Capacitors Questions and Answers

7 The capacitance of a parallel plate capacitor with air as medium is 6 F With the introduction of a dielectric medium the capacitance becomes 30 F The permittivity of the medium is E2Fx Em 0 8 85 10 12 C N 1m 2 0 44 x 10 13 C2 N 1 m 2 1 77 x 10 12 C N 1 m 2 0 44 x 10 10 C2 N 1 m 2 5 00 C2 N 1m 2 1 2 3 4

A capacitor is half filled with a dielectric K 2 as shown in figure A If the same capacitor is to be filled with same dielectric as shown what would be the thickness of dielectric so that capacitor still has same capacity fig A 1 2d 3 2 3d 2 3 3d 4 4 4d 3 d to fig B

Find the equivalent capacitance of the infinite ladder shown in figure between the points A B 2 F HH Aa 2 F HH 2 F HH 2 F HH 2 F HH 1 F 1 F 1 uF 1 uF 1 F

8 Three capacitors of capacitances 2 pF 3 pF and 4 pF are connected in paralle a Write the SI unit of capacitance 1 b Calculate the effective capacitance of the combination 1 c Determine the charge on each capacitor if the combination is connected to 100 V supply 2

14 It is required to construct a 10 F capacitor which can be connected across a 200 V battery Capacitors of capacitance 10 uF are available but they can withstand only 50 V Design a combination which can yield the desired result

6 Find the equivalent capacitances of the combinations shown in figure 31 E15 between the indicated points 1 F 31 4 F 3 F 2 F 36 H 4 F 3 F H H 1 F HH 4 F 4 F H 5 F H 8 F 1 F HH 2 F 4 F 6 4 F H 3 F 2 F H 4 F HH 4 F HH 2 F 6 F 6 F 6 AF 3 F HH 2 F b F 1 F 4 F HH 18 F F 8 F 41 4 F

Find the total energy stored in the capacitors in the network shown below CBSE D 04 Ans 3 6x10 5 J 6V 1 F 2 F 1 1 F HH 2 uF 2 F

21 The particle P shown in figure 31 E11 has a mass of 10 mg and a charge of 0 01 C Each plate has a surface area 100 cm on one side What potential difference V should be applied to the combination to hold the particle P in equilibrium 0 04 FP 0 04 F

What charges will flow through section B of the circuit in the direction shown when switch S is closed A 30 V 60 V B S 2 F 3 F

4 A capacitor with plate separation d is charged to V volts The battery is disconnected and a dielectric slab of thickness and dielectric d 2 constant 2 is inserted between the plates The potential difference across its terminals becomes 1 V 2 2V 3 4V 3 4 3V 4

8 For the circuit arrangement showil ifl C 20 F www 60 S2 30 Q www 20 32 www 30 S2 www 10 Q T K 12 V C 10 F a find the potential difference across each capacitor i the steady state condition b find the current through the 60 2 resistor just afte the instant when the key K is opened

32 What will be the direction of charge flow when th switch S is closed 2C H 4C C 11 From a to b a b S E C HH 3C d 2 From b to a 3 The direction of charge flow will depend on the value of emf E

Q 20 Find the equivalent capacitance across A B B F A uf C 15 F D none 12p 23uF HH 10 F 7 F 13 F luF HH 1pF

Each of the capacitors shown in figure 31 E6 capacitance of 2 F Find the equivalent capacitance of the assembly between the points A and B Suppose a battery of emf 60 volts is connected between A and B Find the potential difference appearing on the individual capacitors A H H HHH Figure 31 E6 B da od ball otionqas

A parallel plate capacitor with plate separation 5 mm is charged by a battery It is found that on introducing a mica sheet 2 mm thick while keeping the battery connections intact the capacitor draws 25 more energy from the battery than before Find the dielectric constant of mica Ans 2

Only switch S closed in figure S 3 F 1022 www S 302 V 692 www S HH 20 V 2 F 20 2 wwww a What is the steady state reading of the voltmeter b What is the charge on the 3 uF capacitor e How much power does the 12 V battery supply in th steady state after all the switches are closed d What is the charge on 2 F capacitor

A parallel plate air capacitor consists of two plates each of area 0 01 sq m separated by a distance of 0 1 mm It is charged to a potential of 50 volt Calculate its capacitance charge on it and energy stored

Five capacitors each of capacitance C and breakdown voltage Vare connected as shown in the figure The capacitance and breakdown voltage of the combination applied across AB will be C 1 2 3 4 0 0 0 0 0 0 7C V 6 2 7C V 3V 6 2 6C V 7 2 A C Hi C C C E

Q 21 Find equivalent capacitance across AB all capacitances in F A B 9 F C 48 F D None A 17 13 S 10

Two identical uniform discs roll without slipping on two different surfaces AB and CD see figure starting at A and C with linear speeds u and U respectively and always remain in contact with the surfaces If they reach B and D with the same linear speed and v 3 m s then u in m s is g 10 m s U 3 m s U 30 m 27 m B D

A charged capacitor has energy U 2 x 104 J and Co 4 x 10 8 F in the absence of a dielectric When the potential difference is kept constant by keeping the capacitor connected to the supply assuming 150 0 i find the new energy stored when the dielectric slab is completely filled with the capacitor Account for this change in energy ii how much excess charge flows from the supply ii find the ratio of the charge on the plate of the capacitor and the charge induced on the dielectric

A parallel plate capacitor has a capacity of 2uF A dielectric salt of constant K 5 is inserted between the plates and the capacitor is charged to 100V and then isolated a What is the new potential difference if the dielectric is removed How much work is required to remove the dielectric slab

Example 54 Seven capacitors each of capacitance 2 uF are to be connected in a configuration to obtain an effective capacitance of 10 11 uF Suggest a suitable combination to achieve the desired result IIT 901

In the given circuit the switch S was initially open If the switch is closed now then amount of charge flown through the switch S is 1 15 C 2 F HH S HH 3 F 1 F HH 2 F 120 V 2 30 C

Two conducting spheres of radii a and b are separated by a large distance The capacity of this system between points A and B is B 4 a b A 4 0 1 1 a b C 4 a b a G D None of the above A B b

In the circuit shown all capacitors are identical Initially the switch is open and capacitor C is the only charged capacitor After the switch is closed the equilibrium is re established and the charge on the capacitor C is Q If initial charge on the capacitor C was Q a 20 b where a and b are positive integer lying between 0 to 9 Find the value a b f t C Jo test C

In the given diagram the capacitors are initially uncharged and now are connected with switch S open Find the potential of point b and the amount of charge flowing through the switch when it is closed 6 F 200V S 3 F 1 66 7V 300 C 2 66 7V 400 C 3 100V 300 C 4 133 3V 400 C 3 F 6 F 0 volt

35 As in the figure if a capacitor of capacitance C is charged by connecting it with resistance R then energy given by the battery will be 1 CV 1 2 2 Less than 3 CV 1 2 CV C HH V R ww

In the circuit shown find the potential difference between points A and B in V 10 F 1002 100V 1002 M 5 F 1092 m 1052 B 1052

For the circuit shown in figure which of the following statement is true A with S closed V 15 V V 20 V B with S3 closed V V 25 V C with S and S closed V V 0 D with S and S3 closed V 30 V V 20 V Tu S V V 30V C 2 F S3 V 7 V2 20V C 3 F S

10 V A H 2 uF 1 7 5 V 2 15 V 3 5 V of B point in given circuit 5 V www 2 F C

Across a capacitor C 10 uF the voltage is changing at a rate of 200 volt second The displacement current in the capacitor is 1 20 mA Id Eo 2 2 mA 3 2 A

given circuit ratio of charge on 2 F capacitor to the charge on 3 uF capacitor will be 1 F 2 F A 3 F HH 1 2 3 9 2 3 2 4 29 visonch

Illustration 6 In the circuit shown in the figure if the point B is earthed find the potential of point C

The capacitor 2C is charged to potential difference Vo while the capacitor C is uncharged at t 0 At this instant the switch S is closed A Charge on the capacitor C is CV in steady state 2 cvo 3 11 B Charge on the capacitor 2C is 3 C Charge on the capacitor C is 3 CV in steady state CV in steady state 5 D Charge on the capacitor 2C is CV in steady state 2C 2R B C allel

diagram shows two capacitors with capacitance and breakdown voltages as mentioned What should be the maximum value of the external emf source such that no capacitor undergoes breaks down 3C 1kV 2C 2kV HH 2 1 1 D 1 kV

Illustration 3 Find capacitance of a conducting sphere of radius R

A capacitor is charged with a battery and energ stored is U After disconnecting the battery anothe capacitor of same capacity is connected in parall with it The energy stored in each capacitor is 1 U 2 2 U 4 3 4 U 4 2 U

A parallel plate capacitor of 6 F is connected across 18 V battery and charged The battery is then disconnected and oil of dielectric constant k 2 1 is introduced between the plates What will be the charge on capacitor MH CET 2001 108 C 92 5 x 10 C A 51 4 C C 8 5 C B D

The two parallel plates of a condenser have been connected to a battery of 300 V and the charge collected at each plate is 1 uC The energy supplied by the battery is 1 6 x 10 4J 3 1 5 x 10 4J 2 3 x 10 4J 4 4 5 x 10 4J

6 Three capacitors each of capacitance 0 3 F are connected in parallel This combination is connected with another capacitor of capacitance 0 1 F in series What is the resultant capacitance 2020

4 The energy required to charge a capacitor of 5 F to 20KV is in kJ

23 The ratio of modulus of rigidity to bulk modulus for a Poisson s ratio of 0 15 would be 1 1 4 2 21 23 3 25 6 4 17 6 24 Two soap bubbles of radil equal to 6 cm and 8 cm are touching each other over a common surface Radius of the common surface will be 1 3 42 cm 2 4 cm 3 24 cm 4 10 cm One mole of an ideal gas at an initial temperature of T K does 15R joules of work adiabatically If the ratio of specific heats of this gas at constant pressure and at constant volume is 5 3 the final temperature of gas will be 25 1 T 2 4 K 2 T 10 K 4 T 10 K 3 T 4 K 26 One mole of an ideal monatomic gas is taken from A to C along the path ABC The temperature of the gas at A is To For the process ABC 2P Po AP To C B Vo 2V 1 Work done by the gas is RTO 2 Change in internal energy of the gas is 11RTO 2 3C 40 5C 3 Heat absorbed by the gas is 21RTd 2 4 Heat absorbed by the gas is 13RTo 2 27 The temperature of sink of Carnot engine is 27 C and Efficiency of engine is 60 Then temperature of source is 1 227 C 2 477 C 4 27 C 3 127 C 28 Three large plates A B and C are placed parallel to each other and charges are given as shown The charge that appears on the left surface of plate B is 1 5 C 3 3 C 4 3 C 29 The lengths of the three wires of copper are in the ratio of 1 4 8 and their masses are in the ratio of 5 3 1 The ratio of their electrical resistance is 1 1 3 5 3 1 25 125 30 In the circuit shown the current through 8 is same before and after connecting E The value of Eis 32 1 12 V 3 4 V 60 www 3 CE CE2 HH 2 6 V 4 2 V 31 In the given circuit diagram when the current reaches steady state in the circuit the charge on the capacitor of capacitance C will be 52 4 4 12 4 S 12 V 822 ww E 1 36 V 36 2 72 V 30 2 3 90 V 36 4 72 V 36 0 2 3 80 960 4 125 15 1 www 12 www 7 ww 10 22 2 CE www 2 5 r 4 CE 12 4 In the series combination of 18 cells each cell having emf 6 V and internal resistance 2 ohm if three cells are wrongly connected i e their polarity is opposite to remaining 15 cells then total emf and internal resistance of this combination will be

In the circuit shown in figure the charge stored in 2 F capacitor on applying a potential difference of 60 V between A and B is A 4 F 1 40 C 2 80 C 3 60 C 4 120 C y 3 F 2 F 8 F O 60 1 F x 6 F 2 B 0 3 x

Figure given below shows two identical parallel plate capacitors connected to a battery with switch S closed The switch is now opened and the free space between the plate of capacitors is filled with a dielectric constant 3 What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric 1 1 2 10 HH A B 2 1 5 AY

3 What charges will flow after the shorting of the switch S in the circuit given in the figure through sections A and B E C2 A C B

An artificial radioactive battery consists of No number of atoms of a radioactive element emitting a particles with a disintegration constant 1 per sec Half of the fraction of x particles emitted are captured at the anode A Rest remains in the surrounding of radioactive substance kept on the cathode B A capacitor C and a resistance R are connected across the battery Charge on a particle is denoted by qo given C F R 500 Q and at t 0 number of atoms are No 10 3 49 Current through a battery as a function of time A N 9 6 2 2 C N 9 2 A B B 9 1 e 21 No D N 9 1 e 2 10 F www 500 Q

To establish an instantaneous displacement cur of ampere in the space between the plates of a 1 dV parallel plate capacitor of farad the value of dt is 2 1 2 1 2 1 2 ask

The minimum number of 2uF identical capacitors which can withstand a maximum potential difference of 400 V require to design a circuit of effective capacitance of 2uF and bearing voltage 1000 V are 1 3 3 9 2 6 4 12

Charge Q 2Q 3Q 4Q are given to four large parallel conducting plates A B C D respectively B and C are connected to each other by a metallic wire If the charge that flows from C to B through this wire is nQ Then find the value of n The area of each plate is A and separation between plates is d