Capacitors Questions and Answers

8 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 connected to another battery and is charged to potential difference 2V The charging batteries are now 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 25CV a zero b 6 c 3CV 2 d 9CV 2

capacitance Option A B C D D fent for the given capacitor arrangement All the 6 capacitors are of same If a battery is connected across AB all 6 capacitors get charged If a battery is connected across AC all 6 capacitors get charged If a battery is connected across AD all 6 capacitors get charged It is not possible to charge all the 6 capacitors using single source Rate this question

Question No 49 to 52 4 questions In the circuit shown in figure four capacitors are connected to a battery The equivalent capacitance of the circuit is A 25 F B 6 F The charge on the 5 F capacitor is A 60 C B 24 C C 8 4 F C 12 C The potential difference across the 6 F capacitor is A 6V B 4V C 5V The maximum energy is stored in the capacitor of A 10 uF B 6 F C 5 F 10 F 4 F HH 6 F 5 F A D none D 20 C D none B D 4 F Tov

A parallel plate capacitor is made of two dielectric blocks in series One of the blocks has thickness d and dielectric constant K and the other has thickness d and dielectric constant K as shown in figure This arrangement can be thought as a dielectric slab of thickness d d d and effective dielectric constant K The K is a c d d K d K d d d K K d d K d K d b d K d K d K K 2K K K K

A cylindrical air capacitor of length l inner radius R and outer radius 2R is connected to a battery of emf E as shown in figure A particle of charge q and mass m is released from rest from inner surface of capacitor The speed of particle when it reaches to the mid point of plates is

A capacitor of capacitance 400 uF is charged upto a potential of 100 volt and another capacitor of capacitance 600 uF is charged upto a potential of 200 volt The two capacitors are connected in such a way that the positive plates are connected at one point and the negative plates are connected at another point The loss of energy will be 1 24 J 2 12 J 3 1 2 J 4 Zero

HP EXAMPLE Find CAB Sol A C A i CAB a cv C C 5C 3 2 6 C IN B 0 0 00 A B sir jis capacitor ke across potential same hota hai use neglect kyo krte hai jb Cnet nikalte hai 56 74

Four identical plates of parallel to each other at equal distance d as shown in the figure The space between 2nd and 3rd is filled with a dielectric of dielectric constant K 2 The capacitance of the system across terminals A and B is 2 A 1 d 2 Eo A d

For the circuit shown in the diagram considering steady state 7 F A B C D The current is 2 4 A The current I is 4 8A Charge on 7 F capacitor is 126 C Power supplied by 18V battery is 49 2 W 22 www 18V 5 40 www 6V

1 CV 2 A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery The ratio of the energy stored in the capacitor and the work done by the battery will be 1 1 S 2 2 3 1 4 4 1 2 ith air between the plates has a capacitance of 9 pF The separation dielectrics One of the

Separation between the plates of a parallel plate capacitor is 5mm This capacitor having air as the dielectric medium between the plates is charged to a potential difference 25V using a battery The battery is then disconnected and a dielectric slab of thickness 3 mm and dielectric constant K 10 is placed between the plates as shown Potential difference between the plates after the dielectric slab has been introduced is 3mm 5mm

100 Current Electricity Cells emf Internal Resistance Cells in Series and Parallel Kirchhoff s Rules 16 The charge in the 2uF capacitor at steady state is 1V 1 5V 2V 222 H1 2 F www 222 1 Zero 2 2 C 3 4 C 4 6 C 17 Consider the combination of resistors as shown in

m A block of mass m kept on a rough horizontal surface is connected to a dielectric slab of mass and 5 dielectric constant k by means of a light and inextensible string passing over a fixed pulley The dielectric can completely fill the space between the plates of parallel plate capacitor each plate is square shaped with side Seperation between plates kept in vertical position is d The coefficient of friction between block and horizontal surface is and ignore any other friction Find the minimum value of emf of the battery so that after closing the switch the block will move mg Lit mg G 2mg 4mg

36 Consider the situation shown in the figure The capacitor A has a charge q on it whereas B is uncharged The charge appearing on the capacitor B a long time after the switch is closed is 2001 a zero q 1 A b a S c a B d 2a 42

26 180 A parallel plate air capacitor is charged to a potential difference 5 V After disconnecting the battery distance between the plates of capacitor is doubled the energy density between the plates Decreases X Increases Remains same May increase or decrease

Terminal A is connected to positive terminal of battery and B is connected to negative terminal of plate and it send same charge Q in all four combination Each plate have same area and separation between two consecutive plate is same Column I A B C A 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 A B A B B p q s Column II Top surface of plate 1 have zero charge Upper surface of plate 4 have Q charge Same charge Appear on both surface of plate 2 Bottom surface of plate 4 have zero charge Total charge on plate 2 is Q

1 In the circuit shown below the charge on the 60 F capacitor is 30 F 60 F 1 150 C 2 100 C 15 F 10 volt 80 F 30 F HH 30 F 3 50 C 50 4 75 C

3 Half portion of a spherical capacitor is filled with a dielectric of dielectric constant k conductivity o The charge given to spherical capacitor is Qo Due to the conductivity of dielectric nEo charge leaks The time constant for the discharge circuit is Find the value of n O b 3 2 and J

If potential difference between the plates of capacitor changes at the rate of V 104 v s and capacitance is 2 F then displacement current between the plate will be 10 mA 5 mA 20 mA 30 mA

A leaky parallel plate capacitor is filled completely with a material having dielectric constant K 5 and electrical conductivity o 7 4 x 10 2 1m 1 If the charge on the capacitor at the instant t 0 is q 8 5 C then calculate the leakage current at the instant t 12s

C D There is a circuit diagram in which capacitors resistors and battery are given Then choose the correct option s Assume initially all the capacitors are uncharged 2 F B A A Option 4Q 10V wwww 100 20 www 6Q B HF 4 F At steady state charge on capacitor A is zero At steady state charge on capacitor B is zero At steady state charge on capacitor B is 40 C Electric current in 2 2 resistor is 5 A Rate this que

Five thin rectangular conducting plates each of constant breadth 1 m are arranged parallel to each other as shown in the figure Any two consecutive plates are separated by a distance d 1mm The plates are arranged in increasing order of height The height of a plate is h 5 12 m as shown in the figure and the height of each successive plate decreases by 5 Then find the equivalent capacitance of the system between the first and the last plate assuming that air is present in between the plates Neglect any edge effects and calculate the capacitance taking only the overlapping areas pal patalana d

When the voltage across the capacitor is rising it gets charge If there is no external load it remains charged t the peak voltage of the rectified output When there is a load it gets discharged through the load and th voltage across it begins to fall In the next half cycle of rectified output it again gets charged to the peak valu but due to large value of time constant of capacitor voltage across the capacitor approximate remains constant output of rectifier C L R output

5 1 For a RLC series circuit with an AC source of angular frequency o A Circuit will be capacitive if B Circuit will be inductive if 1 LC 1 LC C Power factor of circuit will by unity if capacitive reactance equals inductive reactance D Current will be leading voltage if 1 IC

172 The equivalent capacitance between A and B is in uF a 25 3 F 3 F 3 F 84 b 25 c 1 d 25 AH B 2 F 2 F 3 F

If you wish to take a picture of a bullet traveling at 500 m s then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring Assuming 1 00 mm of motion during one RC constant is acceptable and given that the flash is driven by a 500 uF capacitor what is the resistance in the flash tube

In a common emitter configuration with suitable bias it is given that R is the load resistance and RBE is small signal dynamic resistance input side Then voltage gain current gain and power gain are given respectively by is current gain Ig Ic and E are respectively base collector and emitter currents R AL R

A conductor of capacitance 0 5 F has been charged to 100 volts It is now connected to uncharged conductor of capacitance 0 2 F The loss in potential energy is nearly 1 7 10 4 J 2 3 5 10 4 J 3 14 10 4 J 4 7 10 3 J

In the circuit shown in figure the battery is an ideal one with emf V The capacitor is initially uncharged switch S is closed at time t 0 R 2 wwww R 2 www The final charge Q on the capacitor is CV CV 2 B 5R 2 www 3 CV C 4 CV

A 3 33 F B 1 F D 2 F C 0 44 F Two condensers of capacities 2C and C are joined in parallel and charged upto potential V The battery is removed and the condenser of capacity C is filled completely with a medium of dielectric constant K The potential difference across the capacitors will now be A 3V K 2 8 F B V K 2 3V K in figure The capacitor A has a charge q on it whereas B is uncharged The C D K

In the arrangement shown all particles have equal area The amount of spacing between plates is mentioned Find the equivalent capacitance Area L of the system between A and B 5 A C 7 C 7 C c c 7 D None of these B 2LT L LI LI 2L A B

59 A capacitor of unknown capacitance a coil of inductance L and a resistor of resistance R are connected to a source of a c voltage cos ext The current in the circuit is I R cos cot Determine the amplitude U of the voltage across the capacitor plates

air as medium is 6 F With the introduction of dielectric medium the capacitance becomes 30 The permittivity of the medium is 0 8 85 x 10 12 C2 N 1 m 2 5 00 C2 N 1 m 2 0 44 x 10 13 C2 N 1m 2 1 77x10 12 C N 1 m 2 0 44 x 10 10 C2 N 1 m 2 2 3

2 An electron is released from rest at the negative plate of a parallel plate capacitor and accelerates to the positive plate see the drawing The plates are separated by a distance of 2 5 cm Assuming the electron has a speed of v 1 32 x 10 m s as it reaches the positive plate what is the magnitude and direction of the electric field between two parallel plates me 9 11 x 10 31 kg ALFFLLFF Electric field Electron

A parallel plate capacitor is made from circular plates of radius 9 0 3 cm The plates are separated by 0 98 0 14 cm Air is between the plates but the permittivity of air is approximately equal to that of the vacuum 8 854x10 12 F m Calculate the propagated percent error in the capacitance Round to a whole number percentage no decimal points

A capacitor of value 4 F charged at 50V is connected with another capacitor of value 2uF charged at 100V in such a way that plates of similar charges are connected together Before joining and after joining the total energy in multiples 102 J will be A 1 5 and 1 33 M B 1 33 and 1 5 C 3 0 and 2 67 D 2 67 and 3 0

pacitan 8 If dielectric constant and dielectric strength b denoted by K and X respectively then a materia suitable for use as a dielectric in a capacitor mus have a high K and high X b high K and low X c low K and high X d low K and low X

EXAMPLE 87 The capacitance of a parallel plate capacitor is 50 pF and the distance between the plates is 4 mm It is charged to 200 V and then the charging battery is removed Now a dielectric slab K 4 of thickness 2 mm is placed Determine i final charge on each plate ii final potential difference between the plates iii final energy in the capacitor and iv energy loss

19 In the given network of capacitors the equivalent capacitance betweel 1 3 4 C C HH B

Three identical charged capacitors each of capacitance 5 F are connected as shown in figure Potential difference across capacitor 3 long time after the switches K and K are closed is 1 20 V 100 C 100 C 5 K 100 C K 2 10 V

A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacito carrying charge q The induced charge q on the surface of slab is given by 1 q q 9 K 3 9 q 1 1 x 2 a q q K 9 1 4 q q 1

A capacitor is made of a flat plate of area A and a second plate having a stair like structure as shown in figure 31 E9 The width of each stair is a and the height is b Find the capacitance of the assembly dI leb a 3a isoqqu soyqo

An infinite conducting sheet has surface charge density o The distance between two equipotentia surfaces is r The potential difference between these two surfaces is or 1 200 3 O 4 or EO O 28 r

A parallel plate capacitor plate area A connected to battery of emf V and negligible internal resistance so that one of the plate is made to oscillate and dista between plate varies as d d acos t a do If maximum current observed in circuit is 1 then maximum possible amplitude of vibration a is A a 10 VA o B lodo V AS 0 1 d VA o D Lodo VA

0 A charged capacitor of capacitance 10 F is getting discharged through a resistance of 10000 After 1 what time stored energy will reduce to maximum value 1 2 ms 3 7 ms 2 5 ms 4 10 ms of its

A parallel plate capacitor is made from two aluminium foil sheets each 3 00 cm wide and 10 0 m long Between the sheets is a mica strip of the same width and length that is 0 0225 mm thick What is the maximum charge that can be stored in this capacitor 4 0 7 mc 1 22 mc 0 9 mC 1 43mC

3 19 In the given network of capacitors the equivalent capacitance between points A and B is 652 2 20 3 2 c 11C 4 C T B

A H H toet toot 108111061 201 i B

107 Three capacitors with their respective breakdown voltages have been marked 4 F 20V HH A 6 F 5V HE 1 60V 2 30V 3 16 25V B 3 F 10V Find the maximum potential difference that can be applied across terminals A and B to keep each of them safe

a Find the equivalent capacitor for this circuit b Find the charge stored on each capacitor c Find the total energy stored in this circuit 100 V SUF 10 UF