Capacitors Questions and Answers

A parallel plate capacitor has semi circular plates of radius R and spacing d If the dielectric slab of relative permittivity is rotated through an angle o find the torque required to rotate it with constant angular speed if the voltage is kept constant Ans E 1 0R 1 AJ Er Fig 4 85

28 In the given circuit diagram the potential difference across 12 F capacitor is 1 2 V 3 6 V 2 F HH HH 6 F HH 3 F 12 F F 18 V 2 4 V 4 8 V

1 ch plate is A and separation Area of between consecutive plates is d Emf of the battery connected is V The charge on plate 2 is A Id A V d A V INV 2 2 3 4 2A V d 2A V 122 S 45 A p diel Total sharge and in

In the circuit shown when the switch is closed the capacitor is charged with time constant 7 and when switch is open then capacitor discharge with time constant T then T T is R C HH 1 1 3 2 E R www S 2 1 2 4 1 4

In an oscillating LC circuit the maximum charge on the capacitor is Q The charge on the capacito when the energy is stored equally between the electric and magnetic fields is 2 Q 3 4 Q 1 Q 2 3 Q 2

0 Find the final stored energy in the capacitor 12 www HH 5 F F 2 5V 192 ww R 252 ww 0 59 ww 90 IR C

0 0 A capacitor of capacitance Co is charged to a potential V and then isolated A small capacitor C is then charged from Co discharged and charged again the process being repeated 10 times The potential of the capacitor Co has now fallen to V Calculate C

spherical capacitor half space is completely filled with a liquid dielectric Find the 1b 28 Fig 4 80 a capacitance b ratio of charge densities in the regions 1 and 2 on the conductors c total charge on the capacitor d charge induced on the liquid dielectric e energy stored in the capacitor f ratio of radial electric fields in medium 1 and 2 at same

28 A portion of electrical network is as shown in figure The energy stored in the capacitor is 11A 1 12 J 2A M 19 202 2uFT 592 22 12 72 1 A 2 288 J TAY 19 75

3 An infinite ladder is constructed by connecting several sections of 2 F 4 F capacitor combination as shown in figure It is terminated by a capacitor of capacitance C What value should be chosen for C such that the equivalent capacitance of the ladder between points A and B becomes independent of the number of sections in between 4 F A 2 F 4 F HH 2 F 2 F 4 F HH C

122 Consider the circuit shown in the figure below All the resistors are identical The charge stored in the capacitor once it is fully charged is a 0 2 c CV www 5 b C 13 LC wwwwww 5 CV wwww www www KVPY 2013

3 For the circuit shown below when the switch S is closed then the total amount of charge that flows from point a to point b through the switch is 1 84 C 12 F HH ww 60 9V b 4 F HH a 35 2 99 C

Two conducting spheres of radii r and 2r are placed at very large separation Each sphere possesses charge Q These spheres are connected with a conducting wire of resistance R Then which of the following is true Q A Initial current is 8 Eo rR B Initial current is 4 Eo rR C Current reduces to half the initial current after time 8 rRln2 8 Eo rR In 2 dunor to half the initial current after time

of these 25 If key k is plugged in given circuit diagram then the charge will 3 A 10 A A B k 11 6 A 11 5 A

Consider a simple RC circuit as shown in Figure 1 Process 1 In the circuit the switch S is closed at t 0 and the capacitor is fully charged to voltage Vo i e charging continues for time T RC In the process some dissipation ED occurs across the resistance R The amount of energy finally stored in the fully charged capacitor is Ec 3 Process 2 In a different process the voltage is first set to and maintained for a charging time 2V0 without discharging the capacitor and again T RC Then the voltage is raised to maintained for a time T RC The process is repeated one more time by raising the voltage to V and the capacitor is charged to the same final voltage Vo as in Process 1 3 These two processes are depicted in Figure 2 www R N www Figure 1 C V Process 1 2V 3 V 3 Process 2 T T RC 2T Figure 2 7 Q 15 In Process 1 the energy stored in the capacitor Ec and heat dissipated across resistance Ep are related by A Ec Ep B Ec Ep In 2 C Ec Ep D Ec 2ED Q 16 In Process 2 total energy dissipated across the resistance Ep is A Ep CV B Ep 3 CV C Ep CV ED

capacitance C for an isolated conducting sphere of radius a is given by 4 a If the sphere enclosed with an earthed concentric sphere The ratio of the radii of the spheres being n then th n 1 capacitance of such a sphere will be increased by a factor n 1 C A n B n n D a n

48 A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V Another capacitor of capacitance 2C is similarly charged to a potential difference 2V The charging battery is then disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other The final energy of the configuration is P x CV the volume of P is

3 30 J 92 The plates of a capacitor of capacitance 10 F are given the charges q 5 C and q2 10 C The potential difference across the plates of the capacitor is 1 0 25 V 3 1 5 V 2 0 5 V 4 3 0 V oporgy stored in the capacitor in the

Five plates each of same area are placed as given in figure The separation between any two consecutive plates is d and capacitance is C then capacitance across AB is 3C 1 300 2 3 5C 2 12 4 5C 3 4C 5 B A

13 What is the time taken for the plates to have 19 If 0 1 increase in length 99 of maximum charge Assume all are same and R 2 C capacitances occurs the percentage incr wire will be R www a 10 75 sec a 0 2 c 1 b 15 4 sec 20 A piece of uniform wire c 10 2 sec through 180 at its mid are twisted together T d none of these a 89 14 A person decides to use his bath tub water to c 19 number density ch generate electric power to run a 40 W bulb The 21 If n e t and m r bath tub is located at a height of 10 m from the ground and it holds 200 litres of water He installs orator on the ground electron and m resistance of a wi section A will be R www E C R d 140 2 R b d

Two identical plates P and P2 of cross sectional area A are A d separated at a very small distance d where Initially charge on the plate P is 10 C and charge on the plate P2 is 30C Now plate P and P2 are connected to positive and negative terminals of battery of potential difference 10 Volts with the help of switches S and S respectively Choose the correct option s A The work done by the battery is 200 J B The net charge on the plate P is 10C C The charge on the left side of the plate P is 10C D The charge on the right side of the plate P2 is 20C 2 SI unit S P 10 V P2 S2

What is the potential difference between A and B in the circuit shown 4 F 2 F 1 2V X B 2 F 4 F 6V 2 4V 3 3V 4 12V

Three capacitors are connected as shown in fig Then the charge on capacitor C is 2 F A 1 6 C 2 12 C 3 18 C 2 F TH C 6V 4 F 6V

ne of these Three large metal plates are arranged as shown How much charge will flow through the key if it is closed A 500 6 3Q 2 C 2Q H LE B 400 4Q D None of these 34

Example 11 An inductor of inductance 2 0 mH is connected across a charged capacitor of capacitance 5 0 F and the resulting L C circuit is set oscillating at its natural frequency Let Q denotes the instantaneous charge on the capacitor and I the current in the circuit It is found that the maximum value of Q is 200 C JEE 1998 a When Q 100 C what is the value of dIl dt b When Q 200 C what is the value of I c Find the maximum value of I d When I is equal to one half of its maximum value what is the value of IQ

A 1 F capacitor is first charged to the potential difference 100 V and then connected across uncharged capacitors C 2 F and C 4 F by closing switches S and S as shown in the adjacent figure The new potential difference across 1 F capacitor is 100 1 t A 7 300 C V 7 V X G 400 B V 7 D 25 V S C 2 F C 4 F 3 HHH 1 F 00 2 L F 3x 200 22 92 200 57 22 40

45 Find the charge on the capacitor C in the following circuit t 7 202 12V 2uF C 622 422 21 30 C Collec

A parallel plate capacitor is connected with a battery The plates are pulled apart with uniform speed If x is the separation between the plates then rate of change of stored energy of capacitor is proportional to A x B x 1 C 1 D 2 38 The charge on capacitor after a long time in the given circuit would be

Three identical parallel conducting plates A B and C are placed as shown open and can connect A and C to earth when closed Q charge is given to B 2d H A If S is closed with S open a charge of amount Q will pass through S B If S is closed with S open a charge of amount Q will pass through S C If S and S are closed together a charge of amount Q 3 will pass through S and a charg amount 20 3 will pass through S D All the above statements are incorrect

When steady state is reached switch S is opened Then the amount of heat rejected by the resistor is 800 K Joule Then find the value of K 1052 12 F H1 M 6 F HI S

6 The potential difference between X and Y in volts is W 1 1 199 222 2AM 3027 2 1 X Y 392 2 2 2 ACO 3 2 4 2

28 The figure shows a capacitor with a metallic block in between its two plates What is the effective capacitance of the combination A 1 ath 28 A 2 ath B 28 A 3 b 4 a b A

38 Charge on capacitors connected in series to a source of e m f is 1 Always same 2 Always different 3 May be different 4 Cannot be predicted

A charge of 1 C is given to one plate of a PPC of capacitance 0 1 F and a charge of 2 C is given to the other plate Find the potential difference developed b w the plates 1 3 V 2 7 V 3 5 V 4 2 V

1 In the circuit shown C 1 F C 3 F in steady state the energy stored in these capacitors are respectively 50 Luf c 1 6 J 18 J 3 6 J 6u 10V 79 5V 6V 8Q 1092 www W 20 13U 12 1 1092 C 3uf Sv 2 18 J 6 J 4 18 I

A charged isolated parallel plate capacitor is fully filled with a slab of dielectric constant K 4 if the plates are pulled apart such that the energy stored is same as the energy before inserting the slab then increase in the distance between the plates will be d separation between the plates 1 d 2 2 2d 3 3 3d 4 4 4d 5

aidi Following figure shows the initial charges on the capacitors After the switch S is closed find The charge on capacitor C A 0 C 10 C S 10 C C 1 F C 1 uF vode as ws Ar 3 0No sonstioso B 5 C 00 10 V Stoolsil C 10 C 90 Ou St A tolijsqs no spiars Alhw TotioG063 C 1 IN usris

Find the potential difference between the plates of the capacitor C in the circuit shown in figure The internal resistances of sources can be neglected 30 2 www www 20 2 4 V A B 11 C 1 V F www 1092

3 ren 4 be zero since circuit will not work Four plates are located of a distance d apart from one another The extreme plates are inter connected A potential difference of V is applied to inner plates The electric field E between 1 and 2 plates is 1 N 1 13 2 V 3 4 V 2V 4

70 When the key K is pressed at time t 0 then which of the following statements about the current in the resistor PQ of given circuit is true 2 V K www 1000 Q 1 F 1 at t 0 1 2 mA and with time it goes to 1 mA 2 oscillates between 1 mA and 2 mA 3 i 2 mA at all t 4 1 mA at all t www 1000

In the adjoining figure four capacitors are shown with their respective capacities and the P D applied The charge and the P D across the 4uF capacitor will be KCET 2012 a 600 C 150 volts b 300 C 75 volts c 800 C 200 volts d 580 C 145 volts 300 Volt H 20 F 12 F 4 F 4uF

14 of material inserted 1 3 2 4 3 2 4 5 A capacitor of capacitance 5 F is charged to 24 V and another capacitor of capacitance 6 F is charged to 12 V a Find the energy stored in each capacitor If the positive plate of the first capacitor is connected to the negative placte of second then find new charges on the capacitors Find the loss of electrostatic energy in this process spac fille of the of

6 A 2 F capacitor is charged as shown in the figure The percentage of its stored energy dissipated after the switch S is turned to position 2 is n The value of n is 1 2 S 2 F 8 F

and B is circuit the potential difference between A JOV 10 10 V 2 F VOIE A 20 V HH v 16 4 F 41 16MC dou C 8 F 8 F H B 4 2 2 5 V L Q2 16 x 8 1

Four capacitors are connected as shown in figure to a 30 V battery Find the potential difference between points and b 1 0 F 1 5 F a HHH H 2 5 F b 11 0 5 F F 30 V

Four identical metallic plates each having area of cross section A are separated by a distance d as shown in the figure Plate 2 is given a charge Q Find the potential difference between 2 3

A capacitor of capacity C is charged to a steady potential difference V and connected in series with an open key and a pure resistor R At time t 0 the key is closed If I current at time t a plot of log I versus t is as shown as A in the graph Later one of the parameters i e V R or C is changed keeping the other two constant and the graph B is recorded Then A C is increased C R is increased B C is reduced D R is reduced log I 1 t

2 A parallel plate capacitor having plate area 400 cm and separation between the plates 1 0 mm is connected to a power supply of 100 V A dielectric slab of thickness 0 5 mm and dielectric constant 5 0 is inserted into the gap a Find the increase in electrostatic energy b If the power supply is now disconnected and the dielectric slab is taken out find the further increase in energy c Why does the energy increase in inserting the slab as well as in taking it out

A parallel plate air capacitor consists of two circular plates of diameter 8 cm At what distance should the plates be held so as to have the same capa citance as that of a sphere of diameter 20 cm

where Figure shows a wire frame PQSTXYZ placed in a time varying maghet sa positive constant Resistance per unit length of the wire is Find the current induced in the wire nd draw its electrical equivalent diagram b B Z T b a B S a