Capacitors Questions and Answers

A slab of material of dielectric cons k has the same area A as the plates of a parallel plate capacitor and has thickness 3 4d where d is the separation of the plates The change in capacitance when the slab is inserted between the plates is

Question 2 A circuit network has capacitors of values 20 F 30 F 40 F and 60 F The 20 F and 30 F capacitors are in series and connected serially to the parallel combination of the 40 F and 60 F capacitors The circuit is supplied by a 30V source a sketch the circuit diagram and the equivalent circuit b find the total charge delivered to the circuit c find the terminal voltages measured across the 20 F 30 F and the 40 F capacitors

In the circuit shown L 18 Hand C F The left hand capacitor was charged to a voltage 20 V and then at t 0 the switch S is closed The time in micro seconds at which voltage on right hand capacitor becomes 5 V is L 1 u T CI T TR5 20 V cal c 3rafRI7 2T ugl7 C 18 Asc Acuz s m Ba 92 g ug m Auka uz acca 5 V L m C

Plz send a new solution I m not getting how to do charge distribution in this questi on plz send a brief handwritten solution Find the capacitance between A and B 5 F 2 F HH 1 7 5 MP 12 F 5 F 4 F 2 F 2 4 F He B

In the circuit shown in figure all three capacitors are initially uncharged In steady state Afy ukgy ah d Fuka mz 4 C 2 F A B Hr 10 V D C 4 F HH C 6 F HH 20 V 10 Charge on C is C Correct Answer Your Answer C 50 C 70 Charge on C is C 70 Charge on C3 is 50 C Correct Answer Your Answer Work done by battery of 10 V is J 100 3 100

F capacitor is charged to 1230 V and a 4 82 F capacitor is charged to 500 V These capacitors are then disconnected from their batteries and the positive plates are now connected to each other and the negative plates are connec to each other What will be the potential difference across each Submit Answer Tries 0 7 What will be the charge on the 2 92 F capacitor Submit Answer Tries 0 7 What will be the charge on the 4 82 F capacitor

Series and parallel capacitors Question 3 A 60V source supplies a 30uF capacitive load which is connected to a parallel combination of 60 F and 30uF capacitors The terminal of the 60 F load is in turn serially connected to 40 F capacitor a sketch the circuit diagram and the equivalent circuit b find the total charge delivered to the circuit c find the terminal voltages measured across the 20 F 30 F and the 40 F capacitors

Two identical metallic small spheres of radius R are placed at very large separation and they are connected by a coil of inductance L having negligible resistance as shown in the figure One of the sphere is given charge Q and then switch S is closed The maximum current through the coil will be Roy ulah ot na yg gaz fuc uz gy am f a tef aqvu gla u m decca L A yg husd zizfia full gc ma 3T i Q faUI TI at are fchui qu 21 us wa mmmmmm mrrrrrrr L A B Q V TEORL Q 8 E RL S

Two capacitors of capacitances C1 and C2 when connected in series across a 60 V battery the energy stored is 1 2 mJ When the same two capacitors are connected in parallel across the same battery the energy stored is 5 4 mJ The capacitances are 1 2 F 3 F 3 1 F 1 F 2 1 F 3 F 4 1 F 2 F

16 Cz F HH cauf C7 F K co F ca F HHH Co F For the system of the capacitors shown in the figure find the equivalent capacitance of the system the charge and voltage on each Then choose the ranking of the capacitors according to the charge they store from smallest to largest 1 2 3 4 5 6 7 Choose the ranking of the capacitors according to the potential differences across them from smallest to largest A B C D E F G Note Same values should be given them same rank Where C1 3 C2 5 C3 7 C4 11 C5 9 C6 12 C7 13 and K 100V

a 10 points The switch has been closed for a long time With the information given below find the current in every resistor b 20 points The switch is opened at t 0 Find the following items i the frequency of oscillation of the circuit ii the maximum charge on the capacitor iii the energy in the circuit at t 0 03 s iv the charge on the capacitor at t 0 03 s Given capacitance of the capacitor 50 F inductance of the inductor 25 mH 492 W ww 1292 18 V 30Q2 M W 15 92 reeer L C

1 A capacitor of capacitance 100 F is charged by connecting it to a battery of voltage 12 V with internal resistance 2 The time after which 99 of the maximum charge is stored on the capacitor is UP CPMT 2015 d 0 54 ms a 0 92 ms b 0 72 ms c 0 34 ms

In the situation shown in figure the switch has been shifted from position 1 to position 2 at t 0 The current in the 3 Q resistor at t 31n2 seconds is found to be x x A find the value of x 11 32 Az zf RA Ruch t 0 1 fa 2 ach fa fa fu ua 1 t 31n2 us 11 3 fauc x Ax 32 C 36 V 403 92 12 V 1202 392 www 250 mF X

3 58 For the circuit shown in the figure 3 352 calculate the charge on capacitor in steady state 192 A 4 C C luc 2 52 3V RU www 6V 292 102 HH 1uF Figure 3 352 B 6 C Bee D Zero 3V www 122 10V 552

2 The figure shows an experimental plot discharging of a capacitor in an R C circuit The time constant t of this circuit lies between Potential difference in volt 380 81 25 20 15 10 LO 5 0 50 Time in second 100 150 200 250 300 a 150 s and 200 s b 0 and 50 s c 50s and 100 s d 100s and 150 c

Two wire transmission lines having a conductor of length of 0 85 km and the two wires are separated by 0 3 m Calculate the capacitance of the line if the diameter of conductor in each transmission line is of 5 cm a 9 48 nF b 9 85 nF c 9 48 F d 9 58 nF

If W amount of heat in J will be generated in the circuit shown in the figure after the switch is shifted from position 1 to position 2 then value of is equal to given that C W 25 2 F e 20 V e 10 V Rua 1 Rua 2 a fa ed R44 304 F e W 25 20 V e C e faz fa GHI HI fe2I TI fah C 2 10 V S 2 1

In the shown circuit all three capacitors are identical and have capacitance C F each Each resistor has resistance of R Q An ideal cell of emf V volts is connected as shown Then the magnitude of potential difference across capacitor C in steady state is R ww C C R R ww C HE ww R R www R

5 A capacitor is made of two circular plates each of radius 7 cm and separated by 2 cm The capacitor is being charged by an external source The charging current is constant and equal to 0 2 A What is the rate of change of potential deference between the plates NCERT Pg 285 1 1 62 x 101 V s 2 2 94 x 1010 V s 3 3 54 x 1010 V s 1 2 21 x 1010 V s

An LCR circuit as shown in the figure is connected to a voltage source V whose frequency can be varied The frequency at which the voltage across the resistor is maximum is A 902 Hz B 143 Hz D 345 Hz C 23 Hz mmm 24H 2 F 1502 Var Vosinot 2013

Three identical capacitors C C and C3 have a capacitance of 1 0 F each and they are uncharged initially They are connected in a circuit as shown in the figure and C is then filled completely with a dielectric material of relative permittivity The cell electromotive force emf Vo 8 V First the switch S is closed while the switch S is kept open When the capacitor C3 is fully charged S is opened and S2 is closed simultaneously When all the capacitors reach equilibrium the charge on C3 is found to be 5 C The value of 10 x ri is a gy ukat C C C3 1 0 m 4 tez qkqy z a 3 Ga f g Ayarfam qudya qef gufa Ha a 1 a fyd d6c da fa Vo 8 V I H u2H Rau Si ph Vo fa s a ad yg de fchu ulla 1 Gd am auka aze sa a C3 42 5 103 r S C C 1 C3 Correct Answer 15

1 A parallel plate capacitor is charged and the charging battery is then disconnected If the plates of the capacitor are moved further apar by means of insulating handles then a The charge on the capacitor increases b The voltage across the plates decreases c The capacitance increases d The electrostatic energy stored in the capacitor increases

17 In an oscillating L C circuit Qm is the maximum charge on the capacitor If at any time the energy stored in capacitor and inductor are equal then charge stored on the capacitor at that instant is NCERT Pg 256 1 3 9 2 22 2 m 4

7 Three large non conducting plane sheets of charge with charge densities o 20 and 30 are arranged as shown The net electric field in region III will be 20 30 1 30 Eo 0 I II III IV towards left 2 4 20 towards left Eos 30 towards rig

18 A series combination of n capacitors each of value C is charged by a source of potential difference 4 V When another parallel combination of n capacitors each of value C is charged by a source of potential difference V it has the same total energy stored in it as the first combination has The value of C in terms of C is then AIPMT Prelims 2010 1 20 0 72 N 2 162 C n 16C

1 5 45 Initially the capacitor in circuit shown in figure 5 347 is of charged to a potential of 5V and then connected to position 1 with the shown polarity for 1s After 1s it is connected across the inductor at position 2 a e 1000 E 10V 2 10mF oooooo L 25mH Figure 5 347 a Find the potential across the capacitor after 1s of its connection to position 1 b Find the maximum current flowing in the LC circuit when capacitor is connected across the inductor Also find the frequency of LC oscillations Ans a 8 16V b 5 16A 10Hz

01 02 03 04 05 06 07 08 09 10 3 English O Mark for review A constant force F is applied on the rod of Mass M and length L placed between two conducting fixed rails in a uniform Magnetic field A capacitor C is connected between the two rails as shown in the diagram Neglecting the resistance of the rod and the rails which of the following statement is incorrect Question Type Single Correct Type

9 A parallel plate capacitor with plate separation of 1 0 cm has square plates each with an area of 6 0 x 10 2 m2 What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2 4 is placed between the plates completely filling them 0 8 85 x 10 12 C2 N m2 OA 15 x 10 12 F OB 15 x 10 14 F OC 64 x 10 14 F OD 1 3 x 10 12 F OE 1 3 x 10 10 F

2 An uncharged capacitor having capacitance C is connected across a battery of emf V Now the battery is disconnected and reconnected across same battery but with reverse polarity then the ratio of total thermal energy produced to the total energy supplied by the battery is 1 3 2 51 2 1 3 3 E

4 A charged capacitor stores energy U Without connecting this capacitor 1 point to anything dielectric having dielectric constant K is now inserted between the plates of the capacitor completely filling the space between them How much energy does the capacitor now OA 2KU OB KU O CU OD U K E U 2K

2 A ale capacitor of area A plate separation d and capacitance C is filled with four dielectric materials having dielectric constants K K K3 and K as shown in the figure below If a single dielectric material is to be used to have the same capacitance C in this capacitor then its dielectric constant K is given by NEET 2016 A 3 c d 2 K 1 1 F 3 K K K3 1 1 a K K K K3 3K4 phi b K K K K3 2K 1 KA K K K K2 A 3 K KA A 3 3 K3 2K4 K3 T d 2 1

3 An ideal parallel plate capacitor consists of a set of two parallel plates of 1 point area A separated by a very small distance d When the capacitor plates carry charges Qand Q the capacitor stores energy UO If the separation between the plates is doubled how much electrical energy is stored in the capacitor OA 4U0 OB 200 OC UO OD U0 2 E U0 4

5 Each plate of a parallel plate air filled capacitor has an area of 0 0020 m2 and the separation of the plates is 0 020 mm An electric field of 3 9 10 6 V m is present between the plates What is the surface charge density on the plates e0 8 85 x 10 12 C2 N m2 OA 35 C m2 OB 73 C m2 OC 17 C m2 OD 52 C m2 OE 87 C m2

1 The charge on the square plates of a parallel plate capacitor is Q The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation which is small compared to the dimensions of the plates The amount of charge on the plates is now equal to OA 4Q OB 20 O c Q OD Q 2 OE Q 4

2 When two or more capacitors are connected in series across a potential 1 point difference O A the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors OB each capacitor carries the same amount of charge O C the equivalent capacitance of the combination is less than the capacitance of any of the capacitors OD All of the above choices are correct OE None of the above choices are correct

What is the energy stored in the capacitor between terminals a and b of the network shown in the figure Capacitance of eache capacitor C 1 F a 12 5 pJ M b c 25 J 10 V LE Zero d 50 J a C C HH C AIIMS 2009 HYSICS HOLIC

5 57 In the circuit shown the key K is closed at t 0 the current through the key at the instant t 10 In 2 is A 2A C 4A ellele 4Q www L 10mH www 652 K 20V 552 w Figure 5 309 502 H C 0 1mF B 8A D Zero

5 The left capacitor is initially charged using a battery of emf 3V and the right capacitor is initially uncharged Find the current in the circuit as a function of t Find the total heat dissipated over a long time interval C 1 F 292 ww Tc 20

Consider the given circuit Initially there is no energy stored in inductor and capacitor At t 0 the switch K is closed R www 1 the current through battery just after closing the key 12 the current through battery after a long time The value of IS V K R www 6000000 L L eller R www

At an instant the current through the 302 resistor is 3A At this instant a Find the charge across the capacitor b Energy of the capacitor c Force that the capacitor plates exert on each other 10 V 1 F 302

9 At an instant the current through the 302 resistor is 3A At this instant a Find the charge across the capacitor b Energy of the capacitor c Force that the capacitor plates exert on each other 10 V 1 F 352

ii a voltmeter reading up to 250 V 16 A hollow sphere has inner and outer radii R and R2 and the resistivity of the material is p Find the resistance between the inner and the outer surface 17 Ten cells of emf 1 5V and internal resistance 10 are connected across a R O resistor

BEGINNER S BOX 4 Figure shows the graph of the current in a discharging circuit of a capacitor through a resistor of resis 10 02 Find the initial potential difference across the capacitor ii Find the capacitance of the capacitor iii Find the total heat produced in the circuit iv Find the time constant of th A A 2 5

8 Four identical plates each of area A on one side are arranged as shown The separation between adjacent plates is d The effective capacitance between a and b is 4 A 3 d 3 A 4 d A 2 d 280 A b

A capacitor of capacitance C is charged with the help of a 200 V battery It is then discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity 2 5 x 102 J kg and mass 0 1 kg If the temperature of the block rises by 0 4 K the value of C is 1 500 F 2 500 uF 4 50 uF

3 44 A capacitor of capacitance C has potential difference E 2 and another capacitor of capacitance 2C is uncharged They are joined to form a closed circuit as shown in the figure 3 396 a Find the current in the circuit at t 0 b Find the charge on C as a function of time Ans a E 2 F C CE 6 HH 2C Figure 3 396 R b 5 2e 31 2RC 2R E R 2C

Co Co Ro Rotating Fixed Plate Ro 38 It is desired to keep current in discharge process of a capacitor constant For the purpose following three schemes a b and c are suggested a In this scheme after closing the switch you have to vary resistance of the rheostat The initial charge on the capacitance Co is go and range of values of resistance of the rheostat is zero to Ro Find the law R t according to which resistance of the rheostat should be changed with time b In this scheme a variable disk capacitor is connected across a fixed resistance Ro After closing the switch you have to vary the capacitance by rotating one of its plates The initial value of capacitance is Co and charge on it is qo Find the law C t according to which capacitance should be changed with time and corresponding angular velocity t of one plate relative to the other c In this scheme a variable capacitor is used in which one plate can be shifted towards or away from the other fixed plate without changing overlap area After closing the switch you have to move the movable plate The initial value of capacitance is Co and charge on it is qo Find the law C t according to which capacitance and the distance x t between the plates should be changed with time

14 An air filled parallel plate capacitor with the plate area A is connected to a battery of electromotive force V and negligible internal resistance One of the plates is made to vibrate so that the distance between the plates varies as d do acos at where a do If instantaneou current in the circuit reaches a maximum value of Io the maximur possible amplitude of vibrations a is a b c alo VA E 1 d VA E d Indo VAWE Indo V AWE

Figure I igure II 17 Two parallel plate capacitors of capacitances C and 2C consisting of Tic plates of identical dimensions are connected with an ideal battery of by terminal voltage V as shown in the figure I Now the capacitor smaller in volume is completely inserted into the larger capacitor and kept in symmetric position and then connection polarities of the plates are reversed as shown in the figure II Which one of the following statements is correct a Charge flown through the battery is 8CV and it absorbs energy b Charge flown through the battery is 8CV and it delivers energy c Charge flown through the battery is 7CV and it absorbs energy d Charge flown through the battery is 7CV and it delivers energy 18 An air filled parallel plate capacitor of capacitance C is connected

42 Two identical parallel plate capacitors are connected as shown in the figure Initially both have total charge qo and separation between their plates xo At an instant plates of one capacitor begin to move towards each other and plates of the other capacitor away from each other If velocity of a plate relative to the other in both the capacitors has the same magnitude v find current in the circuit A circuit consisting of