Capacitors Questions and Answers

A parallel plate capacitor with a dielectric slab of dielectric constant 3 filling the space between the plates is charged to a potential V The battery is then disconnected and the dielectric slab is withdrawn It is then replaced by another dielectric slab of dielectric constant 2 If the energies stored in the capacitor before and after the dielectric slab is changed are E and E2 then E E2 is

81 A capacitor of capacity 6 F and initial charge 160 C is connected with a key S and different resistors as shown in figure Point M is earthed If key is closed at t 0 then the current through resistance R 122 at t 16 s is www 10 a A 3e 20 3e c 292 A 292 www www 452 N S M 192 www www 292 RZ1Q 10 b A e d None of these

27 A charged capacitor of capacitance C is discharging through a resistor of resistance R At what time the charge on the capacitor is equal to one half of its initial value RC RC b c RC log 2 2 loge 2 a 1 d loge 2 RC

26 When a capacitor is fully charged as shown in the following figure then current drawn from the cell is 7kQ 4 KQ a 1 mA 10 V 8 k www 9 kQ b0 5 mA c 2 mA FC d 5 mA

The area of the positive plate is 125 cm and the area of the negative plate is 100 cm They are parallel to each other and are separated by 0 5 cm The capacity of a condenser with air as dielectric is EO 8 9 10 2 C N M

to V volts The battery is disconnected and a d dielectric slab of thickness and dielectric constant 2 is inserted between the plates The potential difference across its terminals

42 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 19 3 A kx r O 1 40 C VID 4 F A 2 80 C 3 60 C 4 120 C 3 F 2 F HH 8 F A 1 F 6 F B 5165 B A 4 8 4 614

Two thin dielectric slabs of dielectric constants K and K K K are inserted between plates of a parallel plate capacitor as shown in the figure The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by P Q

A parallel plate capacitor is charged from a battery and then isolated from it Now a dielectric slab of dielectric constant K is introduced in the region between plates filling half of it as shown The electric field intensity in dielectric region is E and that in air between plates is E K

3 Consider the capacitor circuit shown in the figure initially switch K is closed and after sufficiently long time K is also closed The charge flowing through section 1 2 after closing the K2 is C 1 a C E d K CE bE from 1 to 2 K 2 CE from 2 to 1 CE CE from 2 to 1 from 1 to 2 2C

2 4 In order to establish an instantaneous displacement current of 1 mA in the space between the plates of 2 F parallel plate capacitor the rate of change of potential difference is a 100 Vs 1 c 300 Vs 1 b 200 V s 1 d 500 V s 11

d The charge on a parallel plate capacitor varies as q cos2rut The plates are very large and close together area A separation d The displacement current through the capacitor is a 4 2nu sinnur 2 2 sinnut b qo2nu sin2rut d qonu sin2rut

c 4 2n sinut d qonu sinnut 4A parallel plate capacitor with plate area A and separation between the plates d is charged by a constant current I Consider a plane surface of area A 2 parallel to the plates and drawn between the plates The displacement current through the area is a I b c I 4 d 8 c d 10 Whic Max a c

A parallel plate capacitor of capacitance C is charged with battery of emf V volts The force between the plates is given by F The battery is disconnected Now a dielectric slab of dielectric constant K is placed between the plates to fully occupy the space The new electrostatic force of attraction between the plates Fis related to original value F as

71 Two capacitors 2C and 4C initially charged to potential difference of Vo and 3V with the polarities as shown are connected to an inductor of inductance L Initial current in the inductor is zero Now the switch S is closed The maximum current in the circuit is 2C HF Vo 4C F 3V0 reeeeeee L Vo C S C

A4 F capacitor is given 20 Ccharge and is connected with an uncharged capacitor of capacitance 2 F as shown in figure When switch Sis closed 4 F 2 F 20 C 10V C S Charged flown through the battery is Charge flown through the battery is Work done by the battery is 200 J C J

Six metallic plates each with a surface area of one side A are placed at a distance d from each other The alternate plates are connected to points P and Q as shown in figure 1 2 3 4 5 6 The capacitance of the system is A B EoA d 5 A d My Answer

18 Four identical plates each of area A placed at equal distance d Find potential energy stored in the space between plate 1 and 2 1 3 2 9 d AV 1 18 d A V 2 3 4 2 v 2 AV 3d 1 9 d A V

5 Three large plates are arranged as shown How much charge will flow through the key k if it is closed

d None 33 When an ac voltage of 220 V is applied to the 40 A c capacitor C then a the maximum voltage between plates is 220 V b the current is in phase with the applied voltage c the charge on the plate is not in phase with the applied voltage d power delivered to the capacitor per cycle is zero capa 50 E a c 41 200 X

7 The plates of a parallel plate capacitor are given charges 4Q and 20 The capacitor is then conneced acros an uncharged capacitor of same capacitance as first one C Find the final potential difference between the plates of the first capacitor

A capacitance of 10 uF is charged to a potential of 50V with a battery The battery is now disconnected and an additional charge 200 C is given to positive plate of the capacitor The potential difference across the capacitor become 0 S 2 70 V 4 60 V 1 100V 3 80 V s OnE 8

Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of Vo volt If one of the capacitors is completely immersed in a liquid with dielectric constant K the potential difference between the plates of the other capacitor will change to K 1 1 Vo K 2 3 K 1 K 1 2K 2K Vo Vo Vo

26 Ifa capacitor of 8 F is connected to a 220 V 100 Hz ac source and the current passing through it is 65 mA then the rms voltage across it is a 129 4 V b 12 94 V d 15 V c 1 294 V difference between voltage and current in

a Using Bohr s postulates derive the expression for the total energy of the electron in the stationary states of the hydrogen atom b Using Rydberg formula calculate the wavelengths of the spectral lines of the first member of le the Lyman series and of the Balmer series rosido

Space between plates of a parallel plate capacitor is filled with three dielectric slabs as shown Equivalent dielectric constant for the arrangement shown between points X and Y is A k 3 k 12 d k 6 d

A parallel plate capacitor of capacity Co is charged by a battery After charging battery is disconnected and a dielectric is filled between the plates of capacitem Column I represents quantity and column II represents the change occurred Column II Column I 1 PE of capacitor PD between plates Capacity of capacitor Charge on 111 iv 5 capacitor Match the columns and choose correct option from the given codes Oi s 11 1 1 q iv p Oi q i q p iv r Oi p ii q 1 1 iv s Oi t 11 5 11 p iv g 9 Increases Decreases Remains same May increase or decrease Marks 4

The two plates of a parallel plate capacitor each having area A 400cm are given charges 7 7 C and 1 1 C then the force exerted per unit area on any one plate will be 1 13 25 x 10 N m 2 6 8 x 102 N m 3 27 50 10 N m 4 38 5 x 10 N m

In the circuit diagram shown all the capacitors are in F The equivalent capacitance between points A B is in F A 14 5 B 7 5 Ao 6 HH 8 3 HH 10 C 3 7 7 HOB D None of these

Three capacitors each of 4 F are to be connected in series and parallel in such a way that the effective capacitance is 6 F If P number of capacitors are connected in series with Q number of capacitor in parallel then the value of 2P Q is

If a 90 W bulb 90 W dissipates when connected across 120 V is connected across a 220 V potential difference as is used in Europe how much power does it dissipate Express your answer using two significant figures VAE P W

PARA QUES The circuit shown is placed in vacuum Both the capacitor are identical and they have the same capacitance C Light is incident on the left plate of the upper capacitor When all the switches are open then the hf versus KEmax when the electron reaches the opposite plate f is frequency of light incident is given by graph 1 When only S3 and S4 are closed then the graph becomes 2 When only the switches S1 and S2 are closed the graph becomes 3 E Q1 What is the work function of the cathode Q2 What is the value of E S E hf KE max 3 1 2

Question 7 Which statements is are corect 10 F C 700 wwwwww S 80 F 5V 300 www P C S 30 F C Q 300 10V www 1000 BBYJU S The Learning App C 80 F Byjus com a At time t 0 the S1 is closed instantaneous current in the closed circuit will be 25 mA b The key S is kept closed for long time such that capacitors are fully charged Now key S is closed at this time the instantaneous across 300 resistor between P Q will be 0 2A c If key S is kept closed for long time such that capacitors are fully charged the voltage across C will be 4V d If S is kept closed for long time such that capacitors are fully charged the voltage difference between P O will be 10V

The capacitances are C 0 5 F and C 1 5 F and both capacitors are charged to a potential difference of V 200 V but with opposite polarity as shown Switches S and S are now closed What is now the potential difference between points a and b in Volts Option1 Option2 Option3 Option4 Options 50 a Option3 b Option4 200 100 150 250 G S C 4

Two conductors of infinite length carry a current i each which varies with time according relation i ine They are parallel and separated by a distance 2a A circular conducting rin of radius a and having a resistance 1 22 length in the plane of wires lies between the two straig conductors and insulated from them as shown A Mutual inductance of system is 2 a B Mutual inductance of system is u a C Net magnetic field at the centre of circle is always zero D Net magnetic field at the centre of circle increases with time c

D The equivalent capacitance between A and B for the combination of Fig 4 82 is 4 F i Calculate the capacitance of the capacitor C ii Calculate the charges on the two capacitors if a 12 V battery is connected across the terminals A and B iii What will be the potential drops across the two capaci tors A 20 F Fig 4 82 C B CBSE 09

22 A 10 F capacitor is charged by a 30 V dc supply and then connected across an uncharged 50 F capacitor Calculate a the final potential difference across the combination and b the initial and final energies CBSE 03 a 5 V b 4 5 x 10 3J 0 75 x 10 J

The AB and CD are two 20 space between AB and CD contains dielectric material of dielectric constant K K and K3 as shown where K 1 K 2 K3 4 Find the capacitance betweer AB and CD 10 cm 10cm C 10 cm Fig 4 86 K3 B 20cm 4 722 pF

Four identical plates of area A and separation d are connected as shown in diagram Each plates of capacitor are in horizontal plane and P Q and R are three points between plates P Q R 1 2 3 4 3mgd e E A Ife is in equilibrium between plates 2 and 3 then emf of battery is B Ratio of electric field at point P Q and R is 2 1 1 respectively C If plate 3 is shifted upward by d 2 ratio of potential difference between plate 1 between 2 and 3 will be 8 3 D ratio of electric field between plate 2 3 and 3 4 will be 4 1 after the shift

Half of the space between a parallel plate capacitor is filled with a medium of dielectric constant K parallel to the plates If initially the capacity was C then the new capacity will be 1 2KC 1 K 2 C K 1 2 3 CK 1 K 4 KC

A series combination of two capacitances of value 0 1 F and 1 F is connected with a source of voltage 500 volts The potential difference in volts across the capacitor of value 0 1 F will be 1 50 3 45 5 2 500 4 454 5

Five identical capacitor plates are arranged such that they make capacitors each of 2uF The plates are connected to a source of emf 10 V The charge on plate Cis 10V A 20 C B D B 40 C A C E C 60 C D 80 C bated

B A Zero C 2r Five conducting large parallel plates each of area A are arrange as shown then find correct statement B Total charge on Hol r A Total charge on III d plate is Vth plate is 28 A d 8 E A E d d E IIId IVth IInd Vth B C Energy stored in the space between IInd and IIId plate is D Total charge on IVth plate is zero 0 A d

In the circuit shown in figure charge stored in the capacitor of capacity 5 ufis A 60 C C 30 C 2uf 2uf 2uf 2uf 5uf 3uf 4uf 3 f F T B 20 C D zero and its capacitance is C There are two other conducting 100 V

An arrangement of five identical capacitors is shown in given circuit the potential at X and Y are respectively 30 V C C C 12 V and 6 V C C 18 V and 12 V 6 V and 24 V 24 V and 6 V

A parallel plate capacitor of capacitance 5 F and plate separation 6 cm is connected to a 1 V battery and charged A dielectric of dielectric constant 4 and thickness 4 cm is introduced between the plates of the capacitor The additional charge that flows into the capacitor from the battery is 1 2 C 2 3 C 35 C

The two plates of an ideal capacitor of capacitance C are given charges Q and Q2 as shown in the circuit below This capacitor is connected across a resistance R as shown key is closed at t 0 Then after time t Q Q Total charge on the right plate is 92 Total charge on the left plate is q Q Q e Alb Initial potential difference across the plates is given by 12 02 Initial potential difference across the plates is given by Q 0 20

9 Between two thin parallel metal plates having charges q and q is inserted a thick metal slab having charge q so that distance between the upper plate and top face of the slab is 2d and the distance between lower plate and bottom face of the slab is d Adjacent surfaces of the plates and that of the slab are equal in area and parallel to each other Now the upper and the lower plates are earthed by closing the switches A and B simultaneously Find amounts of the charges that pass through the switches q 2d q A B

The capacity of a parallel plate condenser is 5uF When a glass plate is placed between the plates of the conductor its new capacitance becomes 50 F of the original value The value of dielectric constant will be 0 1 a c 100 b d 10 0 01

A capacitor consists of two air spaced concentric cylinders The outer of radius b is fixed and the inner is of radius a If breakdown of air occurs at field strengths greater than E show that the inner cylinder should have