Capacitors Questions and Answers

In the circuit shown initially there is no charge on capacitors and keys S and S are open The values of the capacitors are C 10 F C 30 F and C3 C4 80 F 7022 S C 5 V P 302 Q D 15 I S 10 V ww 100 30 22 www Which of the statement s is are correct A If key S is kept closed for long time such that capacitors are fully charged the voltage across the capacitor C will be 4 V B The key S is kept closed for long time such that capacitors are fully charged Now key S is closed at this time the instantaneous current across 30 resistor between points P and Q will be 0 2 A round off to 1st decimal place C At time t 0 the key S is closed the instantaneous current in the closed circuit will be 25 mA C ll

Consider a LC circuit with energy E Now the capacitor plates are slow drawn apart to increase the oscillation frequency 3 times The work done in this process is nE Oscillation frequency of LC circuit is very very high C H q m L q

If in the circuit shown below The internal resistance of the battery is 1 52 and V and V are the potentials at P and Q respectively the potential difference between the points P and Q is 1 zero 20 V Por 1 552 352 www P 252 www 252 Q302 wwwww 2 4V V VQ

Q3 An electron enters the region of a uniform electric field E 300 N C The E field set up by parallel plate capacitors is directed vertically upward The initia velocity of the electron as it enters the field is 2 106 m s By the time the electron leaves the E field it assumes the trajectory of a projectile Find the acceleration of the electron while it is in the electric field a 3 5 m s b 9 5 m s c 5 3 m s c 6 5 m s 2 r 39 m s

The area of the plates of a parallel plate capacitor is A and the gap between them is d The gap is filled with a non homogeneous dielectric whose dielectric constant varies with the distance y from one plate as K sec dimensionless constant The capacitance of this capacitor is 1 3 TE A 2d 2 A d 2d 2 where is a TE A d N 4 None of these Bumpend Ower 8 Pusa Road New Delhi 110005 Ph 011 47623456

15 16 C QS The equivalent resistance between A and G is 3R A 4 7R 12 QE Tags QT COM CA B CC P100208 FACID PVJ RELEXAM PS A www TU www CM 3 WM 0 TagE QS The equivalent resistance between A and C is 3R A 4 7R www B D B C 5R 6 4R 3 5R 6 4R

notation A charged particle having q and mass m accelerated by a potential difference Vo enters inside a parallel plate capacitor parallel to length I of plates at midpoint of its separation between plates at t 0 Electric field between the plates of the capacitor varies with time t as E at where a is constant Angle of deviation as it ma 14 comes out of plates is Value of 4 3 2qV will be

Volume Charge Filled in a Capacitor A parallel plate capacitor filled with a uniform volume charge density between plates of area A and separation d If a constant potential difference V is applied across plates it is observed that electric field in the vicinity of one of the plates becomes zero Determine the volume charge density between the plates

Equivalent capacitance between A and B as shown in the circuit will be A Beka 2uF OPTIONS MARK FOR REVIEW CLEAR SELECTION A 1 F

41 Two conductors of thickness d are inserted inside a parallel capacitor of thickness 3d and capacitance Co The capacitance of new arrangement is de d 3d 1 Co 2 2Co 3 3Co 4 Co

ENERGY DENSITY OF CAPACITOR DIELECTRIC SLAB A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it A dielectric slab of dielectric constant K which can just fill the air gap of the capacitor is now inserted in it Which of the following is incorrect 1 a The change in energy stored is b The charge on the capacitor is not conserved c The potential difference between the decreases K times The energy stored in the capacitor decre

Me 9 A capacitor C is fully charged with voltage Vo After A disconnecting the voltage source it is connected in parallel with another uncharged capacitor of capacitance C The 2 energy loss in the process after the charge is distributed between the two capacitors is Sep 04 2020 II a cv2 2 1 c CV2 4 b CV 3 d CV

135 A small charged particle q lies at the centre of two concentric conducting hollow sres of inner radii R and 5R and outer radii 3R and 7R respectively Then which of the following is are correct a b C 5R 7R 3R kog The energy stored in the space between 3R to 5R cavity is 15R The energy stored in the space between 3R to 5R cavity is kq 307 Ask Do The amount of work has to be performed to slowly transfer the charge q from center through the office to infinity is km

Capacitors shown in figure are made of square plate of edge length A particle Pof mass m is in equilibrium if placed between plates of capacitor 1 If the same particle is placed between the plates of the capacitor 2 its acceleration is found to be x m s Find the value of x 2 d 2d V

13 A network of four capacitors each 10 F are connected as shown with 500V supply Calculate the ratio of charges stored on C and C 1 1 2 500 V 3 B 1 CA HH C C C NCERT Pg 802 LAT3 14 A 900 pF parallel plate capacitor is charge by 100 V ideal battery The space betwee the plates is 1cm How much electrostat energy is stored per unit volume of emp space of capacitor Apa batter nedic apac ateri Bectr nduce PO

15 A 90 pF capacitor is charged by a 10 V battery The capacitor is then disconnected from battery and connected to another charged 90 pF capacitor Final electrostatic energy stored by the system is 1 225 pJ 3 45 pl C NCERT Pg 82 F 2 25 nJ 4 4 5 nJ F C 17 1 3 Capacitance C decreases from initial value Co to Co K 4 Both 1 and 2 are correct A parallel plate capacitor with each plate of area 6 x 10 m has plate separation of 3 mm A 3 mm thick mica sheet of dielectric constant K 6 was inserted between the plates If this capacitor is connected to 100 volt supply what is charge on positives plate of capacitor INCERT Pg 871 21 06 10 C 1 1 92 10 C X 3 4 2 x 10 C 4 4 36 107 C 18 Equivalent capacitance of the networ

conductor is placed inside uniform INCERT Pg 68 eld Then surface of conductor electrostatic es normal to the surface at every the conductor electrostatic field ectrostatic potential is constant mout the volume of conductor and same value on its surface cove are correct tors are separated by distance The dielectric strength of air is O Vm What maximum safe ference can be applied across INCERT Pg 78 2 6 x 10 V 4 1 5x 10 V OAI DUAL CAMERA ene hodiny dielectric constant the same Maps 13 A network of four capacitors each 10 uF a connected as shown with 500V Supply Calculate the ratio of charges stored on C and C A 1 1 2 500 V 3 3 B C 4 C C C NCERT Pg 80 NCERT Maps 15 A 90 pF capacitor is charged by a 10 V battery The capacitor is then disconnected from battery and connected to another charged 90 pF capacitor Final electrostatic energy stored by the system is NCERT Pg 82 HE C U 1 225 pJ 3 4 5 pJ 15 A parallel plate capacitor is charged by a battery Now battery is removed and medium between the plates of the capacitor is filled with an insulating material of dielectric constant K then NCERT Pg 85 1 Electric field 22 25 nJ 4 4 5 nJ 17 1 3 Capacitance C decreases value Co to Ca K Both 1 and 2 are correct A parallel plate capacitor with e area 6 x 10 m has plate s 3 mm A 3 mm thick mica shee constant K 6 was inserted plates If this capacitor is c 100 volt supply what is charg plate of capacitor INC 1 1 92 10 C 3 4 2 10 C 12110 4 4 3 18 Equivalent capacitance of across points A and B is HI 100 pF 200 pF 200 pF 2021 09 08 23 31

3 Equivalent capacitance of the network across points A and B is 1 200 pF 3 100 pF AL CAMERA 11 100 pF 11 200 pF HH 16 200 pF 200 pF A B V NCERT Pg 90 2 150 pF 4 700 pF safety we should like t 20 of dielectric stre area of plate is capacitance of 60 pF3 1 1 2 106 m 2 4 75 x 10 m 31 88 10 m 4 5 65 x 103 m

3 Lass 14 A 900 pF parallel plate capacitor is charged dielectric insulating material by 100 V ideal battery The space between the plates is 1cm How much electrostatic energy is stored per unit volume of empty space of capacitor NCERT Pg 82 omallin NCERT Pg 85 Electric field due to charged plates induces a net dipole moment in the 4 42 4 42 10 4 Jm 3 2 8 85 10 6 Jm 3 3 2 21 10 7 Jm 3 14 6 2x106Jm 3 mater Net potential difference between the plates is reduced electric field is discontinuous across the e of a charged conductor but electric tal is continuous over the surface The ement is T 1 2 1 2 Two char 2021 09 08 23

7 A thin metallic spherical shell carries a charge Q on it A point charge q is placed at the centre of the shell and another charge q is placed outside it as shown in figure All the three charges are positive The force on the charge at the centre is O 1 Towards left 2 Towards right 3 Upward 4 Zero

21 In the arrangement the value of each capacitor is Xu F Then the equivalent capacitance between point a and c is In uF 1 3 8063 InslevIL 12X 7 7X 12 HH C 2 4 6X 5 4X 3 ni 01

Two identical capacitors 1 and 2 are connected in series The capacitor 2 contains a dielectric slab of constant k as shown They are connected to a battery of emf vo volt The dielectric slab is then removed Let Q and Q be the charge stored in capacitor before removing the slab and Q and Q be the values after removing the slab Then 0 an Q k 1 k 1 Q 3 1 2700 Q K 1 O Vo 0 2 Q Q2 4 dimo fo Q k 1 2 Q k

A capacitor of capacitance 500 F is connected to a battery through a 10k resistor The charge stored on capacitor in the first 5 seconds is larger than the charge stored in the next A 50 sec B 500 sec C 5 sec OD all of the above

A conductor is made of an isotropic material resistivity p has rectangular cross section Horizontal dimension of the rectangle decreases linearly from 2x at one end to x at the other end and vertical dimension increases from y to 2y as shown in figure Length of the conduction along the axis is equal to l A battery is connected across this conduction between the two rectangular faces Then 2 2y A resistance of the conductor is equal t50 pl 2xy B rate of generation of heat per unit length is maximum at middle cross section C drift velocity of conduction electrons is minimum at middle section

6 Resistance of each part is R and resistance of circumferece is negligible as shown in figure Find the equivalent resistance across AB A is the common centre of both circles A 3R C 3R 4 www 7 B B 3R 2 D 3R 16

ductance coil are connected in 201 A capacito 35 separate AC circuits with a bulb glowing in both the circuits The bulb glows more brightly when a an iron rod is introduced into the inductance coil b the number of turns in the inductance coil is separation between the plates of the capacitor is d a dielectric is introduced into the gap between the plates of the capacitor Karnataka CET 201 AC Voltage Appul ed Fur res

Q7 For the circuit shown which of the following state ments is true 1999 S V 30V S3 V2 20V C 2 F C 3 F S2 A with S closed V 15 V V 20 V B with S3 closed V V 25 V C with S and S2 closed V V 0 T with S and S closed V 30 V V 20 V

7 Which of the following characteristics of electrons determines the current in a conductor O Thermal velocity alone O Both drift and thermal velocity O Drift velocity alone ONeither drift not thermal velocity

12 identical capacitors are connected in series between two points Out of these for n capacitors the spacing between the plates is reduced to half and for the remaining it is doubled What is the value of n for which the effective capacitance remains uncharged

When two or more capacitors are connected in parallel across a potential difference O All of the above choices are correct O the potential difference across each capacitor is the same O each capacitor carries the same amount of charge O the equivalent capacitance of the combination is less than the capacitance of any of the capacitors O None of the above choices are correct

For the circuit shown in figure equivalent capacitance between A and Bis 2C Answer 00 01 C C HH 2C 02 20 03 B 04 05 260 Find n 7n 06 07

A parallel plate capacitor is charged and then charging battery is disconnected If the plates are now pulled apart with insulated handles The capacitance increases Potential energy decreases Potential difference increases Charge and potential difference both remains same

V Find heat dissipated in the circuit after switch S is closed C o 112cv2 2 NIW 3232cv2 2 S 2V C hr V 3

A battery of e m f E and internal resistance r is connected to a variable extern resistance R i Find the value of R so that a current in the circuit is maximu and b terminal potential across the battery is maximum ii Find the maximum value of current in case a and maximum terminal potential difference in case b

In the circuit shown in figure C 1 F and C 2 F Capacitor C is charged to 100 V and C2 is charged to 20 V After charging they are connected as shown S C S2 C DEE 100 V 20 V S3 When S is closed no charge flows through S When S and S2 are closed together no charge flows through the switch S When all the three switches are closed 80 c charge flows through the switch s When all the three switches are closed both the capacitors lose energy

Two identical parallel plate capacitors 1 and 2 are placed vertically and connected in series to a battery In capacitor 2 there is a charged small particle attache by a thin wire to a fixed point as shown ignore the effect of the charge particle on the charge distribution of the capacitor plates At equilibrium the angle between the wire and the vertical direction is a Now slowly we will pull a plate of capacitor 1 until the distance between its two plates is doubled After equilibrium angle between the wire and the vertical direction is HHN 1 2 A tan tana 101

28 One plate of a capacitor is connected to a spring as shown in figure Area of both the plates is A In steady state separation between the plates 0 8 d spring was unstretched and the distance between the plates was d when the capacitor was uncharged The force constant of the spring is approximately a 4 80AE d 9 3 b 280AE hod 680E Ad3 Toswiad d is c E E0AE3 2d3 00000

In a parallel plate capacitor the separation between the plates is 3mm with air between them Now a 1mm thick layer of a material of dielectric constant 2 is introduced between the plates due to which the capacity increases In order to bring its capacity to the original value the separation between the plates must be made 1 1 5 mm 2 2 5 mm 3 3 5 mm 4 4 5 mm

The metallic plates of same areas shown in figure with their charges Q 5Q 10Q A B C The final charges on inner and outer surfaces of plate Care respectively B 5Q 5Q 7Q 3Q 6Q 4Q 80 20

In the circuit shown in the figure C C C and capacitor C is having initial charge Q The switch is closed at t 0 Which of the following options are correct A The current at time t through the circuit will be RC 21 RC B The charge on capacitor C at time t will be 1 e 2 RC C The charge on the capacitor C at time t will be 1 21 R D Total heat loss in the process of charge transfer will be 8C R www C

Three identical metal plates of area S are at equal distances b as shown Initially metal plate A is uncharged while metal plates B and C have respective charges Q and Q as shown Metal plates A and C are connected by switch K through a resistor of resistance R The key K is closed at time t 0 A R B

Current through the battery in the circuit shown in the figure A immediately after the switch S is closed is e R B immediately after the switch S is closed is 2R C after long time is 2R D after long time is 3 4R R C R C www H R wwwww R C HH C

5 12 te The particles P shown in figure has a mass of 10 mg and a charge of 0 01 surface area 100 cm on one side What potential difference V in mV should be applied to combination to hold the particle P in equilibrium 0 04 F P 0 04 F

20 180 A combination of parallel plate capacitors is maintained at a certain potential difference when a 3 mm thick slab is introduced between all the plates then to maintain the same potential difference the distance between the plates is increased by 2 4 mm The dielectric constant of the slab is A 6 5 C HH C B

A cylindrical capacitor has two co axial cylinders of length 20 cm and radii 2r and r Inner cylinder is given a charge 10 C and outer cylinder a charge of 10 C The potential difference between the two cylinders will be 0 1 In 2 4TE 1 VOL Fm V 10 In 2 my 2 In 2 4 E mV 0 01 In 2 mV

The circuit shown in the diagram is in steady state with the switch open When th switch is closed which of the following will not change immediately 3 R mmmmm L R A Potential difference across capacitor C B Current through the inductor L C Potential difference across resistance R D Current through the resistance R 2 C R 2

31 Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure Capacitor 2 contains a dielectric slab of dielectric constant K as shown Qand Q2 are the charges stored in the capacitors Now the dielectric slab is removed and the corresponding charges are Q 1 and Q 2 Then a c Q K 1 Q Q 2 Q K K 1 2K 1 15 E 2 b Q 2 K 1 Q 2 d Q 1 K Q 2

If V denotes the potential difference across the plates of a capacitor of capacitance C the dimensions of CV are This question includes concepts from 12th syllabus 1 Not expressible in MLT 2 MLT 3 M LT 1 0 MI T 2

5 Three conducting spheres A B and C are as shown in figure The radii of the spheres are a b and c respectively A and B are connected by a conducting wire The capacity of the system is B C 0000 J 03264 TU

37 The ratio between the energy stored in 5 F capacitor to the 4uF capacitor in the given circuit is a 1 2 c 1 25 552 ww Q 4 F www 10V 202 5 F www 402 b 1 d 3 6