Capacitors Questions and Answers

In a parallel plate capacitor the distance between the plates is 10 cm Two dielectric slabs of thickness 5 cm each and dielectric constant K 2 and K 4 respectively are inserted between the plates A potential of 100 V is applied across the capacitor as shown in the figure The value of the net bound surface charge density at the interface of the two dielectrics is 10 cm 1 Question Type Single Correct Type 2000 3 0 K 4 K 2 1000 100 V

If a slab of insulating material 4 x 103 m thick is introduced between the plates of a parallel plate capacitor the separation between plates has to be increased by 3 5 x 10 3 m to restore the capacity to original value The dielectric constant of the material will be a 6 b 8 c 10 d 12

A 7 5 F capacitor that is initially uncharged is connected in series with a 1 4 MQ resistor and an emf source with 18 V with negligible internal resistance a Just after the circuit is completed means switched on what is the current in UA through the resistor b Find the maximum charge in uC that will appear on the capacitor a long time after the circuit is completed after many time constants c How long in seconds does it take for the charge on the capacitor plates to build up to 54 C

For the capacitor network shown in the figure below the potential difference across ab is V40 V The capacitors have values C 6 nF and C 22 nF C C a b a Calculate the total energy in J stored in the network b Calculate the energy in UJ stored in the capacitor C 22 nF c Calculate the potential difference in Volts across the capacitor C 6 nF

A parallel plate capacitor has plates of are A separated by distance d between them It i filled with a dielectric which has a dielectri constant that varies as k x K 1 ax wher x is the distance measured from one of the plates If ad 1 the total capacitance of th system is best given by the expression 1 AKEO ad 1 d 2 AEK

An infinite number of point charges each carrying 14C charge are placed along the y axis at y 1 m 2 m 4 m 8 m The total force on a 1C point charge placed at the origin is x 10 N The value of x to the nearest integer is mathongo Take 9 10 Nm C 4x60 mathongo mothongo mathong

A parallel plate capacitor whose capacitance C is 14pF is charged by a battery to a potential difference methongo V 12 V between its plates The charging battery is now disconnected and a porcelin plate with k 7 is inserted between the plates then the plate would oscillate back and forth between the plates with a constant mechanical energy of pJ mathongo Assume no friction mothongo mothongo mothongo

For changing the capacitance of a given parallel plate capacitor a dielectric material of dielectric constant K is used which has the same area as the plates of the capacitor The thickness of the mathonijo mathongo dielectric slab isd where d is the separation mathongo mathonge between the plates of parallel plate capacitor The new capacitance C in terms of original capacitance Co is given by the following relation mathango 3 K 1 C Co 4K 4 K 2 C Co 3 C Co 4K mat 4 C 4 Ca mathongo mathongo mathongo mathongo mathongs mathango mathongo mathongo mathongo mathongo mathongo mathongo mathongo y mathongo

4 Initially the capacitor is charged to a potential of 5 V and then connected to position 1 with the shown polarity for 1 s After 1 s it is connected across the inductor at position 2 2 100 2 1 www E 10 V 10 F 0000000 L 25 mH a Find the potential across the capacitor after 1 s of its connection to position 1 b Find the maximum current flowing in the L C circuit when capacitor is connected across the inductor Also find the frequency of LC oscillations

When a capacitor of value 200 uF charged to 200V is discharged separately through resistance of 2 ohms and 8 ohms then heat produced in joule will respectively be 1 4 and 16 3 4 and 8 2 16 and 4 4 4 and 4

4 If an AC ammeter an AC voltmeter and a resistor are connected in series and the combination is connected across an AC voltage source the instruments read A and V respectively The instruments are purely resistive in nature If a capacitor is now connected across the voltmeter a both A and V will increase b both A and V will decrease c A will decrease V will increase d A will increase V will decrease A circuit shown consists of two resistances R and R of equal and fixed

Four concentric conducting spherical shell A B C D having radius R 2R 3R 4R respectively as shown in figure Shell B C are connected by thin conducting wire Then calculate the capacitance of this system between shell A shell D 48 HE OR ANS 5 3RI 4R D

A 4 0 F parallel plate capacitor is connected to a 5 V battery The work done by an external agent to slowly increase the separation between the plates to double of its original value is 25 J 20 J

The figure for this problem shows a planar circuit containing five 5 capacitors having capacitances C 10 nF C 20 nF C3 30 nF C4 40 nF and C5 50 nF along with three ideal batteries having emfs 1 100 V 2 200 V and 3 600 V F a C C HE 1 1 HH 2 4 2 C3 HH C5 A circuit having 5 capacitors and 3 batteries 5 1 3 b Ez

The capacitance C of a capacitor is 1 independent of the charge and potential of the capacitor 2 dependent on the charge and independent of potential 3 independent of the geometrical configuration of the capacitor 4 independent of the dielectric medium between the two conducting surfaces of the capacitor

Calculate the charge on each capacitor in the steady state When capacitor is fully charged no current will flow through it Solution current in the circuit will be I 10 1 4 2 A voltage drop across 4 2 resistance is V IR 2 x 4 8 V This voltage will get divided between the two capacitors So voltage across each capacitor is Ve 4V charge on each capacitor Q CV 4 x3 x 106 C 12 C 3 F TH 402 3 F 4H Toult 4C w

d 61 A parallel plate capacitor having area A and separated by distance d is filled by copper plate of thickness b The new capacity is C E Area 3 2 A d c b d E A 2d 2E A 66 d b allel plate capacitor of capacitance 5 F and 67

c d d 28 A b d 62 A parallel plate capacitor of capacitance 5 F and 67 plate separation 6 cm is connected to a 1 V battery and charged A dielectric of dielectric constant 4 and thickness 4 cm is introduced between the plates of the capacitor The additional charge that flows into

c 5 C 63 A slab of material of dielectric constant K has the same area A as the plates of a parallel plate capacitor and has thickness d where is the separation of the plates The change in capacitance when the slab is inserted between the plates is a C A K 3 EA 2K c C CoA K b C 50 d K 3 C 04 X 3 EA K d COMBINATION OF CAPACITORS d C A4K d K 3 69 70

31 An inductor is connected to a direct voltage source through a switch Now 1 Very large emf is induced in inductor when switch is closed 2 Larger emf is induced when switch is opened 3 Large emf is induced whether switch is closed or opened 4 No emf is induced whether switch is closed or opened

second option in this cas in 1 marks Selecting any incorrect option s second option in this case with or without selection of any correct option s will result in 2 m Inside a parallel plate capacitor of capacitance C without dielectrics dielectrics are filled which have dielectric constant k and k2 such that k k2 The capacitor is now connected to a battery of voltage V then e K K C 2 New capacitance of the capacitor will be Field in dielectric 1 will be more than the field in dielectric 2 Surface charge density on the capacitor plates will be uniform Field in both the dielectric regions will be the same K A 2 K A 2

a 38 Four identical metallic plates are arranged very close and parallel to each other as shown in the figure Plates A and D are connected across voltage source which maintains potential of plate A higher than that A of D by an amount Vo Plates B and C are connected by a short conducting wire for a while and then the wire is removed Now the voltage source is removed and then plates A and D are connected by another short conducting wire Find potential differences between the pairs A B A C and B D VA VB V VA VC V VB VD Vo 6 D

In the given circuit find the charge on C C C3 C4 and C A battery is connected as shown in the figure V 10v A C C 2 f HH C 4uf C 10uf HH 4 f 2 f Co B H Select the correct options A The charge on C 10 C B The charge on C 20 C C The charge on C zero C I D J E C 2 f

In the given circuit diagram on closing the switch S C A work done by battery is CV B Heat generated in the circuit is C work done by battery is CV CV D heat generated in the circuit is CV

2 35 A 600 pF capacitor is charged by a 200 V supply It is then disconnected from the suppl and is connected the another uncharged 600 pF capacitor How much electrostatic energy lost in the process

In the given circuit initially switch S is closed and S and S3 are open after charging of capacitor at t 0 S is open and S and S3 are closed If the relation between inductance capacitance and resistance is L 4CR2 then find the time in sec after which current passing through capacitor and inductor will be same given R In 2 m2 L 2mH 0000000 L 2 R mim

A circuit is shown in the figure The charge on the capacitor at time t 5RC In 2 if switch K is closed at time t 0 sec is initially capacitor was fully uncharged Given CE 240 C R www R R www R

1 OA 2 OB 3 OC 4 OD 31 The effective capacitance between the points P an Q of the arrangement shown in the figure is Po 2uF 1 F 3 QUE 2 F 5 F 2 F 1 F HH 2 F l F 2 1 F Q

2 Four condensers are joined as shown in the adjoining figure The capacity of each is 8 F The equivalent capacity between the points A and B will be A HHH B 4 16 uF

A4 70 F capacitor that is initially uncharged is connected in series with a 5 00 kn resistor and an emf source with 150 V negligible internal resistance Part C Just after the circuit is completed what is the charge on the capacitor VAE 4

7 Two capacitors of capacitances 3uF and 6 F are charged to a potential of 12V each They are now connected to each other with the positive plate of each joined to the negative plate of the other The potential difference across each will be 1 6 V 2 4 V 3 3 V 4 zero

23 Four identical capacitors are connected as shown in diagram When a battery of 6V is connected between A and B the charge stored is found to be 1 5 C The value of C is 1 2 5 F C C C C 2 15 F

31 Three capacitors each of capacitance 9 pF are connected in series a What is the total capacitance of the combination b Determine the charge on each capacitor if the combination is connected to 120 V supply

In the figure shown the total resistance is 30 k0 and battery s emf is V If the time constant to be 12 0 s calculate a the total capacitance of the circuit b the maximum charge to capacitor to acquire c What is voltage across the capacitor at the instant the voltage across the resistor is 12 V d What is the current in the circuit expected to be at this instantand e What is the time it takes for the voltage across the resistor to reach 12 0 V after the switch is closed R www 8

3 C C E 4 Zero As shown in figure very thin sheet of aluminium is placed between plates of capacitor What wil happen to capacity of capacitor 1 Will increase 2 Will decrease 3 Remains unchanged Al strip or decrease

The switch is closed at t 0 in the adjoining circuit Which of the following is correct Initially capacitor is uncharged X R R Y R Z A The potential difference across YZ just after S is closed is 2E 3 B The potential difference across XY at t is E2 C The potential difference across YZ just after S is closed is E 2 D The potential difference across XY att is 2E 3

Two conductors are separated by a distance of 1cm in air The dielectric strength of air is about3 x 106Vm 1 What maximum safe potential difference can be applied across conductors A 2 10 V B 6 104V C 3 104V D 1 5 10 V

Two conducting spheres of radius a and 2a having charge Q and Q are separated by d a then Choose correct statement s Q d 2a A Potential difference between spheres is B Potential difference between spheres is C Capacitance of given arrangement is Q 4 La 3 4me 2a d 4 3 2 2a d 4 TE D Capacitance of given arrangement is 1 d 1 2 D 21 4

1 Capacitor of given system is C Find the capacitance if dielectric is removed A is the area of plate K dielectric constant 4 A C C Im Ulm 2 3 B C D C A 3 K 2 d

Suppose the parallel plates in figure each have an area of 0 2 m 2 and are 0 01m apart We connect the capacitor to a power supply charge it to a potential difference VO 3 kV and disconnect the power supply We then insert a sheet of insulating plastic material between the plates completely filling the space between them We find that the potential difference decreases to 1 00 kV while the charge on each capacitor plate remains constant Find the capacitance C in picoFarads units only after the dielectric is inserted Vacuum 0 Dielectric 0 0 Eo 0 0 0 E 0 Infand charges b 0

A 5 F capacitor is charged fully by a 220V supply It is then disconnected from the supply and is connected in series to another uncharged 2 5 F capacitor If the energy change during the charge redistribution is J then value of X to the nearest integer is 100

a Using Gauss law derive the expression for capacitance per unit length of an infinite straight coaxial cable with inner radius a and outer radius b Dielectric is air Sketch the electric field everywhere inside and outside the coaxial cable

Example 64 Five identical capacitor plates each of area A are arranged such that the adjacent plates are at distance d apart The plates are connected to a source of emf V as shown in Fig 2 78 Find the charges on the various plates IIT 84 B 1 2 3 4 5 A V

Example 42 The negative plate of a parallel plate capacitor is given a charge of 20 108 C Find the charges appearing on the four surfaces of the capacitor plates 2 51 lot the

21 An isolated spherical capacitor having radius 18cm Find its capacitance and energy stored if a potential of 100V is applied on it 22 Find the capacitance of a parallel plate capacitor having plate area 20cm separation

Two capacitor of capacitance 3 F and 1 F ha break down voltage 2 kV and 5 kV If capacitance are connected in series then what will be breal down voltage of combination 1 2 kV 3 5 kV 20 3 4 7 kV 2 kV

132 A light bulb a capacitor and a battery are connected together as shown here with switch S initially open When the switch S is closed then which one of the following is true Q 137 13 S a the bulb will light up for an instant when the capacitor starts charging b the bulb will light up when the capacitor is fully charged c the bulb will not light up at all d the bulb will light up and go off at regular intervals

ics as ation d k Four plates of the same area of cross section are joined as shown in the figure The distance between each plate is d The equivalent capacity across A and B will be 1 2 2 d 3 34 3e A B

Four plates of equal area A are separated by equal distances d and are arranged as shown in the figure The equivalent capacity is A 1 A d 3gA De 450A 3 d 4 A B 5 In res 1 2 3

Four capacitors of each of capacity 3 uF are connected as shown in the adjoining figure The ratio of equivalent capacitance between A and B and between A and C will be HK 1 4 3 2 3 4 3 2 3 4 3 2 HH B C