts (C) (26/5) Volts (D) None
Q.37 Find equivalent capacitance acrossAB (all capacitances in F)
(A) F
3
20
 (B) 9F
(C) 48 F (D) None
Q.38 Three longconcentricconductingcylindrical shells haveradii R,2R and 22 R.Innerandouter shells
are connectedto each other.Thecapacitance across middle andinner shells per unit length is:
(A)
2n
3
1
0
l

(B)
2n
6 0
l

(C)
2n
0
2l

(D) None
Q.39 A charged capacitor is allowed to discharge through a resistance 2 byclosing
the switch S at the instant t = 0.At time t = ln 2 s, the reading of the ammeter
fallshalfofitsinitialvalue.Theresistanceoftheammeterequalto
(A) 0 (B) 2
(C)  (D) 2M
Q.40 AcapacitorC =100 Fisconnectedto three resistoreach ofresistance
1 k and a battery of emf 9V. The switch S has been closed for long
time so as to charge the capacitor. When switch S is opened, the
capacitordischargeswithtimeconstant
(A) 33 ms (B) 5 ms
(C) 3.3 ms (D) 50 ms
Q.41 A capacitor C = 100 F is connectedto three resistors each ofresistance 1 kW and
a batteryof emf 9V.The switch S has been closed for long time so as to charge the
capacitor.Whenswitch S is opened,the capacitor discharges withtime constant.
(A) 33 ms (B) 5 ms (C) 3.3 ms (D) 50 ms

8. Q.42 Inthetransient shown thetimeconstant of thecircuitis :
(A)
3
5
RC (B)
2
5
RC
(C) RC
4
7
(D) RC
3
7
Q.43 In the circuit shown in figure C1=2C2. Switch S is closed at time t=0.
Let i1 and i2 be the currents flowing through C1 and C2 at anytime t,
then the ratio i1/ i2
(A) is constant
(B)increases withincreaseintimet
(C) decreases with increase in time t
(D) first increases then decreases
Q.44 Find heat producedin the capacitors on closingthe switch S
(A) 0.0002 J (B) 0.0005 J
(C) 0.00075 (D) zero
Q.45 In the circuit shown, when the keyk is pressed at time t = 0, which of the following statements about
current Iin the resistorABis true
(A) I = 2mA at all t
(B) Ioscillates between 1 mAand 2mA
(C) I = 1 mA at all t
(D)At t = 0, I= 2mAand with time it goes to 1 mA
Q.46 In the R–C circuit shown in the figure the total energyof 3.6 ×10–3 J is dissipated in the 10  resistor
when theswitch S is closed. Theinitial charge onthe capacitor is
(A) 60 C (B) 120 C (C) 60 2 C (D)
2
60
C
Q.47 A chargedcapacitor is allowed to discharge through a resistor by closing the
keyat the instant t =0.At the instant t = (ln 4) s, the reading of the ammeter
fallshalftheinitial value. Theresistanceoftheammeterisequal to
(A) 1 M (B) 1 (C) 2 (D) 2M
Q.48 In thecircuit shown, the cell is ideal, with emf= 15V. Eachresistance is
of 3.Thepotential difference across thecapacitor is
(A) zero (B) 9 V
(C) 12 V (D) 15 V
Question No. 49 to 52 (4 questions)
In the circuit shown in figure, four capacitors are connected to a battery.
Q.49 Theequivalentcapacitanceofthecircuitis
(A) 25 F (B) 6 F (C) 8.4 F (D) none

9. Q.50 The charge on the 5 F capacitor is
(A) 60 C (B) 24 C (C) 12 C (D) 20 C
Q.51 The potential difference across the 6 Fcapacitor is
(A) 6V (B) 4V (C) 5V (D) none
Q.52 Themaximum energyis storedinthecapacitorof
(A) 10 F (B) 6 F (C) 5 F (D) 4 F
Q.53 Aparallelplatecapacitorhasanelectricfieldof105V/mbetweentheplates.Ifthechargeonthecapacitor
plate is 1C, then the force on each capacitor plate is
(A) 0.1Nt (B) 0.05Nt (C) 0.02Nt (D) 0.01Nt
Q.54 Acapacitor is connected to a battery. The force of attraction between the plates when the separation
betweenthemis halved
(A)remainsthesame (B)becomeseight times
(C) becomes four times (D) becomes two times
ONE OR MORE THAN ONE OPTION MAY BE CORRECT
Take approx. 3 minutes for answering each question.
Q.1 AparallelplatecapacitorAisfilledwithadielectricwhosedielectricconstantvarieswithappliedvoltage
as K=V.Anidentical capacitorBof capacitanceC0 withairas dielectricis connectedto voltagesource
V0 = 30V and then connected to the first capacitor after disconnecting the voltage source. The charge
and voltageon capacitor.
(A) Aare 25C0 and 25V (B) A are 25C0 and 5 V
(C) B are 5c0 and 5V (D) B are 5C0 and 25 V
Q.2 Two capacitors of 2 F and 3 F are charged to 150 volt and
120 volt respectively.The plates of capacitorare connected as
shown in thefigure.Adischarged capacitor ofcapacity1.5 F
falls to the free ends ofthe wire. Then
(A) charge on the 1.5 F capacitors is 180 C
(B) charge on the 2F capacitor is 120 C
(C)chargeflows throughAfromright to left.
(D)chargeflows throughAfromleft toright.
Q.3 Inthecircuitshown,eachcapacitorhasacapacitanceC.TheemfofthecellisE.IftheswitchS is closed
(A)positivechargewillflowoutofthepositiveterminalofthecell
(B)positivechargewillenterthepositiveterminalofthecell
(C)theamountofchargeflowingthrough thecell willbeCE.
(D) the amount of charge flowingthrough thecell willbe4/3 CE.
Q.4 In thecircuit shown initially C1, C2 are uncharged.After closing the
switch
(A) The charge on C2 is greater that on C1
(B) The charge on C1 and C2 are the same
(C) The potential drops across C1 and C2 are the same
(D) The potential drops across C2 is greater than that across C1

10. Q.5 Aparallelplateair-corecapacitorisconnected across asourceofconstant potential difference.When a
dielectric plateisintroduced between the twoplates then :
(A) somecharge from the capacitor will flow back into the source.
(B) someextra charge from thesource will flow back into the capacitor.
(C) the electric field intensitybetween the two plate does not change.
(D) the electricfieldintensitybetweenthe two plates will decrease.
Q.6 A parallel platecapacitor has a parallel sheet of copper inserted between and parallel to thetwo plates,
without touchingtheplates. Thecapacityofthecapacitor aftertheintroduction of the coppersheet is :
(A)minimum whenthe coppersheet touches one of the plates.
(B) maximum whenthe copper sheet touches oneof the plates.
(C)invariant forall positions of the sheet between theplates.
(D)greaterthan that beforeintroducingthe sheet.
Q.7 In the circuit shown in the figure, the switch S is initiallyopenand the
capacitor is initiallyuncharged. I1, I2 and I3 represent thecurrent in the
resistance 2, 4 and 8 respectively.
(A) Just after the switch S is closed, I1 = 3A, I2 = 3A and I3 = 0
(B) Just after the switch S is closed, I1 = 3A, I2 = 0 and I3 = 0
(C) long time after the switch S is closed, I1 = 0.6A, I2 = 0 and I3 = 0
(D) long after the switch S is closed, I1 = I2 = I3 = 0.6A.
Q.8 Thecircuitshowninthefigureconsists ofabatteryofemf=10V;acapacitor
of capacitance C = 1.0 F and three resistor of values R1 = 2, R2 = 2 and
R3 = 1. Initiallythe capacitor is completelyuncharged and the switch S is
open. The switch S is closed at t = 0.
(A) The current through resistor R3 at the moment the switch closed is zero.
(B) The current through resistor R3 a longtime after the switch closed is 5A.
(C) The ratio of current through R1 and R2 is always constant.
(D)The maximum charge on thecapacitor duringtheoperationis 5C.
Q.9 In the circuit shown in figure C1 = C2 = 2F.Then charge stored in
(A) capacitor C1 is zero (B) capacitor C2 is zero
(C) both capacitor is zero (D) capacitor C1 is 40 C
Q.10 A capacitor of capacity C is charged to a steady potential difference V and
connected in series with an open keyand a pure resistor 'R'.At time t = 0, the
keyis closed. If I= current at time t, aplot of log Iagainst 't' is as shown in (1)
in the graph. Later one of the parameters i.e.V, R or C is changed keeping the
other two constant, and the graph (2) is recorded. Then
(A) C is reduced (B) C is increased
(C) R is reduced (D) R is increased

11. Question No.11 to 12 (2 questions)
The charge across the capacitor intwodifferent RC circuits 1 and
2 are plottedas shown in figure.
Q.11 Choose the correct statement(s) related to the two circuits.
(A) Both the capacitors are charged to the same charge.
(B) The emf's of cells in both thecircuit are equal.
(C) Theemf's of the cells maybe different.
(D) The emf E1 is more than E2
Q.12 Identifythe correct statement(s) related to the R1, R2, C1 and C2 of the two RC circuits.
(A) R1 > R2 if E1 = E2 (B) C1 < C2 if E1 = E2
(C) R1C1 > R2C2 (D)
2
1
R
R
<
1
2
C
C
Q.13 Aparallel plate capacitor is charged byconnecting it to a battery. The battery is disconnected and the
plates of the capacitor are pulled apart to make the separation between the plates twice. Again the
capacitor is connected to the battery(withsame polarity) then
(A) Charge from the batteryflows into thecapacitorafter reconnection
(B) Charge from capacitor flows into thebatteryafter reconnection.
(C) The potential differencebetween the plates increases when the plates are pulled apart.
(D)Afterreconnectionofbatterypotentialdifferencebetweentheplatewillimmediatelybecomeshalfof
theinitialpotentialdifference. (Just afterdisconnectingthebattery)
Q.14 The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a
dielectric of dielectric constant K is inserted to fill the whole space between the plates with voltage
source remainingconnectedtothe capacitor.
(A) the energystored in the capacitorwill become Ktimes
(B)the electricfield insidethecapacitorwill decrease to Ktimes
(C) the force of attraction betweenthe plates will increaseto K2–times
(D) the chargeon the capacitor will increase to Ktimes
Q.15 Fourcapacitors andabatteryareconnected asshown.Thepotential
drop across the 7 F capacitor is 6 V. Then the :
(A) potential difference across the 3 F capacitor is 10 V
(B) charge on the 3 F capacitor is 42 C
(C) e.m.f. of the batteryis 30 V
(D) potential difference across the 12 F capacitor is 10V.
Q.16 A circuit shown in the figure consists of a battery of emf 10 V and two capacitance C1 and C2 of
capacitances 1.0 F and 2.0 F respectively.The potential differenceVA – VB is 5V
(A) charge on capacitor C1 is equal to charge on capacitor C2
(B) Voltage across capacitor C1 is 5V.
(C) Voltage across capacitor C2 is 10 V
(D) Energystored in capacitor C1 is two times the energystored in capacitor C2.
Q.17 A capacitor C is charged to a potential difference V and batteryis disconnected. Now if the capacitor
plates arebrought close slowlybysome distance :
(A) some +ve work is done byexternal agent (B) energyof capacitor will decrease
(C) energyof capacitor will increase (D) none of the above

12. Q.18 The capacitance ofaparallel plate capacitoris C when the region between the platehasair.This region
is nowfilledwith adielectricslabof dielectricconstantk. Thecapacitor isconnected to acellofemfE,
and the slab is taken out
(A) chargeCE(k – 1) flows through the cell (B) energyE2C(k – 1) is absorbed bythe cell.
(C) the energy stored in the capacitor is reduced by E2C(k – 1)
(D) the external agent has to do
1
2
E2C(k – 1) amount of work to take the slab out.
Q.19 Two capacitors of capacitances 1Fand 3F are charged to the same voltages 5V.Theyare connected
inparallel withoppositelychargedplatesconnectedtogether.Then:
(A)Final commonvoltagewill be5V. (B)Finalcommon voltage will be2.5 V
(C) Heat produced in the circuit will be zero. (D)Heat produced in the circuit will be 37.5 J
Q.20 The two plates X andYof a parallel plate capacitor of capacitance C are given a charge of amount Q
each. X is now joined to thepositive terminal andYto the negative terminal ofa cell of emfE = Q/C.
(A)Chargeofamount Qwillflowfromthenegativeterminaltothepositiveterminalofthecellinsideit.
(B) The total charge on the plate X will be 2Q.
(C)The total charge on the plateYwill be zero.
(D)The cellwill supplyCE2 amountofenergy.
Q.21 Adielectricslabis inserted betweenthe plates ofanisolated charged capacitor.Whichof the following
quantitieswillremainthesame?
(A) the electricfield inthe capacitor (B) the charge on the capacitor
(C)the potential differencebetween theplates (D) the stored energy in the capacitor.
Q.22 The separationbetween the plates ofa isolated charged parallel plate capacitor is increased. Which of
thefollowingquantitieswillchange?
(A) charge on the capacitor (B) potential differenceacross the capacitor
(C) energyof the capacitor (D) energydensitybetween the plates.
Q.23 Eachplateofaparallelplatecapacitorhasachargeqonit.Thecapacitorisnowconnectedtoabattery.Now,
(A) the facing surfaces of the capacitor have equal and opposite charges.
(B) the two plates of the capacitor have equal and opposite charges.
(C) the batterysupplies equal and opposite charges to the two plates.
(D) the outer surfaces of the plates have equal charges.
Q.24 Followingoperations can be performed on a capacitor :
X – connect the capacitor to a batteryof emf E. Y – disconnect the battery
Z –reconnect the batterywith polarityreversed. W – insert a dielectric slab in the capacitor
(A) In XYZ (perform X, thenY, then Z) the stored electric energyremains unchanged and no thermal
energyis developed.
(B)The charge appearingon thecapacitor is greater aftertheaction XWYthan afterthe action XYW.
(C)TheelectricenergystoredinthecapacitorisgreateraftertheactionWXYthanaftertheactionXYW.
(D) The electricfield in the capacitor after the action XW is the same as that after WX.
Q.25 Aparallelplatecapacitoris chargedandthendisconnectedfromthesourceofpotentialdifference.Ifthe
plates of the condenser are then moved farther apart bythe use of insulated handle, which one of the
followingistrue?
(A) the charge on the capacitor increases (B) the charge on the capacitor decreases
(C) the capacitance of the capacitor increases (D) thepotential difference across theplate increases

13. Q.26 Aparallel plate capacitor is charged and then disconnected from the source steady E.M.F.The plates
are then drawn apart farther.Again it is connected to the same source.Then :
(A) the potential difference across the plate increases, while the plates arebeing drawn apart.
(B) the charge from the capacitor flows into the source, when thecapacitor is reconnected.
(C) more chargeis drawn to the capacitor from the source, during the reconnection.
(D) the electricintensitybetween theplatesremains constant duringthedrawingapart of plates.
Q.27 When a parallel plates capacitor is connectedto a source ofconstant potential difference,
(A) all the charge drawn from the source is stored in the capacitor.
(B) all the energydrawn from the source is stored in the capacitor.
(C) the potential difference across the capacitor grows veryrapidlyinitiallyand this rate decreases to
zeroeventually.
(D) the capacityof the capacitorincreases with the increase of the charge in the capacitor.
Q.28 Whentwoidenticalcapacitors arecharged individuallytodifferent potentials andconnectedparallel to
each other,after disconnectingthem fromthesource:
(A)net chargeonconnectedplates isless than the sum ofinitial individual charges.
(B)net chargeonconnected platesequals thesum ofinitial charges.
(C)thenetpotentialdifferenceacrossthemisdifferentfromthesumoftheindividualinitialpotentialdifferences.
(D)the netenergystoredinthetwo capacitors is less than thesum of theinitial individual energies.
Q.29 Aparallel platecapacitor of plate areaAand plate seperation d is charged to potential differenceVand
thenthe batteryis disconnected.AslabofdielectricconstantKis theninserted between theplates ofthe
capacitor soas to fill thespace between the plates. IfQ, E andWdenote respectively, the magnitude of
charge on eachplate, the electric field between the plates (after theslab is inserted) and the work done
on thesystem,in question, inthe process of insertingthe slab,then
(A) Q =
d
AV0
(B) Q =
d
KAV0
(C) E = dK
V
(D) W = – 







K
1
1
d2
AV2
0
Q.30 Aparallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and
energy associated with the capacitor are given by Q0, V0, E0 and U0 respectively.Adielectric slab is
introduced between plates of capacitor but batteryis still in connection. The corresponding quantities
now givenbyQ,V, E and U related to previous ones are
(A) Q > Q0 (B) V > V0 (C) E > E0 (D) U < U0
Q.31 Aparallel-platecapacitoris connected toacell.Its positiveplateAand its negativeplateBhavecharges
+Q and –Q respectively. A third plate C, identical to A and B, with charge +Q, is now introduced
midwaybetweenAand B, parallel tothem.Which of thefollowing are correct?
(A) The charge on the inner face of B is now
2
Q3

(B)Thereis no change inthe potential difference betweenAand B.
(C)The potential difference betweenAandC is one-third ofthepotentialdifference betweenB and C.
(D) The charge on the inner face ofAis now 2Q .
Q.32 Two capacitors C1 = 4 F and C2 = 2F are charged to same potential
V = 500 Volt,butwith oppositepolarityasshown inthefigure.TheswitchesS1
and S2 are closed.
(A) The potential difference across the two capacitors are same and is given by V3500
(B) The potential difference across the two capacitors are same and is given by V31000
(C) The ratioof final energytoinitial energyofthesystem is 1/9.
(D) The ratiooffinal energytoinitial energyofthesystem is 4/9.

14. Q.33 Aparallelplatecapacitoris chargedtoacertainpotentialandthe chargingbatteryis then disconnected.
Now, if the plates of the capacitor are moved apart then:
(A) The stored energyof the capacitor increases
(B) Charge onthe capacitor increases
(C) Voltage of the capacitor decreases
(D) The capacitance increases
Q.34 If a batteryof voltage V is connected across terminals I of the block box
showninfigure,an ideal voltmeterconnectedtoterminalsIIgivesareading
of V/2, whileifthe batteryis connectedto terminals II, avoltmeter across
terminals
I reads V.The black box maycontain
(A) (B)
(C) (D)
Q.35 Two capacitors of equal capacitance (C1 = C2) are shown in the figure.
Initially,whiletheswitchS is open,oneofthecapacitorsis uncharged and
the othercarries charge Q0. The energystored in thecharged capacitor is
U0. Sometimes after the switch is closed, the capacitors C1 and C2 carry
charges Q1 and Q2, respectively; the voltages across thecapacitors are V1
and V2; and the energies storedin the capacitors are U1 and U2. Which of
the followingstatements is INCORRECT?
(A) Q0 =
2
1
(Q1 + Q2) (B) Q1 = Q2
(C) V1 = V2 (D) U1 = U2
(E) U0 = U1 + U2
Question No.36 to 39 (4 questions)
The figureshowsa diagonal symmetricarrangement ofcapacitors and a
battery
Q.36 Identifythecorrect statements.
(A) Both the 4F capacitors carryequal charges in opposite sense.
(B) Both the 4F capacitors carryequal charges in same sense.
(C) VB – VD > 0
(D) VD – VB > 0
Q.37 If thepotential of C is zero, then
(A) VA = + 20V (B) 4(VA – VB) + 2(VD – VB) = 2VB
(C) 2(VA – VD) + 2(VB – VD) = 4VD (D) VA = VB + VD
Q.38 The potential of the point B and D are
(A) VB = 8V (B) VB = 12V (C) VD = 8V (D) VD = 12V

15. Q.39 The value of charge q1, q2 and q3 as shownin the figure are
(A) q1 = 32 C ; q2 = 24 C ; q3 = – 8 C
(B) q1 = 48 C ; q2 = 16 C ; q3 = + 8 C
(C) q1 = 32 C ; q2 = 24 C ; q3 = + 8 C
(D) q1 = 3 C ; q2 = 4 C ; q3 = + 2 C
Q.40 IfQisthechargeontheplatesofacapacitorofcapacitanceC,Vthepotentialdifferencebetweentheplates,
Atheareaofeachplateanddthedistancebetweentheplates,theforceofattractionbetweentheplatesis
(A) 







 A
Q
2
1
0
2
(B) 







d
CV
2
1 2
(C) 







0
2
A
CV
2
1
(D) 







 2
0
2
d
Q
4
1

16. ONLYONEOPTIONISCORRECT
Q.1BQ.2AQ.3CQ.4AQ.5BQ.6A
Q.7BQ.8CQ.9DQ.10AQ.11BQ.12D
Q.13CQ.14AQ.15CQ.16CQ.17BQ.18B
Q.19BQ.20BQ.21AQ.22CQ.23BQ.24B
Q.25DQ.26BQ.27AQ.28AQ.29DQ.30B
Q.31CQ.32DQ.33BQ.34CQ.35AQ.36B
Q.37BQ.38BQ.39AQ.40DQ.41DQ.42C
Q.43BQ.44DQ.45DQ.46BQ.47CQ.48C
Q.49BQ.50DQ.51BQ.52BQ.53BQ.54C
ONEORMORETHANONEOPTIONMAYBECORRECT
Q.1B,CQ.2A,B,CQ.3A,DQ.4B
Q.5B,CQ.6C,DQ.7BQ.8A,B,C,D
Q.9B,DQ.10BQ.11A,CQ.12D
Q.13B,CQ.14A,C,DQ.15B,C,DQ.16A,D
Q.17BQ.18A,B,DQ.19B,DQ.20A,B,C,D
Q.21BQ.22B,CQ.23A,C,DQ.24B,C,D
Q.25DQ.26A,B,DQ.27A,CQ.28B,C,D
Q.29A,C,DQ.30AQ.31A,B,C,DQ.32A,C
Q.33AQ.34DQ.35EQ.36B,C
Q.37A,B,C,DQ.38B,CQ.39CQ.40A,B
ANSWER KEY