Capacitors Questions and Answers

c 2 C X 14 Four capacitors are connected as shown in the figure Their capacities are indicated in the figure The effective capacitance between points x and y is in uF 1 F 1uf w 0 0 0 d 2 16 MIR 1 F HH 2 f In cap Bi 1 2 3 18

4 2 15 A 10 uF capacitor and a 20 F capacitor are connected in series across a 200 V supply line The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied What is the potential difference across each capacitor 1 400V 2 500 V 3 400 V 4 200 V are com 1 9 2 G 3 2

21 Three capacitors each of capacity 4 F are to be connected in such a way that the effective capacitance is 6 F This can be done by 1 Connecting them in parallel 2 Connecting two in series and one in parallel 3 Connecting two in parallel and one in series 4 Connecting all of them in series

A heart defibrillator delivers 360 J of energy by discharging a capacitor initially at 3 kV What is its capacitance Select one O 1 08 KF O 0 08 mF O 0 8 F O 0 12 F

An axon is the relatively long tail like part of a neuron or nerve cell The outer surface of the axon membrane dielectric constant 2 thickness 9 nm is charged positively and the inner portion is charged negatively Thus the membrane is a kind of capacitor Assuming that the membrane acts like a parallel plate capacitor with a plate area of 0 06 cm2 what is its capacitance Choose one answer O 0 118 F O 1 18 mF O 118 pF O 11 8 nF

5 A capacitor of capacitance 12 0 F is joined to an AC source of frequency 200 Hz The rms current in the circui is 2 00 A a Find the rms voltage across the capacitor b Find the average energy stored in the electric field between the plates of the capacitor

4 A spherical drop of capacitance 1 uF is broken into eight drops of equal radius Then the capacitance of each small drop is 1 AIIMS 2012 a 2 1 b F 0 HF F d 8 F itor having capacity of 2 F is charged to for are

A metal plate of thickness half the plate separation is introduced between the plates of parallel plate capacitor The capacitance a remains unchanged c gets halved b gets doubled d becomes infinite

7 After the switch S shown in Figure A is closed there is current i through resistance R Figure B indicates current variation curves a b c and d for four sets of values of R and capacitance C 1 R and Co 2 2R and Co 3 R and 2C 4 2R and 2C Which set goes with which curve So R www Figure A C 1 a 1 b 3 c 2 d 4 2 a 2 b 4 c 1 d 3 3 a 4 b 2 c 1 d 3 C a Figure B

The two plates of a capacitor of capacitance C are given charges Q and Q This capacitor is connected across a resistance R as shown key is closed at t 0 Find the charges on the plates after time t Q1 Q2 C K R Q Q Q Q e 2 2 Q Q A Total charge of the right plate 92 B Total charge on the left plate q Q Q 2 C Initial potential difference across the plates is given by D Initial potential difference across the plates is given by e Q Q 2C Q Q 2C

Assume initially all the capacitors are uncharged 2 F All 492 10V 10 92 292 62 4 F B At steady state charge on capacitor A is zero YOUR ANSWER At steady state charge on capacitor B is zero At steady state charge on capacitor B is 40 C YOUR ANSWER

A capacitor is charged with a di electric slab in the space between the plates of capacitor The battery is disconnected and the di electric slab is pulled out of the space Then the force of capacitor upon slab 1 Remains constant 2 Increases 3 Decreases 4 First increases then decreases

A small charged particle q lies at the centre of two concentric conducting hollow spheres finner radii R and 5R and outer radil 3R and 7R respectively Then which of the following is are CORRECT Kq2 A The energy stored in the space between 3R to 5R cavity is B The energy stored in the space between 3R to 5R cavity is 15R Kq 30R 30 Ke C The amount of work has to be performed to slowly transfer the charge q from centre through the orifice to infinity is D The amount of work has to be performed to slowly transfer the charge q from centre through the orifice to infinity is Your Answer A Answer A C 105 R 38 Ko 210 R 38 Fuera Juara Solution Work performed 22 35R

10 Between conductive parallel plates a point particle with q charge is moved along the KLMN path Accordingly which of the following statements are correct 1 Work done on KL and LM paths are equal II Work done on KL and MN paths are equal III Along the way the electrical potential energy of the particle increases NOTE The zone between the plates is equally divided in x and y directions a b d e N M IN Only Only Ill I and II II and lit Only Il

i A parallel plate capacitor of plate area A 10 2m and plate separation d 10 2m is charged to V 100V Then after removing the charging battery a slab of insulating material of thickness b 0 5 10 2m and dielectric constant k 7 is inserted between the plates Calculate the free charge on the plates of the capacitor electric field intensity in air electric field intensity in the dielectric potential difference between the plates and capacitance with dielectric present between plates 16 F

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric slab as shown What is the capacitance of the arrangement 1 2 3 A ON A 2 K K 3 A 2 K 1 d 3 K A 4 d 4 K A 3 d K 1 A K d

101 When a potential difference of 10 V is applied between A and B a charge of 0 75 mC is stored in the system of capacitors as shown The value of Cis in F 1 a b 2 c 2 5 d 3 2 10 V B 2 uF CuF 2 F 46 1H 2 F

1 Three concentric thin spherical shells are of radii a b c a b c The first and third shells are connected by a fine wire through a small hole in the second and the second is connected to earth through a small hole in the third as shown in figure 2 74 Find the capacitance of this system 41 ab c b a c h Figure 2 74 viii capa Wha 6 G

2 2 The capacitance of a parallel plate capacitor with plate area A and separation d is C The space between the plates in filled with two wedges of dielectric constants K and K respectively figure 2 280 Find the capacitance of resulting capacitor

the following is are CORRECT K Sr Super 60 All haitanya IIT Academy 4 Space for rough work 5R 16 05 2021 Sr Super60 All Jee Adv 2019 P2 GTA 05 Q P Page 3 3R centre through the orifice to infinity is Kq A The energy stored in the space between 3R to 5R cavity is 15R Kq B The energy stored in the space between 3R to 5R cavity is 30R C The amount of work has to be performed to slowly transfer the charge q from 38 Kq 105 R

2 19 The space between the plates of a parallel plate air Vcapacitor is filled with an isotropic dielectric medium of which dielectric constant varies in the direction perpendicular to the plates according to the relation given as k k 1 sin TC d S Where d is the separation between the plates and k is a constant The area of the plates is A Determine the capacitance of the capacitor slog

Two parallel plate of area A are separated by two different dielectrics as shown in figure The net capacitance is 1 2 Question Type Single Correct Type 3 4 0A 3d 3 A 4d K 1 K 2 2 A d 2 4 2

The energy required from a battery to charge a parallel plate condenser of plate separation d and plate area of cross section A such that the surface charge density on the plate will be o is Question Type Single Correct Type 1 2 3 Ao d 2 Ao d o d 2 Afg

Figure shows a solid metal sphere of radius a surrounded by a concentric thin metal shell of radius 2a Initially both are having charges Q each When the two are connected by a conducting wire as shown in KQ a figure then amount of heat produced in this process will be Find the value of 2

Bonus Problem 2 points The voltage shown is applied across a 0 2 F capacitor Draw the current flowing throug the capacitor as a function of time for the period from 0 to 6 seconds i t A 1 V 10 5 H 2 f 9 8 t s 2 4 6 8

2 6 A capacitor is charged until its stored energy is 3J and then the charging battery is removed Now another uncharged capacitor is connected across it and it is found that charge is distributed equally in the two capacitors The final value of total energy stored in the electric fields is ST A 1 5 J B 3J C 2 5 J D 2J

2 8 A capacitor of capacitance of 2uF is charged to a potential difference of 200V after disconnecting from the battery it is connected in parallel with another uncharged capacitor The final common potential is 20V then the capacitance of second capacitor is A 2 F C 18 F B 4 F D 16 F

are connected 2 42 Six capacitors each of capacitance of 2 F as shown in the figure 2 260 The effective capacitance between A and B is A 12 F C 3 F C Figure 2 260 An B 8 3 F D 6 F B

70 Three plates A B and C each of area A 0 1 m are separated by 0 885 mm B from each other as shown in the C figure A 10 V battery is used to charge the system The energy stored in the system is a 1 J c 10 J b 10 1 d 10 3 J MJ 10V

59 Two capacitors having capacitances 8 F and 16 F have breaking voltages 20V and 80V They are combined in series The maximum charge they can store individually in the combination is a 160 C c 320 C b 200 C d 480 C

A parallel plate capacitor is charged and then disconnected from charging battery If the plates are allowed to move little closer by means of an insulating handle then The energy stored in capacitor increases Capacity of capacitor increases Charge on capacitor increases Potential difference across the capacitor increases

2 21 Find the capacitance between the inner and outer curved cylindrical conductor surface as shown in figure 2 248 Space between conductor surface is filled with dielectric of dielectric constant k Consider b R A C khRa b EnkhRa 2b R Ja Figure 2 248 B D kbRa h EnkbRa 2h b

Two capacitors of capacities C and 4C are charged to potential of V and 2V respectively Now these capacitors are connected to each other by joining plates with opposite polarities positive of one to negative of other and vice versa The amount of heat loss is 25 cv 96 cv 18 CV

A metal sphere of radius r 10 cm is placed concentrically inside another thin metal hollow sphere of radius R 20 cm Both spheres are separated from one another The inner sphere is earthed by a long wire through an opening of the outer sphere See Fig 4 4 If the outer sphere carries charge Q 10 C find potential V of the outer sphere 1 Given k 9 10 N m C 47E0 R

A charged particle Q is placed at the centre of cube of side length L Another identical charge Q is placed at distance L from first charge shown in figure The electri flux through face ABCD is C Q 2TEOL 2Q TEOL TEOL B Q

9 A charged capacitor when filled with a dielectric K 3 has charge Qo voltage Vo and field Eo If the dielectric is replaced with another one having K 9 the new values of charge voltage and field will be respectively a 3Q 3V 3Eo Vo c Qo 3E0 b Qo 3V 3Eo Qo Yo Eo Jen

1 A capacitor of capacitance 3 F is charged 20 pc Now it is connected with three other capacitors as shown in diagram to on 3 F capacitor Final charge is a 12 ec b 8 F c 20 F a 40 F HHH 6PF 6 F 6HF F 3 F

Two capacitors C1 3 F and C2 6 F are connected in series and charged by connecting a battery of voltage V 10v olt in series with them They are then di sconnected from the battery and loose wires are connected together What isth e final charge on each

D 2 2 A capacitor is composed of three parallel conducting plates All three plates are of same area A The first pair of plates are kept a distance d apart and the space between them is filled with a medium of a dielectric The corresponding values for E2 the second pair of plates are d and respectively What is the surface charge density on the middle plate d d A V E1 E2 d d Vo En Figure 2 226 B V1 E2 d d OS SO Friends

ination ectric arged oved 2 32 To form a composite 16 F 1000V capacitor from a supply of identical capacitors marked 8 F 250V we require a minimum number of n capacitors where n is A 2 C 16 B 8 D 32

t 2 28 A variable parallel plate capacitor and an electroscope are connected in parallel to a battery The reading of the electroscope would be decreased by i Increasing the area of overlap of the plates ii Placing a block of paraffin wax between the plates iii Decreasing the distance between the plates iv Decreasing the battery voltage F A Only i ii and iii are correct B Only i and ii are correct C Only ii and iv are correct D Only iv is correct 5 a

Three capacitors are connected to a DC battery with an electric potential difference of V as shown in Figure Given C C C3 1 00 uF 0 60 F 0 40 F a 33 Calculate the equivalent capacitance of the circuit b 33 Find the charge on the C capacitor c 34 Find the voltage across the C capacitor V V 6 00 V C C C3

A parallel plate capacitor of capacitance C without dielectric is filled by dielectric slabs as shown in figure Ther the new capacitance of the capacitor is K 6 A 2 5C 11 3 c 121 1300 K 2 K 4 A 2 d 2

In the given circuit charge Q on the 2 F capacitor changes as C is varied from 1 F to 3 F Q as a function of C is given properly by figures are drawn schematically and are not to scale 1 3 Charge Q l F 3 F A Charge l F 3 F C C 2 4 Q Charge Q A Charge H1 C E 1 F 3 F l F 3 F 1 F HH 2 F C C

Six equal capacitors each of capacitance 10 F are connected as shown in the figure Then the equivalent capacitance between A and B is C a A B 20 F e C f C d HH g C3 HH C5 b h C6

iii Two spherical conductors each of capacity C are charged to potential and V These are then connected by means of a fine wire The loss of energy is Initial Energy of the two V c V 0 Final Energy of the two 2 2 7 20 a zero b 1 2CV c CV d 2 CV

Initially switch S is open in the given circult If switch is closed then to obtain steady state again is S A C 1 Charge 2 Charge 3 Charge B CV 6 CV 6 CV 3 V C HE C flows from A to B flows from B to A flows from B to A

Figure shows two oppositely charged parallel plates that are separated by a distance d 20 cm The electric field between the plates is uniform and has a magnitude E 10 kV m A proton is released from rest at the positive plate Calculate the speed of the proton when it strikes the plate a b NOTE k 9x10 Nm2 C2 lel 1 6x10 19 C mp 1 67x10 27kg E V 0 0 Proton 62 105 m s 31 x 105 m s 6 2 x 10 m s d 31x105 m s UB

Two concentric conducting spheres of radii a and b outer is given a charge and inner is earthed The equivalent capacity of system will be b a ab 1 4 EO b a 3 4 e a b 4 b b a 2 4 4 b

If ring of radius R is placed on smooth floor connected by a string at the top Other end of string is connected to upper plate of capacitor of same mass M and charge density and area A Lower plate of capacitor is rigidly fixed Then which of the following statements are correct if upper plate of capacitor is falling freely with acceleration g Mass M Rigidity fixed plates Ring H Mass M The charge density of plates of capacitor must be Mg o Find the value of n