cs - arride learning · 2017-07-05 · a capacitor of capacitance c is charged to a potential...

Topic Page No.

Theory 01 - 02

Exercise - 1 03 - 21




Answer Key 42 - 44

Contents

Syllabus

CAPACITANCE

Capacitance ; Parallel plate capacitor with and without dielectrics ;

Capacitors in series and parallel ; Energy stored in a capacitor.

Name : ____________________________ Contact No. __________________

ARRIDE LEARNING ONLINE E-LEARNING ACADEMYA-479 indra Vihar, Kota Rajasthan 324005

Contact No. 8033545007

Page No. # 1Arride learning Online E-learning AcademyA-479 Indra Vihar, Kota Rajasthan 324005

1. CAPACITANCE OF AN ISOLATED SPHERICAL CONDUCTOR :C = 4p Î0Îr R in a medium C = 4p Î0 R in air

* This sphere is at infinite distance from all the conductors .* The capacitance C = 4p Î0 R exists between the surface of the sphere & earth .

2. SPHERICAL CAPACITOR :It consists of two concentric spherical shells as shown in figure. Here capacitance of regionbetween thetwo shells is C1 and that outside the shell is C2. We have

C1 = 4 0p Î

-ab

b a and C2 = 4p Î0 b

Depending on connection, it may have different combinations of C1 and C2.

3. PARALLEL PLATE CAPACITOR :(i) UNIFORM DI-ELECTRIC MEDIUM :

If two parallel plates each of area A & separated by a distance d are charged withequal & opposite charge Q, then the system is called a parallel plate capacitor & its capacitance isgiven by,

C = Î Î0 r A

d in a medium ; C =

Î0 Ad

with air as medium

This result is only valid when the electric field between plates of capacitor is constant.

(ii) MEDIUM PARTLY AIR : C = Î

- -æèç

öø÷Î

0 A

d t tr

When a di-electric slab of thickness t & relative permittivity Îr isintroduced between the plates of an air capacitor, then the distance between

the plates is effectively reduced by t t

r-

Îæèç

öø÷ irrespective of the position of

the di-electric slab .

(iii) COMPOSITE MEDIUM : C =

3r3

2r2

1r1 ttt

A0

ÎÎÎ ++

Î

4. CYLINDRICAL CAPACITOR :It consist of two co-axial cylinders of radii a & b, the outer conductor is earthed . Thedi-electric constant of the medium filled in the space between the cylinder is

Îr . The capacitance per unit length is C = ( )abn

2 r0l

ÎÎp Farad

m.

5. CONCEPT OF VARIATION OF PARAMETERS:

As capacitance of a parallel plate capacitor isC = Î0 kA

d, if either of k, A or d varies in the region between the

plates, we choose a small dc in between the plates and for total capacitance of system.

If all dC's are in series òÎ=

)x(A)x(kdx

C1

0T, If all dC's are in parallel CT = dCò

CAPACITANCE


6. COMBINATION OF CAPACITORS :(i) CAPACITORS IN SERIES :In this arrangement all the capacitors when uncharged get the same charge Qbut the potential difference across each will differ (if the capacitance areunequal).

.eqC1

= 1C

1 +

2C1

+ 3C

1 + ........ +

nC1

.

(ii) CAPACITORS IN PARALLEL :When one plate of each capacitor is connected to the positiveterminal of the battery & the other plate of each capacitor isconnected to the negative terminals of the battery, then thecapacitors are said to be in parallel connection.The capacitors have the same potential difference, V but thecharge on each one is different (if the capacitors are unequal). Ceq. = C1 + C2 + C3 + ...... + Cn .

7. ENERGY STORED IN A CHARGED CAPACITOR :Capacitance C, charge Q & potential difference V ; then energy stored is

U = 12

CV2 = 12

QV = 12

QC

2

. This energy is stored in the electrostatic field set up in the di-electric

medium between the conducting plates of the capacitor .

8. HEAT PRODUCED IN SWITCHING IN CAPACITIVE CIRCUIT

Due to charge flow always some amount of heat is produced when a switch is closed in a circuit which canbe obtained by energy conservation as –Heat = Work done by battery – Energy absorbed by capacitor.

9. SHARING OF CHARGES :When two charged conductors of capacitance C1 & C2 at potential V1 & V2 respectively are connectedby a conducting wire, the charge flows from higher potential conductor to lower potential conductor,until the potential of the two condensers becomes equal. The common potential (V) after sharing ofcharges;

V = net ch e

net capaci cearg

tan = q qC C

1 2

1 2

++

= C V C V

C C1 1 2 2

1 2

++

.

charges after sharing q1 = C1V & q2 = C2V. In this process energy is lost in the connecting wire as heat

. This loss of energy is Uinitial - Ureal = ( )C CC C

1 2

1 22 + (V1 - V2)

2 .


PART - I : OBJECTIVE QUESTIONS

* Marked Questions are having more than one correct option.

Section (A) : Definition of capacitance, Circuits with capacitor and use of KCL and KVLA-1. In the figure initial status of capacitor and their connection is shown. Which of the following

is incorrect about this circuit :

(A) Final charge on each capacitor will be zero(B) Final total electrical energy of the capacitors will be zero(C) Total charge flown from A to D is 30µC(D) Total charge flown from A to D is – 30µC

A-2. One plate of a capacitor is connected with a spring as shown in figure. Area of both the plates is A. In steadystate separation between the plates is 0.8 d (spring was unstretched and the distance between the plateswas d when the capacitor was uncharged). The force constant of the spring is approximately-

(A) 3

2o

dAE4ε

(B) 20

dAE5.2 e

(C) 3

2o

AdE6ε

(D) 3

3o

2dAEε

A-3. A circuit has a section AB shown in the figure. The emf of the source equals e = 10V, the capacitor capacitancesare equal to C1 = 1.0 mF and C2 = 2.0 mF, the potential difference fA - fB = 5.0V. The voltage across eachcapacitor are

(A) V1 = 3V5

, V2 = 3V10

(B) V1 = 3V10

, V2 = 3V10

(C) V1 = 3V10

, V2 = 3V5

(D) V1 = 3V5

, V2 = 3V5


A-4. A 1 µF capacitor is connected in the circuit shown below. The e.m.f. of the cell is 3 volts and internalresistance is 0.5 ohms. The resistors R1 and R2 have values 4 ohms and 1 ohm respectively. Thecharge on the capacitor in steady state must be :

(A) 2 m C (B) 1 m C (C) 1.33 m C (D) zero

A-5. A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it.A charge +Q is now given to its positive plate. The potential difference across the capacitor is now :

(A) V (B) V + CQ

(C) V + C2Q

(D) V – C2Q

A-6. In the given arrangement of capacitors 6µC charge is added to point A, find the charge on upper capacitor:

2C CA

3C

(A) 3 µC (B) 1 µC (C) 2 µC (D) 6 µC

A-7. In the circuit shown, switch S2 is closed first and is kept closed for a long time. Now S1 is closed. Justafter that instant the current through S1 is:

(A) eR1

towards right (B) eR1

towards left

(C) zero (D) 2

1

eR

A-8. Initially switch S is connected to position 1 for a long time. The net amount of heat generated in the circuitafter it is shifted to position 2 is

(A) ( ) 2212C

ee+e (B) ( ) 221C ee+e (C) ( )2212C

e+e (D) ( )221C e+e


A-9. A parallel plate capacitor having capacitance C is connected to a source of constant emf E. Which of thefollowing statements is correct ?(A) Net charge supplied by the battery to the capacitor is equal to CE.(B) Net charge supplied by the battery to the capacitor is equal to 2 CE.(C) Net charge supplied by the battery to capacitor is equal to zero.(D) None of these.

A-10.* Two capacitors of capacitances 1µF and 3µF are charged to the same voltages 5V. They are connected inparallel with oppositely charged plates connected together. Then :(A) Final common voltage will be 5 V(B) Final common voltage will be 2.5 V(C) Heat produced in the circuit will be zero

. (D) Heat produced in the circuit will be 37.5mJ.

A-11. A capacitor of capacitance C is charged to a potential difference V0. The charging battery is disconnectedand the capacitor is connected to a capacitor of unknown capacitance Cx. The P.D. across the combinationis V. The value of Cx should be :

(A) V

)VV(C 0 -(B) 0C(V V )

V-

(C) 0V

CV(D)

VCV0

A-12. The capacitance of capacitor of plate areas A1 and A2 (A1 < A2) at a distance d is :

(A) 0 1Ad

e(B) 0 2A

de

(C) 0 1 2(A A )2d

e +(D) 0 1 2A A

de

A-13. In the circuit shown, the energy stored in 1mF capacitor is

(A) 40 mJ (B) 64 mJ

(C) 32 mJ (D) none

A-14. If charge on left plane of the 5mF capacitor in the circuit segment shown in the figure is –20mC, the charge onthe right plate of 3mF capacitor is :

(A) +8.57 mC (B) –8.57 mC (C) +11.42 mC (D) –11.42 mC

A-15. The plates S and T of an uncharged parallel plate capacitor are connected across a battery. The battery isthen disconnected and the charged plates are now connected in a system as shown in the figure. Thesystem shown is in equilibrium. All the strings are insulating and massless. The magnitude of charge on oneof the capacitor plates is: [Area of plates = A]

(A) 0mgA2 Î (B) k

mgA4 0Î

(C) 0mgA Î (D) k

mgA2 0Î


A-16. A parallel plate capacitor has an electric field of 105V/m between the plates. If the charge on the capacitorplate is 1mC, then the force on each capacitor plate is

(A) 0.1Nt (B) 0.05Nt (C) 0.02Nt (D) 0.01Nt

A-17. A capacitor is connected to a battery. The force of attraction between the plates when the separation betweenthem is halved

(A) remains the same (B) becomes eight times (C) becomes four times (D) becomes two times

Section (B) : Combination of capacitors

B-1. In the figure shown the equivalent capacitance between 'A' and 'B' is :

(A) 3.75 F (B) 2 F (C) 21 F (D) 16 F

B-2. N identical capacitors are connected in parallel to a potential difference V. These capacitors are thenreconnected in series such that positively charged plate of one capacitor is connected to negatively chargedplate of the other, their charges being left undisturbed. The potential difference obtained is :

(A) zero (B) (N - 1) V (C) N V (D) N2V

B-3. 10 identical capacitors are connected as shown. The capacitance of each capacitor is 30 mF. Find theequivalent capacitance between A and B.

A B

(A) 30 mF (B) 60 mF (C) 120 mF (D) ¥

B-4. The equivalent capacitance between point A and B is:

(A) 1 mF (B) 2mF (C) 3mF (D) 4mF


B-5. Consider the circuit shown in the figure. Charge stored in capacitor of capacitance 2C

is

C

V

C2

C

C

(A) CV (B) VC4

(C) VC2

(D) 2CV

B-6. Fig (a) Shows two capacitors connected in series and joined to a battery. The graph in fig (b) shows thevariation in potential as one moves from left to right on the branch containing the capacitors if -

(A) C1 > C2 (B) C1 = C2 (C) C1 < C2

(D) The information is not sufficient to decide the relation between C1 and C2

B-7. In the circuit shown, a potential difference of 60V is applied across AB. The potential difference between thepoint M and N is

(A) 10 V (B) 15 V (C) 20 V (D) 30 V

B-8. In the circuit shown in figure, the ratio of charges on 5mF and 4mF capacitor is :

(A) 4/5 (B) 3/5

(C) 3/8 (D) 1/2

B-9. On each side of a polygon of n sides a capacitor of capacitance C is placed as shown in figure. Equivalentcapacitance across A and B is

A

C

B

C

C

(A) n

Cn )1( -(B)

1-nnC

(C) (n – 1)C (D) nC


B-10. From a supply of identical capacitors rated 8 mF, 250 V, the minimum number of capacitors required to forma composite 16 mF, 1000 V is :

(A) 2 (B) 4 (C) 16 (D) 32

B-11. A, B, C, D, E, F are conducting plates each of area A and any two consecutive plates separated by adistance d. The net energy stored in the system after the switch S is closed is:

(A) 20 Vd2A3e

(B) 20 Vd12A5e

(C) 20 Vd2Ae

(D) 20 VdAe

B-12. In the circuit shown, a potential difference of 60V is applied across AB. The potential difference between thepoint M and N is

(A) 10 V (B) 15 V

(C) 20 V (D) 30 V

B-13. In the circuit shown in figure, the ratio of charges on 5mF and 4mF capacitor is :

(A) 4/5 (B) 3/5

(C) 3/8 (D) 1/2

B-14. The minimum number of capacitors each of 3 mF required to make a circuit with an equivalent capacitance2.25 mF is

(A) 3 (B) 4 (C) 5 (D) 6

B-15. From a supply of identical capacitors rated 8 mF, 250 V, the minimum number of capacitors required to forma composite 16 mF, 1000 V is :

(A) 2 (B) 4 (C) 16 (D) 32

B-16. What is the equivalent capacitance of the system of capacitors between A & B

(A) 76 C (B) 1.6 C (C) C (D) None

B-17. Two capacitor having capacitances 8 mF and 16 mF have breaking voltages 20 V and 80 V. They are combinedin series. The maximum charge they can store individually in the combination is

(A) 160 mC (B) 200 mC (C) 1280 mC (D) none of these


B-18. Three plates A, B and C each of area 0.1 m2 are separated by 0.885 mm from each other as shown in thefigure. A 10 V battery is used to charge the system. The energy stored in the system is

(A) 1 mJ (B) 10–1 mJ (C) 10–2 mJ (D) 10–3 mJ

B-19. Five conducting parallel plates having area A and separation between them d, are placed as shown in thefigure. Plate number 2 and 4 are connected wire and between point A and B, a cell of emf E is connected. Thecharge flown through the cell is

(A) dAE

43 0e

(B) dAE

32 0e

(C) dAE4 0e

(D) d2AE0e

B-20. Three long concentric conducting cylindrical shells have radii R, 2R and 22 R. Inner and outer shells areconnected to each other. The capacitance across middle and inner shells per unit length is:

(A) 2n

31

0

l

Î(B) 2n

6 0l

Îp(C) 2n

02l

Îp(D) None

B-21. Four metallic plates arearranged as shown in the figure. If the distance between each plate then capacitanceof the given system between points A and B is (Given d << A)

(A) dA0e

(B) dA2 0e

(C) dA3 0e

(D) dA4 0e

B-22. Find the equivalent capacitance across A & B

(A) 328

mf (B) 215

mF

(C) 15 mF (D) none

B-23. The diagram shows four capacitors with capacitances and break down voltages as mentioned. What shouldbe the maximum value of the external emf source such that no capacitor breaks down?

[Hint: First of all find out the break down voltages of each branch. After that compare them.]

(A) 2.5 kV (B) 10 / 3kV

(C) 3 kV (D) 1 kV

B-24. Three capacitors 2 mF, 3 mF and 5 mF can withstand voltages to 3V, 2V and 1V respectively. Their seriescombination can withstand a maximum voltage equal to(A) 5 Volts (B) (31/6) Volts (C) (26/5) Volts (D) None


Section (C) : Equation of charging and discharging

C-1. In the circuit shown the capacitor is initially uncharged. The charge passed through an imaginarycircular loop parallel to the plates (also circular) and having the area equal to halfof the area of the plates, in one time constant is:

(A) 0.63 e C (B) 0.37 e C (C) e C

2(D) zero

C-2. An uncharged capacitor is connected in series with a resistor and a battery. The charging of thecapacitor starts at t = 0. The rate at which energy in capacitor is stored :(A) first increases then decreases (B) first decreases then increases(C) remains constant (D) continuously decreases

C-3.* The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor ofresistance 10 W.

(A) The initial potential difference across the capacitor is 100 volt.

(B) The capacitance of the capacitor is 2n101l

F..

(C) The total heat produced in the circuit will be 2n500l

joules.

(D) The thermal power in the resistor will decrease with a time constant 2n21l

second.

C-4. Three identical capacitors are given a charge Q each and they are then allowed to discharge through resis-tance R1, R2 and R3 separately. Their charges, as a function of time are shown in the graph below. Thesmallest of the three resistances is

(A) R3 (B) R2 (C) R1 (D) cannot be predicted


C-5. A graph between current & time during charging of a capacitor by a battery in series with a resistor is shown.The graphs are drawn for two circuits. R1, R2, C1, C2 and V1V2 are the values of resistance, capacitance andEMF of the cell in the two circuits. If only two parameters (out of resistance, capacitance, EMF) are differentin the two circuits. What is /are the correct option(s)

(A) V1 = V2; R1 > R2, C1> C2 (B) V1 > V2, R1 > R2 ; C1 = C2

(C) V1 < V2, R1< R2, C1 = C2 (D) V1 < V2, C1< C2, R1 = R2

C-6.* Capacitor C1 of capacitance 1 mircofarad and capacitor C2 of capacitance 2 microfarad are separately chargedfully by a common battery. The two capacitors are then separately allowed to discharge through equalresistors, at time t = 0 :(A) the current in each of two discharging circuits at t = 0 are equal and non-zero.(B) The current in the two discharging circuits at t = 0 are equal(C) The currents in the two discharging circuits at t = 0 are unequal.(D) Capacitor C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.

C-7. A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it.A charge +Q is now given to its positive plate. The potential difference across the capacitor is now

(A) V (B) V + CQ

(C) V + C2Q

(D) V – CQ

, if V < CV

C-8. A capacitor of capacitance C is initially charged to a potential difference of V volt. Now it is connected to abattery of 2V Volt 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

C-9. A conducting body 1 has some initial charge Q, and its capacitance is C. There are two other conductingbodies, 2 and 3, having capacitances : C2 = 2C and C3 ® ¥. Bodies 2 and 3 are initially uncharged. "Body2 is touched with body 1. Then, body 2 is removed from body 1 and touched with body 3, and then removed."This process is repeated N times. Then, the charge on body 1 at the end must be

(A) Q/3N (B) Q/3N–1 (C) Q/N3 (D) None

C-10. A charged capacitor is allowed to discharge through a resistance 2W by closing the switch S at the instantt = 0. At time t = ln 2 ms, the reading of the ammeter falls half of its initial value. The resistance of the ammeterequal to

(A) 0 (B) 2W

(C) ¥ (D) 2MW

C-11. A capacitor C = 100 mF is connected to three resistor each of resistance 1 kW and a battery of emf 9V. Theswitch S has been closed for long time so as to charge the capacitor. When switch S is opened, thecapacitor discharges with time constant

(A) 33 ms (B) 5 ms

(C) 3.3 ms (D) 50 ms


C-12. In the circuit shown in figure C1=2C2. Switch S is closed at time t=0. Let i1 and i2 be the currents flowingthrough C1 and C2 at any time t, then the ratio i1/ i2(A) is constant

(B) increases with increase in time t

(C) decreases with increase in time t

(D) first increases then decreases

C-13. In the circuit shown, when the key k is pressed at time t = 0, which of the following statements about currentI in the resistor AB is true

(A) I = 2mA at all t

(B) I oscillates between 1 mA and 2mA

(C) I = 1 mA at all t

(D) At t = 0, I = 2mA and with time it goes to 1 mA

C-14. In the R–C circuit shown in the figure the total energy of 3.6 ×10–3 J is dissipated in the 10 W resistor whenthe switch S is closed. The initial charge on the capacitor is

(A) 60 mC (B) 120 mC (C) 60 2 mC (D) 260

mC

C-15. A charged capacitor is allowed to discharge through a resistor by closing the key at the instant t =0. At theinstant t = (ln 4) ms, the reading of the ammeter falls half the initial value. The resistance of the ammeter isequal to

(A) 1 MW (B) 1W (C) 2W (D) 2MW

C-16. In the circuit shown, the cell is ideal, with emf = 15 V. Each resistance is of 3W. The potential differenceacross the capacitor is

(A) zero (B) 9 V (C) 12 V (D) 15 V


Section (D) : Capacitor with dielectric

D-1.* A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field andenergy associated with this capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric slab isnow introduced to fill the space between the plates with battery still in connection. The correspondingquantities now given by Q, V, E and U are related to the previous one as(A) Q > Q0 (B) V > V0 (C) E > E0 (D) U > U0

D-2. A parallel plate capacitor (without dielectric) is charged and disconnected from a battery. Now a dielectricis inserted between the plates. The electric force on a plate of the capacitor will:(A) decrease (B) increase(C) remain same (D) depends on the width of the dielectric.

D-3. Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to apotential difference V by a battery. The battery is then disconnected and the space between the platesof capacitor C is completely filled with a material of dielectric constant K. The potential differenceacross the capacitors now becomes.

(A) 1K

V+

(B) 2K

V2+

(C) 2K

V3+

(D) 3KV3+

D-4. Two conductors of thickness d are inserted inside a parallel capacitor of thickness 3d and capacitanceC0. The capacitance of new arrangement is :

d d

3d

(A) C0 (B) 2C0 (C) 3C0 (D) 30C

D-5.* A parallel plate capacitor of plate area A and plate seperation d is charged to potential difference V and thenthe battery is disconnected. A slab of dielectric constant K is then inserted between the plates of thecapacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude ofcharge on each plate, the electric field between the plates (after the slab is inserted) and the work done onthe system, in question, in the process of inserting the slab, then

(A) Q = dAV0e

(B) Q = dKAV0e

(C) E = dKV

(D) W = – ÷øö

çèæ -

eK11

d2AV2

0

D-6. A parallel plate capacitor made from two square plates of side a and separation b (<< a) is charged bya battery of emf V. After disconnecting the battery, a conductor of thickness slightly less than b is insertedas shown in figure. The potential energy of the system is

b

a

x

(A) 23

0

)(2V

xaba-

e(B) 2

20

)(2V

xaa-

e(C) 2

20 )(2

Vxaba

-e

(D) 22

30

2)( V

bxaa -e


D-7. A parallel plate capacitor without any dielectric has capacitance C0. A dielectric slab is made up of twodielectric slabs of dielectric constants K and 2K and is of same dimensions as that of capacitor plates andboth the parts are of equal dimensions arranged serially as shown. If this dielectric slab is introduced(dielectric K enters first) in between the plates at constant speed, then variation of capacitance with time willbe best represented by :

(A) (B) (C) (D)

D-8. Two parallel plate air filled capacitors each of capacitance C, are joined in series to a battery of emfV. The space between the plates of one of the capacitors is then completely filled up with a uniformdielectric having dielectric constant K. The quantity of charge which flows through the battery is -

(A) ÷÷ø

öççè

æ+1K

1–K2

CV(B) ÷÷

ø

öççè

æ +1–K1K

2CV

(C) CV ÷÷ø

öççè

æ+1K

1–K(D) CV ÷÷

ø

öççè

æ +1–K1K

D-9. Two identical capacitor C1 and C2 are connected in series with a battery. They are fully charged. Now adielectric slab is inserted between the plates of C2. The potential difference across C1 will :

(A) increase (B) decrease(C) remain same (D) depend on internal resistance of the cell

D-10. A parallel plate capacitor has two layers of dielectric as shown in figure. This capacitor is connected across abattery. The graph which shows the variation of electric field (E) and distance (x) from left plate.

(A) (B) (C) (D)


D-11. In the figure shown a parallel plate capacitor has a dielectric of width d/2 and dielectric constant K = 2.The other dimensions of the dielectric are same as that of the plates. The plates P1 and P2 of thecapacitor have area 'A' each. The energy of the capacitor is :

(A) d3

AV20Î

(B) dAV2 2

0Î(C)

dAV

23 2

0Î(D)

d3AV2 2

0Î

D-12. In the figure a capacitor of capacitance 2µF is connected to a cell of emf 20 volt. The plates of thecapacitor are drawn apart slowly to double the distance between them. The work done by the externalagent on the plates is :

(A) – 200 µJ (B) 200 µJ (C) 400 µJ (D) – 400 µJ

D-13. A dielectric slab of relative permittivity er and thickness t is inserted into the capacitor. Then,

(A) the capacitance of the system increases by 0

r

A1t 1–

eæ öç ÷eè ø

(B) free r

bound r

qq – 1

e=

e

(C) the fraction change in the energy stored is er –1

(D) the plates are moved apart by a relative distance tr

11–æ öç ÷eè ø

to recover the original energy stored.


D-14. A parallel plate capacitor has two layers of dielectric as shown in figure. This capacitor is connected across abattery. The graph which shows the variation of electric field (E) and distance (x) from left plate.

(A) (B) (C) (D)

D-15. A capacitor stores 60mC charge when connected across a battery. When the gap between the plates is filledwith a dielectric , a charge of 120mC flows through the battery. The dielectric constant of the material insertedis :(A) 1 (B) 2 (C) 3 (D) none

D-16. In the adjoining figure, capacitor (1) and (2) have a capacitance ‘C’ each. When the dielectric of dielectricconsatnt K is inserted between the plates of one of the capacitor, the total charge flowing through battery is

(A) 1KKCE

+from B to C (B) 1K

KCE+

from C to B

(C) )1K(2CE)1K(

+-

from B to C (D) )1K(2CE)1K(

+-

from C to B

D-17. The distance between plates of a parallel plate capacitor is 5d. Let the positively charged plate is at x=0 andnegatively charged plate is at x=5d. Two slabs one of conductor and other of a dielectric of equal thicknessd are inserted between the plates as shown in figure. Potential versus distance graph will look like :

(A) (B) (C) (D)


D-18. The distance between the plates of a charged parallel plate capacitor is 5 cm and electric field inside theplates is 200 Vcm–1. An uncharged metal bar of width 2 cm is fully immersed into the capacitor. The lengthof the metal bar is same as that of plate of capacitor. The voltage across capacitor after the immersion of thebar is :

(A) zero (B) 400 V (C) 600 V (D) 100 V

D-19. Condenser A has a capacity of 15 Fm when it is filled with a medium of dielectric constant 15. Another

condenser B has a capacity 1 Fm with air between the plates. Both are charged separately by a battery of

100V . After charging, both are connected in parallel without the battery and the dielectric material beingremoved. The common potential now is

(A) 400V (B) 800V (C) 1200V (D) 1600V

D-20. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains adielectric slab of dielectric constant k as shown. Q1 and Q2 are the charges stored in the capacitors. Now thedielectric slab is removed and the corresponding charges are Q’1 and Q’2. Then

(A) k1k

QQ

1

1 +=

¢(B) 2

1kQQ

2

2 +=

¢

(C) k21k

QQ

2

2 +=

¢(D) 2

kQQ

1

1 =¢

D-21. 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 dielectricconstant k = 2. The capacitance of the system between 1 and 3 & 2 and 4 are C1 and C2 respectively. The

ratio 2

1

CC

is :

(A) 35

(B) 1 (C) 53

(D) 75


PART - II : MISLLANEOUS QUESTIONS

1. COMPREHENSION :COMPREHENSION # 1

Capacitor C3 in the circuit is a variable capacitor (its capacitance can be varied). Graph is plottedbetween potential difference V1 (across capacitor C1) versus C3. Electric potential V1 approaches onasymptote of 10 V as C3 ® ¥.

C1

C2 C3

V

1. The ratio of the capacitance 1

2

CC will be

(A)23 (B)

43 (C)

34

(D)32

2. The value of C3 for which potential across C1 will become 8 V

(A) 1.5 C1 (B) 2.5 C1 (C) 3.5 C1 (D) 4.5 C1

3. The ratio of energy stored in capacitor C1 to that of total energy when C3 ® ¥

(A) Zero (B) 13 (C) 1 (D) Data insufficient

COMPREHENSION # 2The potential energy of a charged conductor or a capacitor is stored in electric field. The energy per unit

volume is called the energy density (u). Energy density in a dielectric media is given by u = 20KE

21

e . This

relation shows that the energy stored per unit volume depends on 2E . If E is the electric field in a space of

volume dV, then total stored energy in an electrostatic field is given by U = dVEK21 2

0 òe and if E is uniform

throughout the volume, then total energy stored can be given by VEK21 2

0e .

4. The energy density in the electric field created by a point charge falls off with distance from the point chargeas.

(A) r1

(B) 2r1

(C) 3r1

(D) 4r1

5. A charges q1 is placed at the centre of a spherical conducting shell of radius R. Conducting shell has a totalcharge q2. Electrostatic potential energy of the system is -

(A) R8qq2q

0

2121

pe+

(B) R8qq2q

0

2122

pe+

(C) R4qqq

0

2121

pe+

(D) R4qqq

0

2122

pe+


6. Let ua and ud represent the energy density in air and in a dielectric respectively, for the same field in both.Let K = dielectric constant. Then(A) ua = ud (B) ua = Kud (C) ud = Kua (D) ua = (K–1)ud

7. A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If x isthe separation between the plates, then the rate of change of electrostatic energy of the capacitor is propor-tional to-

(A) x (B) x2 (C) x1

(D) 2x1

COMPREHENSION # 3

The charge across the capacitor in two different RC circuits 1 and 2 are plotted as shown in figure.

8.* 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 the circuit are equal.(C) The emf's of the cells may be different.(D) The emf E1 is more than E2

9. Identify the 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

1RR

< 1

2

CC

COMPREHENSION # 4In the circuit as shown in figure the switch is closed at t = 0.

10. At the instant of closing the switch(A) the battery delivers maximum current.(B) no current flows through C(C) Voltage drop across R2 is zero.(D) the current through the battery decreases with time finally becomes zero.

11.* A long time after closing the switch(A) voltage drop across the capacitor is E.

(B) current through the battery is 21 RR

E+

(C) energy stores in the capacitor is 2

21

2RRER

C21

÷÷ø

öççè

æ

+

(D) current through the capacitor becomes zero.


2. ASSERTION AND REASON

12. Statement-1 : The electrostatic force between the plates of a charged isolated capacitor decreases whendielectric fills whole space between plates.Statement-2 : The electric field between the plates of a charged isolated capacitance decreases whendielectric fills whole space between plates.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

13. Statement-1 If temperature is increased, the dielectric constant of a polar dielectric decreases whereasthat of a non-polar dielectric does not change significantly.

Statement-2 The magnitude of dipole moment of individual polar molecule decreases significantlywith increase in temperature.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true.

14. Statement-1 : The heat produced by a resistor in any time t during the charging of a capacitorin a series circuit is half the energy stored in the capacitor by that time.Statement-2 : Current in the circuit is equal to the rate of increase in charge on the capacitor.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

3. MATCH THE COLUMN

15. Consider the situation shown. The switch S is open for a long time and then closed. Then:

E S

CC

Column I Column II

(A) Charge flown through battery when S is closed (p) 2

2CE

(B) Work done by battery. (q) 2CE

(C) Change in energy stored in capacitor. (r) 2

4CE

(D) Heat developed in the system.

(t) 8

CE2

(s) 4

CE


16. In the figure shown, area of each plate is A. Match the following :

2d

V

d1 2 3 4 5 6

Column-I Column-II

(A) Charge on plate 3 (p) zero(B) Charge on plate 5 (q) V

(C) Potential difference between plates 2 and 3 (r) 0 A V2d

e

(D) Potential difference between plates 2 and 5 (s) 0 A Vd

e

(t) none of these

17. Arrangements of Parallel Plates Capacitance

(A) (p) 03 A

2de

(B) (q) 03 Ad

e

(C) (r) 02 A3de

(D) (s) 02 Ad

e

(t) none of these

4. TRUE & FALSE :18. If the charge on capacitor is constant, on increasing the separation (still keeping it very less change) between

its plates the force between the plates does not change.

19. If the potential difference between two plates of a capacitor is constant, on increasing the plate's separationthe electric field remains constant.

5. FILL IN THE BLANKS :20. Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential

difference V. The battery is then disconnected and the region between the plates of capacitor C is completelyfilled with a material of dielectric constant K. The potential difference across the capacitors now becomes..........

21. The capacity of a conductor ........................ when an earth connected uncharged conductor is brought near it.

22. Capacity of parallel plate capacitor ........................ by decreasing the separation between two plates.


PART - I : MIXED OBJECTIVE


1. The plates of a parallel plate capacitor are charged with surface densities s1 and s2 respectively. Theelectric field at points :(A) inside the region between the plates will be zero(B) above the upper plate & below the lower plate will be zero(C) every where in the space will be zero(D) inside the region between the plates will be uniform & non-zero

2. Two large conducting plates A and B have charges Q1 and Q2 on them. The charges on the sides 1, 2, 3, and4 respectively are :

(A) q1 = q4 = 2QQ 21 +

and q2 = – q3 = 2QQ 21 -

(B) q1 = q3 = 2QQ 21 +

and q2 = q4 = 2QQ 21 -

(C) q2 = q3 = 2QQ 21 +

and q1 = q4 = 2QQ 21 -

(D) q1 = q2 = q3 = q4 = 2QQ 21 +

3. A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If X isthe separation between the plates, then the rate of change of the electrostatic energy of the capacitor isproportional to :(A) X2 (B) X (C) 1/X (D) 1/X2

4. Two metal spheres of radii a and b are connected by a thin wire. Their separation is large compared with theirdimensions. The capacitance of this system is :(A) 4pÎ0ab (B) 2pÎ0(a + b) (C) 4pÎ0(a + b) (D) 4pÎ0(a

2 + b2)/2

5.* An uncharged capacitor having capacitance C is connected across a battery of emf V. Now the capacitor isdisconnected and then reconnected across the same battery but with reversed polarity. Then :(A) after reconnection, thermal energy produced in the circuit will be equal to 2CV2.(B) after reconnection, thermal energy produced in the circuit will be equal to two-third of the total energysupplied by the battery.(C) after reconnection, no energy is supplied by the battery.(D) after reconnection, whole of the energy supplied by the battery is converted into heat.


6. A parallel plate capacitor is filled with a uniform dielectric. Maximum charge that can be given to it, does notdepend upon :(A) dielectric constant of the dielectric. (B) dielectric strength of the dielectric.(C) separation between the plates. (D) area of the plates.

7. In the given figure, a capacitor of non-parallel plates is shown. The plates of capacitor are connected bya cell of emf V0. If s denotes surface charge density and E denotes electric field. Then :

A

B

D FV0

(A) sA > sB (B) EF > ED (C) EF = ED (D) sA = sB

8. In the circuit, capacitor is initially uncharged. The equivalent resistance will be (in steady – state) :

(A) 1 W (B) 3 W (C) 4 W (D) 5 W

9. In the circuit shown the cells are ideal & of equal e.m.f. , the capacitance of the capacitor is C & theresistance of the resistor is R . X is first joined to Y and then to Z . After a long time the total heatproduced in the resistor will be :

(A) equal to the energy finally stored in the capacitor(B) half of the energy finally stored in the capacitor(C) twice the energy finally stored in the capacitor(D) 4 times the energy finally stored in the capacitor .

10.* In the circuit shown, all the capacitors are initially uncharged. When switch S is closed, a total chargeof 12mC passes through point A and a charge of 8mC passes through point B.

9V

SC1 C2=3 Fm

A B

C3 C4=4 Fm

(A) Value of capacitance of C1 is 2m F (B) Value of capacitance of C1 is 4m F(C) Value of capacitance of C3 is 2m F (D) Value of capacitance of C3 is 6m F


11. An ideal cell is connected across a capacitor as shown in figure. The initial separation between theplates of a parallel plate capacitor is d. The lower plate is pulled down with a uniform velocity v. Neglectthe resistance of the circuit. Then the variation of charge on capacitor with time is given by

v

C E

(A)

q

t

(B)

q

t

(C)

q

t

(D)

q

t

12.* A parallel plate capacitor of capacitance 'C' has charges on its plates initially as shown in the figure.Now at t = 0, the switch 'S' is closed. Select the correct alternative(s) for this circuit diagram.

t=0 -2 ce ec

e

S A B

(A) In steady state the charges on the outer surfaces of plates 'A' and 'B' will be same in magnitude andsign.(B) In steady state the charges on the outer surfaces of plates 'A' and 'B' will be same in magnitude andopposite in sign.(C) In steady state the charges on the inner surfaces of the plates 'A' and 'B' will be same in magnitudeand opposite in sign.

(D) The work done by the cell by the time steady state is reached is 2

C5 2e .

13. An isolated parallel plate capacitor of capacitance C has four surfaces with charges Q1, Q2, Q3 and Q4

as shown in figure. The potential difference between the plates is

Q1 Q3

Q2 Q4

(A) C2QQQQ 4321 +++

(B) C2QQ 32 +

(C) C2QQ 32 -

(D) C2QQ 41 +


14. Two metallic spheres of radii a and b are separated by a distance d as shown in figure. The capacity of thesystem is :

(A) 4pÎ0/(1/a + 1/b – 2/d) (B) 2pÎ0/(1/a – 1/b + 1/d)

(C) 4pÎ0/(1/a + 1/b – 1/d) (D) 4pÎ0(a + b)

15. A capacitor of capacity C is charged to a steady potential difference V and connected in series with an openkey and a pure resistor 'R'. At time t = 0, the key is closed. If I = current at time t, a plot of log I against 't' isas shown in (1) in the graph. Later one of the parameters i.e. V, R or C is changed keeping the other twoconstant, and the graph (2) is recorded. Then

(A) C is reduced (B) C is increased (C) R is reduced (D) R is increased

16. The distance between plates of a parallel plate capacitor is 5d. Let the positively charged plate is at x=0 andnegatively charged plate is at x=5d. Two slabs one of conductor and other of a dielectric of equal thicknessd are inserted between the plates as shown in figure. Potential versus distance graph will look like :

(A) (B) (C) (D)

17. A capacitor is charged fully using a cell. With the cell connected, the capacitor plates are slowly pulled apartso that new capacitance becomes half of the original capacitance. Let the work done by pulling agent be w

(A) Energy absorbed by the cell will be less than w

(B) Energy absorbed by the cell will be more than w

(C) Energy stored in the capacitor will increase by w

(D) There will be heat loss in this process.


18.* A parallel plate capacitor of area A and separation d is charged to potential difference V and removed

from the charging source. A dielectric slab of constant K = 2, thickness d and area 2A

is inserted, as

shown in the figure. Let s1 be free charge density at the conductor-dielectric surface and s2 be thecharge density at the conductor-vacuum surface.

d

A

Ks2

– s2– s1

s1

(A) The electric field have the same value inside the dielectric as in the free space between the plates.

(B) The ratio 2

1

ss

is equal to 12

.

(C) The new capacitance is d2A3 0Î

(D) The new potential difference is 32

V

19. A and C are concentric conducting spherical shells of radius a and c respectively. A is surrounded by aconcentric dielectric medium of inner radius a, outer radius b and dielectric constant k. If sphere A is given acharges Q, the potential at the outer surface of the dielectric is.

(A) kb4Q

0pe (B) 04

Qpe ÷÷

ø

öççè

æ-

+)ab(k

1a1

(C) b4Q

0pe (D) None of these

20. If n drops, each of capacitance C and charged to a potential V, coalesce to form a big drop, the ratio ofthe energy stored in the big drop to that in each small drop will be(A) n : 1 (B) n4/3 : 1 (C) n5/3 : 1 (D) n2 : 1

21. Figure shows a part of network of a capacitor and resistors. The potential indicated at A, B and C are withrespect to the ground. The charge on the capacitor in steady state is

B

A

C

2W4W

8W

4W

+8V

+4V

+6V

1 Fm 10V

(A) 4 mC (B) 6 mC (C) 10 mC (D) 16 mC


22. A student charges a capacitor in such a manner that it stores energy of 1 J. Now he wants to increase thepotential energy to 4 J. He should :(A) quadruple the potential difference across the capacitor without changing the carge

(B) double the potential difference across the capacitor without changing the charge

(C) double both the potential difference and charge

(D) double the charge without changing the potential difference

23. The capacitance (C) for an isolated conducting sphere of radius (a) is given by 4pe0a. If the sphere is enclosed

with an earthed concentric sphere. The ratio of the radii of the spheres being )1n(

n-

then the capacitance

of such a sphere will be increased by a factor

(A) n (B) )1n(n- (C) n

)1n( -(D) a . n

24. A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energyassociated with the capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric slab is introducedbetween plates of capacitor but battery is still in connection. The corresponding quantities now given by Q,V, E and U related to previous ones are(A) Q > Q0 (B) V > V0 (C) E > E0 (D) U < U0

25. In the transient circuit shown the time constant of the circuit is :

(A) 35

RC (B) 25

RC

(C) RC47

(D) RC37

26. Find heat produced on closing the switch S

(A) 0.0002 J (B) 0.0005 J

(C) 0.00075 (D) zero

Multiple Choice Questions :27. Two capacitors of 2 mF and 3 mF are charged to 150 volt and 120 volt respectively. The plates of capacitor are

connected as shown in the figure. A discharged capacitor of capacity 1.5 mF falls to the free ends of the wire.Then

(A) charge on the 1.5 mF capacitors is 180 mC

(B) charge on the 2mF capacitor is 120 mC

(C) positive charge flows through A from right to left.

(D) positive charge flows through A from left to right.

28. In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is closed(A) positive charge will flow out of the positive terminal of the cell

(B) positive charge will enter the positive terminal of the cell

(C) the amount of charge flowing through the cell will be CE.

(D) the amount of charge flowing through the cell will be 4/3 CE.


29. In the circuit 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

30. A circuit shown in the figure consists of a battery of emf 10 V and two capacitance C1 and C2 of capacitances1.0 mF and 2.0 mF respectively. The potential difference VA – 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) Energy stored in capacitor C1 is two times the energy stored in capacitor C2.

31. If Q is the charge on the plates of a capacitor of capacitance C, V the potential difference between the plates, A thearea of each plate and d the distance between the plates, the force of attraction between the plates is

(A) ÷÷ø

öççè

æ

e AQ

21

0

2(B) ÷

÷ø

öççè

æ

dCV

21 2

(C) ÷÷ø

öççè

æ

e0

2

ACV

21

(D) ÷÷ø

öççè

æ

ep 20

2

dQ

41

32. A capacitor C is charged to a potential difference V and battery is disconnected. Now if the capacitor platesare brought close slowly by some distance :(A) some +ve work is done by external agent (B) energy of capacitor will decrease(C) energy of capacitor will increase (D) none of the above

33. Four capacitors and a battery are connected as shown. The potential drop across the 7 mF capacitor is 6 V. Then the:(A) potential difference across the 3 mF capacitor is 10 V

(B) charge on the 3 mF capacitor is 42 mC

(C) e.m.f. of the battery is 30 V

(D) potential difference across the 12 mF capacitor is 10 V.

34. The capacitance of a parallel plate capacitor is C when the region between the plate has air. This region isnow filled with a dielectric slab of dielectric constant k. The capacitor is connected to a cell of emf E, and theslab is taken out(A) charge CE(k – 1) flows through the cell(B) energy E2C(k – 1) is absorbed by the cell.(C) the energy stored in the capacitor is reduced by E2C(k – 1)

(D) the external agent has to do 12

E2C(k – 1) amount of work to take the slab out.

35. A parallel plate air-core capacitor is connected across a source of constant potential difference. When adielectric plate is introduced between the two plates then :(A) some charge from the capacitor will flow back into the source.(B) some extra charge from the source will flow back into the capacitor.(C) the electric field intensity between the two plate does not change.(D) the electric field intensity between the two plates will decrease.

36. A parallel plate capacitor of plate area A and plate seperation d is charged to potential difference V and thenthe battery is disconnected. A slab of dielectric constant K is then inserted between the plates of thecapacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude ofcharge on each plate, the electric field between the plates (after the slab is inserted) and the work done onthe system, in question, in the process of inserting the slab, then

(A) Q = dAV0e

(B) Q = dKAV0e

(C) E = dKV

(D) W = – ÷øö

çèæ -

eK11

d2AV2

0

37. A parallel plate capacitor has a parallel slab of copper inserted between and parallel to the two plates, withouttouching the plates. The capacity of the capacitor after the introduction of the copper sheet is :(A) minimum when the copper slab touches one of the plates.(B) maximum when the copper slab touches one of the plates.(C) invariant for all positions of the slab between the plates.(D) greater than that before introducing the slab.


38. Two thin conducting shells of radii R and 3R are shown in the figure. The outer shell carries a charge +Q andthe inner shell is neutral. The inner shell is earthed with the help of a switch S.(A) With the switch S open, the potential of the inner sphere is equal to that of the outer.(B) When the switch S is closed, the potential of the inner sphere becomes zero.(C) With the switch S closed, the charge attained by the inner sphere is – Q/3. (D) By closing the switch the capacitance of the system increases.

39. The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectricof dielectric constant K is inserted to fill the whole space between the plates with voltage source remainingconnected to the capacitor.(A) the energy stored in the capacitor will become K-times(B) the electric field inside the capacitor will decrease to K-times(C) the force of attraction between the plates will increase to K2–times(D) the charge on the capacitor will increase to K-times

40. A parallel-plate capacitor is connected to a cell. Its positive plate A and its negative plate B have charges +Qand –Q respectively. A third plate C, identical to A and B, with charge +Q, is now introduced midway betweenA and B, parallel to them. Which of the following are correct?

(A) The charge on the inner face of B is now 2Q3

-

(B) There is no change in the potential difference between A and B.(C) The potential difference between A and C is one-third of the potential difference between B and C.

(D) The charge on the inner face of A is now 2Q .

41. In the circuit shown in the figure, the switch S is initially open and the capacitor is initially uncharged. I1, I2and I3 represent the current in the resistance 2W, 4W and 8W 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 = 0.6 A, I2 = 0 and I3 = 0(D) long after the switch S is closed, I1 = I2 = I3 = 0.6 A.

42. The circuit shown in the figure consists of a battery of emf e = 10 V ; a capacitor of capacitance C = 1.0 mFand three resistor of values R1 = 2W, R2 = 2W and R3 = 1W. Initially the capacitor is completely uncharged andthe 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 long time after the switch closed is 5A.(C) The ratio of current through R1 and R2 is always constant.(D) The maximum charge on the capacitor during the operation is 5mC.

43. In the circuit shown in figure C1 = C2 = 2mF. Then charge stored in

(A) capacitor C1 is zero (B) capacitor C2 is zero

(C) both capacitor is zero (D) capacitor C1 is 40 mC

44. A capacitor of capacity C is charged to a steady potential difference V and connected in series with an openkey and a pure resistor 'R'. At time t = 0, the key is closed. If I = current at time t, a plot of log I against 't' isas shown in (1) in the graph. Later one of the parameters i.e. V, R or C is changed keeping the other twoconstant, and the graph (2) is recorded. Then

(A) C is reduced (B) C is increased (C) R is reduced (D) R is increased


PART - II : SUBJECTIVE QUESTIONS

1. A charged capacitor C1 = 3 mF is discharged through R = 1 kW by putting the switch is position 1. When thecurrent reaches I0 = 2 A, the switch is thrown to position 2 to discharge through uncharged capacitor C2 = 6mF and steady state is allowed to reach. Find the heat dissipated (in Joules) in the resistor R after switch isthrown to position 2.

+–

R

1 2

2. A spherical capacitor is made of two conducting spherical shells of radii a and b = 3a. The space between theshells is filled with a dielectric of dielectric constant K = 3 upto a radius c = 2a as shown. If the capacitanceof given arrangement is n times the capacitance of an isolated spherical conducting shell of radius a. Thenfind value of n.

3. Find the potential difference between points A and B of the system shown in the figure, if the emf is equal to

e = 110V and the capacitance ratio 1

2

CC

= h = 2.0.

4. Find the equivalent capacitance between terminals ‘A’ and ‘B’. The letters have their usual meaning.

5. The plates of a parallel plate capacitor are given charges +4Q and –2Q. The capacitor is then connectedacross an uncharged capacitor of same capacitance as first one (= C). Find the final potential differencebetween the plates of the first capacitor.


6. In the given network if potential difference between p and q is 2V and C2 = 3C1. Then find the potentialdifference between a & b.

7. Find the equivalent capacitance of the circuit between point A and B.

8. Find heat produced in the circuit shown in figure on closing the switch S.

9. In the following circuit, the resultant capacitance between A and B is 1 mF. Find the value of C.

10. The figure shows a circuit consisting of four capacitors. Find the effective capacitance between X and Y.

11. Five identical capacitor plates, each of area A, are arranged such that adjacent plates are at a distance 'd'apart, the plates are connected to a source of emf V as shown in figure. The charge on plate 1is______________ and that on plate 4 is _________.

12. In the circuit shown in the figure, intially SW is open. When the switch is closed, the charge passing throughthe switch ____________ in the direction ________ to ________ .


13. Find the capacitance of the system shown in figure.

14. Figure shows three concentric conducting spherical shells with inner and outer shells earthed and themiddle shell is given a charge q. Find the electrostatic energy of the system stored in the region I and II.

15. Find the ratio between the energy stored in 5 mF capacitor to the 4 mF capacitor in the given circuit in steady state.

16. A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge q= 20mC is given to the inner sphere. Find the heat generated in the process, the inner sphere is connected tothe shell by a conducting wire

17. In the circuit shown here, at the steady state, the charge on the capacitor is ____.

18. In the circuit shown in figure R1 = R2 = 6R3 = 300 MW, C = 0.01 mF and E = 10V. The switch is closed at t = 0, find

(a) Charge on capacitor as a function of time.(b) energy of the capacitor at t = 20s.

19. In the circuit shown in figure the capacitance of each capacitor isequal toC and resistance R. One of the capacitors was charge to avoltage V and then at the moment t = 0 was shorted by means of theswitch S.Find:(a) the current in the circuit as a function of time t.(b) the amount of generated heat.

20. The two identical parallel plates are given charges as shown in figure. If the plate area of either face of eachplate is A and separation between plates is d, then find the amount of heat liberate after closing the switch.


21. Five identical conducting plates 1, 2, 3, 4 & 5 are fixed parallel to and equdistant from each other (see figure).Plates 2 & 5 are connected by a conductor while 1 & 3 are joined by another conductor . The junction of 1 &3 and the plate 4 are connected to a source of constant e.m.f. V0. Find ;

(i) the effective capacity of the system between the terminals of the source.(ii) the charges on plates 3 & 5.Given d = distance between any 2 successive plates & A = area of either face of each plate .

22. Three capacitors of 2mF, 3mF and 5mF are independently charged with batteries of emf’s 5V, 20V and 10Vrespectively. After disconnecting from the voltage sources. These capacitors are connected as shown infigure with their positive polarity plates are connected to A and negative polarity is earthed. Now a battery of20V and an uncharged capacitor of 4mF capacitance are connected to the junction A as shown with a switchS. When switch is closed, find :

(a) the potential of the junction A.(b) final charges on all four capacitors.

23. In the circuit shown in figure, find the amount of heat generated when switch s is closed.

24. The connections shown in figure are established with the switch S open. How much charge will flow throughthe switch if it is closed?

25. A potential difference of 300 V is applied between the plates of a plane capacitor spaced 1 cm apart. A planeparallel glass plate with a thickness of 0.5 cm and a plane parallel paraffin plate with a thickness of 0.5 cmare placed in the space between the capacitor plates find :(i) Intensity of electric field in each layer.(ii) The drop of potential in each layer.(iii) The surface charge density of the charge on capacitor the plates. Given that : kglass = 6, kparaffin= 2

26. A parallel plate capacitor has plates with area A & separation d . A battery charges the plates to a potentialdifference of V0. The battery is then disconnected & a di-electric slab of constant K & thickness d is introduced.Calculate the positive work done by the system (capacitor + slab) on the man who introduces the slab.

27. A parallel plate capacitor is filled by a di-electric whose relative permittivity varies with the applied voltageaccording to the law = aV, where a = 1 per volt. The same (but containing no di-electric) capacitor chargedto a voltage V = 156 volt is connected in parallel to the first "non-linear" uncharged capacitor. Determine thefinal voltage Vf across the capacitors.


28. Two parallel plate capacitors A & B have the same separation d = 8.85 × 10-4 m between the plates. The plate areasof A & B are 0.04 m2 & 0.02 m2 respectively. A slab of di-electric constant (relative permittivity) K=9 has dimensionssuch that it can exactly fill the space between the plates of capacitor B.

(i) the di-electric slab is placed inside A as shown in the figure (i) A is then charged to a potential differenceof 110 volt. Calculate the capacitance of A and the energy stored in it.(ii) the battery is disconnected & then the di-electric slab is removed from A . Find the work done by theexternal agency in removing the slab from A .(iii) the same di-electric slab is now placed inside B, filling it completely. The two capacitors A & B are thenconnected as shown in figure (iii). Calculate the energy stored in the system.

29. Two square metallic plates of 1 m side are kept 0.01 m apart, like a parallel plate capacitor, in air in such away that one of their edges is perpendicular, to an oil surface in a tank filled with an insulating oil. The platesare connected to a battery of e.m.f. 500 volt . The plates are then lowered vertically into the oil at a speed of0.001 m/s. Calculate the current drawn from the battery during the process.[di-electric constant of oil = 11, Î0 = 8.85 × 10-12 C2/N2 m2]

30. A 10 mF and 20 mF capacitor are connected to a 10 V cell in parallel for some time after which the capacitorsare disconnected from the cell and reconnected at t = 0 with each other , in series, through wires of finiteresistance. The +ve plate of the first capacitor is connected to the –ve plate of the second capacitor. Draw thegraph which best describes the charge on the +ve plate of the 20 mF capacitor with increasing time.

31. A capacitor of capacitance C0 is charged to a potential V0 and then isolated. A small capacitor C is thencharged from C0, discharged & charged again, the process being repeated n times. The potential of the largecapacitor has now fallen to V. Find the capacitance of the small capacitor. If V0 = 100 volt, V=35volt, find thevalue of n for C0 = 0.2 mF & C = 0.01075 mF . Is it possible to remove charge on C0 this way?

32. In the figure shown initially switch is open for a long time. Now the switch is closed at t = 0. Find the chargeon the rightmost capacitor as a function of time given that it was intially unchanged.

33. Two capacitors A and B with capacities 3 mF and 2 mF are charged to a potential difference of 100 V and 180V respectively. The plates of the capacitors are connected as shown in figure with one wire from eachcapacitor free. The upper plate of a is positive and that of B is negative. an uncharged 2 mF capacitor C withlead wires falls on the free ends to complete the circuit. Calculate :

(i) the final charges on the three capacitors(ii) The amount of electrostatic energy stored in the system before and after the completion of the circuit.


PART-I IIT-JEE (PREVIOUS YEARS PROBLEMS)


1. A parallel combination of 0.1 M W resistor and a 10 mF capacitor is connected across a1.5 volt source of negligible resistance. The time required for the capacitor to set charged upto 0.75 voltis approximately (in seconds) : [JEE - 97' 2/100]

(A) ¥ (B) loge 2 (C) log10 2 (D) zero

2. A leaky parallel plate capacitor is filled completely with a dielectric having dielectric constant k = 5 andelectrical conductivity s = 7.4 x 10-12 W-1 m-1. If the charge on the plate of the capacitor at t = 0 is Q= 8.8 mC, then calculate the leakage current at the instant t = 12 s. [JEE - 97' 5/100]

3. An electron enters the region between the plates of a parallel plate capacitor at a point equidistant fromeither plate. The capacitor plates are 2 x 10-2 m apart and 10-1 m long. A potential difference of 300volt is kept across the plates. Assuming that the initial velocity of the electron is parallel to the capacitorplates, calculate the largest value of the velocity of the electron so that they do not fly out of thecapacitor at the other end. (take mass of electron = 9 × 10–31 kg) [JEE - 97' 5/100]

4. Two capacitors A and B with capacitors 3µF and 2µF are charged to a potential difference of 100 V and180 V respectively. The plates of the capacitors are connected as shown in fig. with one wire from eachcapacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2µF capacitor Cwith lead wires falls on the free ends to complete the circuit. Calculate. [JEE - 97' 5/100]

(i) The final charge on the three capacitors and(ii) The amount of electrostatic energy stored in the system before and after the completion of the circuit.

5*. A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is atx = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. The capacitor is givensome charge. As x goes from 0 to 3d. [JEE - 98' 2/200](A) The magnitude of the electric field remains the same(B) The direction of the electric field remains the same(C) The electric potential increases continuously(D) The electric potential increases at first, then decreases and again increases.


6. In the circuit shown in the figure, the battery is an ideal one, with e.m.f. V. The capacitor is initiallyuncharged. The switch S is closed at time t = 0. [JEE - 98' 8/200]

A

B

S

(a) Find the charge Q on the capacitor at time t.(b) Find the current in AB at time t. What is its limiting value as t ® ¥ ?

7. For the circuit shown, which of the following statements is true?

(A) With S1 closed, V1 = 15 V, V2 = 20 V(B) With S3 closed, V1 = V2 = 25 V(C) With S1 and S2 closed, V1 = V2 = 0(D) With S1 and S2 closed, V1 = 30 V, V2 = 20 V [JEE - 99' 2/200]

8. In the given circuit with steady current the potential drop across the capacitor must be :

[JEE(Scr)- 2001' 3/105]

(A) V (B) V/2 (C) V/3 (D) 2V/3

9. Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. Thecharge appearing on the capacitor B a long time after the switch is closed is : [JEE(Scr) - 2001' 3/105]

(A) zero (B) q/2 (C) q (D) 2 q

10. Two identical capacitors have the same capacitance C. One of them is charged to potential V1 and the otherto V2. The negative ends of the capacitors are connected together. When the positive ends are also connected,the decrease in energy of the combined system is: [ JEE(Scr) 2002' 3/105]

(A) 41 C (V1

2 - V22) (B)

41 C (V1

2 + V22)

(C) 41 C (V1 - V2)2 (D)

41 C (V1 + V2)2


11. Dotted line represents the charging of a capacitor with resistance X. If resistance is made 2X then which willbe the graph of charging [JEE Scr. 2004' 3/84]

(A) P (B) Q (C) R (D) S

12. An uncharged capacitor of capacitance 4µF, a battery of emf 12 volt and a resistor of 2.5 MW are connectedin series. The time after which VC = 3VR is (take ln2 = 0.693)(A) 6.93 seconds (B) 13.86 seconds(C) 7 seconds (D) 14 seconds [JEE Scr. 2005' 3/84]

13. In the given circuit the capacitor C is uncharged initially and switch ‘S’ is closed at t = 0. If charge oncapacitor at time ‘t’ is given by equation Q = Q0 (1 – e– at ). Find value of Q0 and a ?

[JEE Mains 2005' 4/60]

14. A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the totalamount of charge that flows from Y to X is [JEE 2007' 3/81]

X3 Fm 6 Fm

6 W3 W

9 V

Y

(A) 0 (B) 54 mC (C) 27 mC (D) 81 mC

15. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant

K = 2. The level of liquid is 3d

initially. Suppose the liquid level decreases at a constant speed V, the time

constant as a function of time t is [JEE' 2008 ; 3/163 ]Figure :

dd3

C

R

(A) tV3d5R6 0

+e

(B) 2220

tV9–tVd3–d2R)tV9d15( e+

(C) tV3–d5R6 0e

(D) 2220

tV9–tVd3d2R)tV9–d15(

+

e


16. At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors haveno charge initially, at what time (in seconds) does the voltage across them become 4 V?

[Take : ln 5 = 1.6, ln 3 = 1.1] [JEE' 2010 ; 3/163 ]

17. A 2 mF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after theswitch S is turned to position 2 is [JEE' 2011 ]

(A) 0% (B) 20% (C) 75% (D) 80%

18.* In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1 ispressed first to fully charge the capacitor C1 and then released. The Switch S2 is then pressed to charged thecapacitor C2 After some time, S2 is released and then S3 is pressed. After some time, [JEE Advanced 2013]

S1 S2 S3

C1 C2

V02V0

(A) the charge on the upper plate of C1 is 2CV0.

(B) the charge on the upper plate of C1 is CV0.

(C) the charge on the upper plate of C2 is 0.

(D) the charge on the upper plate of C2 is –CV0.


PART-II AIEEE (PREVIOUS YEARS PROBLEMS)


1. If there are n capacitors of capacitance C in parallel connected to V volt source, then the energy stored isequal to : [AIEEE-2002, 4/300]

(1) CV (2) 21

nCV2

(3) CV2

(4) n21

CV2

2. Capacitance (in F) of a spherical conductor having radius 1m, is : [AIEEE-2002, 4/300](1) 1.1 × 10–10 (2) 10–6 (3) 9 × 10–9 (4) 10–3

3. The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is :[ AIEEE-2003, 4/300]

(1) 16 × 10–32 joule (2) 3.1 × 10–26 joule (3) 4 × 10–10 joule (4) 32 × 10–32 joule

4. A fully charged capacitor has a capacitance ‘C’. It is discharged through a small coil of resistance wireembedded in a thermally insulated block of specific heat capacity ‘s’ and mass ‘m’. If the temperature of theblock is raised by ‘DT’, the potential difference ‘V’ across the capacitance is : [AIEEE-2005, 4/300]

(1) sTmC2 D

(2) sTmCD

(3) CTmsD

(4) CTms2 D

5. A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capaci-tance between any two adjacent plates is ‘C’, then the resultant capacitance is : [AIEEE-2005, 4/300](1) (n – 1)C (2) (n + 1) C (3) C (4) nC

6. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomesequal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the workdone by the battery will be [AIEEE-2007, 3/120](1) 1 (2) 2 (3) 1/4 (4) 1/2

7. A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C andis charged to a potential V volts. The dielectric slab is slowly removed from between the plates and thenreinserted. The net work done by the system in this process is : [AIEEE-2007, 3/120]

(1) 21

(K–1)CV2 (2) CV2(K – 1)/K (3) (K – 1)CV2 (4) zero

8. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between itsplates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics hasdielectric constant k1 = 3 and thickness d/3 while the other one has dielectric constant k2 = 6 and thick-ness 2d/3. Capacitance of the capacitor is now : [AIEEE-2008, 3/105](1) 45 pF (2) 40.5 pF (3) 20.25 pF (4) 1.8 pF

9. Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for theenergy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge toreduce to one-fourth its initial value. Then the ratio t1/t2 will be [AIEEE-2010, 8/144]

(1) 1 (2) 21

(3) 41

(4) 2

10. Two capacitors C1 and C2 are charged to 120 V and 200 V respectively. It is found that by connecting themtogether the potential on each one can be made zero. Then : [JEE Mains 2013](1) 5C1 = 3C2 (2) 3C1 = 5C2 (3) 3C1 + 5C2 = 0 (4) 9C1 = 4C2


NCERT QUESTIONS

1. A parallel plate capacitor with air between the plates has a capacitance of 8 pF(1pF= 1F). What will bethe capacitance if the distance between the plates is reduced by half , and the space between then isfilled with a substance to dielectric constant 6 ?

2. Three capacitors of capacitances 9 pF are connected in series.(a) What is the total capacitance of the combination ?(b) Determine the charge on each capacitor of the combination is connected to a 120 V supply?

3. Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel.(a) What is the total capacitance of the combination?(b) Determine the charge on each capacitor if the combination is connected is connected to a 100 Vsupply ?

4. In a parallel plate capacitor with air between the plates, each plate has an area of 6 x10|–3 m2 and thedistance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor isconnected to a 100 V supply, what is the charge on each plate of the capacitor ?

5. Explain what would happen if in the capacitor given in question 4, a 3 mm thick mica sheet (of dielectricconstant = 6 ) were inserted between the plates.(a) while the voltage supply remained connected.(b) after the supply was disconnected.

6. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in thecapacitor ?

7. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and isconnected to another uncharged 600 pF capacitor . How much electrostatic energy is lost in theprocess ?

8. An electrical technician requires a capacitance of 2 m F in a circuit across a potential difference of 1 kV..A large number of 1 m F capacitors are available to him each of which can withstand a potential differenceof not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.

9. What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between theplates is 0.5 cm? [you will realise from your answer why ordinary capacitors are in the range of m F orless. However, electrolytic capacitors do have a much larger capacitance ( 0.1 F ) because of veryminute separation between the conductors,]

10. Obtain the equivalent capacitance of the network in Fig. For a 300 V supply, determine the charge andvoltage across each capacitor.


11. The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. Thecapacitor is charged by connecting it to a 400 V supply.(a) How much electrostatic energy is stored by the capacitor?(b) View this energy as stored in the electrostatic field between the plates, and obtain the energy perunit volume u and the magnitude of electric field E between the relation.

12. A 4 m F capacitor is charged by a 200 V supply. It is then disconnected from the supply, and isconnected to another uncharged 2 m F capacitor. How much electrostatic energy of the first capacitoris lost in the form of heat and electromagnetic radiation ?

13. Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (½ ) QE, whereQ is the charge on the capacitor ,and E is the magnitude of electric field between the plates. Explainthe origin of the factor ½.

14. A spherical capacitor consists of two concentric spherical conductors, held in position by suitable

insulating supports . Show that the supports. Show that the capacitor is given by 21

21

rrrr4C

-ep

= o

where r1 and r2 are the radii of outer and inner spheres respectively.

15. A spherical capacitor has an inner sphere of radius 12cm and an sphere of radius 13 cm. The outersphere is earthed and the inner sphere is given a charge of 2.5 m C. The space between the concentricspheres is filled with a liquid of dielectric constant 32.(a) Determine the capacitance of the capacitor.(b) What is the potential of the inner sphere?(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explainwhy the latter is much smaller.

16. A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. Theouter cylinder is earthed and the inner cylinder is given a charge of 3.5 m C. Determine the capacitanceof the system and the potential; of the inner cylinder. Neglect end effects ( i,e., bending of field lines atthe ends).

17. A parallel plate capacitor is to be designed with a voltage rating 1kV, using a material of dielectricconstant 3 and dielectric strength about 107 Vm–1 ( Dielectric strength is maximum electric field amaterial can tolerate without breakdown, i.e., without starting to conduct electricity through partialionisation ).For safety, we should like the field never to exceed, say 10% of the dielectric strength.What minimum area of the plates is required to have capacitance of 50 pF.


Exercise # 1PART-I

A-1. (C) A-2. (B) A-3. (C) A-4. (A) A-5. (C) A-6. (A) A-7. (B)

A-8. (C) A-9. (C) A-10.* (BD) A-11. (B) A-12. (A) A-13. (C) A-14. (A)

A-15. (A) A-16. (B) A-17. (C) B-1. (B) B-2. (C) B-3. (B) B-4. (D)

B-5. (B) B-6. (C) B-7. (D) B-8. (C) B-9. (B) B-10. (D) B-11. (C)

B-12. (D) B-13. (C) B-14. (B) B-15. (D) B-16. (B) B-17. (A) B-18. (B)

B-19. (B) B-20. (B) B-21. (B) B-22. (B) B-23. (A) B-24. (B) C-1. (D)

C-2. (A) C-3.* (ABCD) C-4. (C) C-5. (C) C-6.* (BD) C-7. (C) C-8. (B)

C-9. (A) C-10. (A) C-11. (D) C-12. (B) C-13. (D) C-14. (B) C-15. (C)

C-16. (C) D-1.* (AD) D-2. (C) D-3. (C) D-4. (C) D-5.* (ACD) D-6. (A)

D-7. (B) D-8. (A) D-9. (A) D-10. (A) D-11. (D) D-12. (B) D-13.* (BD)

D-14. (A) D-15. (C) D-16. (D) D-17. (B) D-18. (C) D-19. (B) D-20. (C)

D-21. (B)

PART-II1. (A) 2. (B) 3. (D) 4. (D) 5. (B) 6. (C) 7. (D)

8.* (AC) 9. (D) 10. (AC) 11.* (BCD) 12. (D) 13. (C) 14. (D)

15. (A) – q ; (B) – p ; (C) – r ; (D) – r 16. (A) – t ; (B) – s ; (C) – q ; (D) – p

17. (A) – q ; (B) – p ; (C) – s ; (D) – r 18. True 19. False 20. ÷øö

çèæ

+ 2K3

V

21. increases 22. increases

Exercise # 2PART-I

1. (D) 2. (A) 3. (D) 4. (C) 5.* (ABD) 6. (C) 7. (A)

8. (D) 9. (D) 10.* (BC) 11. (B) 12.* (ACD) 13. (C) 14. (A)

15. (B) 16. (B) 17. (B) 18.* (ABCD) 19. (C) 20. (C) 21. (A)

22. (C) 23. (A) 24. (A) 25. (C) 26. (D) 27. (ABC) 28. (AD)

29. (B) 30. (AD) 31. (AB) 32. (B) 33. (BCD) 34. (ABD) 35. (BC)

36. (ACD) 37. (CD) 38. (ABCD) 39. (ACD) 40. (ABCD) 41. (B) 42. (ABCD)

43. (BD) 44. (B)


PART-II

1. 4 2. n = 3 3. VAB = ( )231 h+h+e

= 10V 4. dA

1013 0Î

5. 3Q/2C

6. 30 V 7. C 8. 0 9.2332

mF 10. F38

m

11.d

VA 0Î , –

dVA2 0Î

12. 60 mc , A to B 13.2524

0e Ad

14. UI = r10kq3 2

1 where 5q2q1 -= ; UII = r35)qq(K2 2

1+ 15. 0.8 16. 9J

17. 331

RRR

EC ÷÷ø

öççè

æ+

18. (a) q = 0.05(1 – e–t/2) mC; (b) 0.125 mJ

19. (a) I = RV0 e–2t/Rc; (b)

14

CV02 20.

12

q dA

2

0Î

21. (i) 53 ÷

øö

çèæÎ

dA0 ; (ii) Q3=

43

÷øö

çèæÎ

dAVa0

, Q5 = 32

÷øö

çèæÎ

dAVa0

22. (a) 100

7 volts; (b) 28.56 mC, 42.84 mC, 71.4 mC, 22.88 mC

23. 150 mJ 24. 12mC 25. (i) 1.5 × 104 V/m, 4.5 × 104 V/m, (ii) 75 V, 225 V, (iii) 8 × 10–7 C/m2

26. W = 12

C0 V02 ÷

øö

çèæ -

K11 27. 12 volt

28. (i) 0.2 × 10-8 F, 1.2 × 10-5 J ; (ii) 4.84 × 10-5 J ; (iii) 1.1 × 10-5 J 29. 4.425 × 10-9 Ampere

30. 31. C = C0 úúû

ù

êêë

é-÷

øö

çèæ 1

VV n/1

0 = 0.01078 mF, n = 20, No

32. q = ÷øö

çèæ - - RC/te

211

2CV

33. QA = 90 mC, QB = 150 mC, QC = 210 mC, Ui = 47.4 mJ, Uf = 18 mJ

Exercise # 3PART-I

1. (D) 2. i = k/t–

0

0ekQ Îs

Îs

@ 0.2 mA 3. 302

× 108 m/s

4. (i) QA = 90 µC, QB = 150 µC, QC = 210 µC (ii) 18 mJ

5*. (BC) 6. (a) q = 2

CV [1 - e-2t/3RC] (b) i =

R2V

1 13

2 3RC-éëê

ùûú

-e t / ; i =

R2V

as t ® ¥

7. (D) 8. (C) 9. (A) 10. (C) 11. (B) 12. (B)

13. Q0 = 21

2

RRVCR

+ & a = 21

21

RCR)RR( +

14. (C) 15. (A) 16. t = 2 sec

17. (D) 18.* (BD)


PART-II

1. (2) 2. (1) 3. (4) 4. (4) 5. (1) 6. (4) 7. (4)

8. (2) 9. (3) 10. (2)

Exercise # 4

1. 96 pF 2. (a) 3 pF, (b) 40 V 3. (a) 9 pF, (b) 2 x 10-10 C, 3 x 10-10 C, 4 x 10-10 C

4. 18 pF, 1.8 x 10-9 C.

5. (a) V = 100 V, C = 108 pF , Q = 1.08 x 10-8 C, (b) Q = 1.8 x 10-9 C, C = 108 pF, V = 16.6 V

6. 1.5 x 10-8 J 7. 6 x 10-6 J.

8. Eighteen 1 m F capacitors arranged in 6 parallel rows, each row consisting of 3 capacitors in series.

9. 1130 km2

10. Equivalent capacitance = 3200

pF;

Q1 = 10-8 C, V1 = 1000 V ; Q2 = Q3 10-8 C;V2 = V3 = 50 VQ4 = 2.55 x 10-8 C, V4 = 200 V.

11. (a) 2.55 x 10-6 J (b) u = 0.113 J m-3 , u = (1/2) e E2

12. 2.67 x 10-2 J

13. Hint: Suppose we increase the separation of the plates by D x . Work done (by external agency) = F D x.Thos goes to increase the potential energy of the capacitor by u a D x where u os energy density. ThereforeF = u a which os easily seen to be ( 1/2) QE,using u = (½ ) e

0E2 . The physical origin of the factor ½ in the

force formula lies in the fact that just outside the conductor, field os E, and inside it is zero. So the averagevalue E/2 contributes to the force.

15. (a) 5.5 x 10-9 F (b) 4.5 x 10-2 V (c) 1.3 x 10-11 F.

16. 1.2 x 10-10 F, 2.9 x 104 V.

17. 19cm2

cs - arride learning · 2017-07-05 · a capacitor of capacitance c is charged to a potential...

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