Capacitors Questions and Answers

A parallel plate capacitor with air between the plates has capacitance of 8 pF What will be capacitance if the distance between plates is reduced by half and space between them is filled with a material of dielectric constant 6 32 pF 64 pF 96 pF O 16 RF

Two identical parallel plate capacitors are placed 9 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 Vo 1 3 K 1 2K Vo 25 4 K K 1 2K K 1 Vo Vo

charge A conductor A of capacity 20 C and another condenser B of capacity 10 F has a charge 40 C If they are connected parallel then 1 charge flows from B to A till the charges on them are equal 2 charge flows from B to A till common potential is reached 3 charge flows from A to B pill common potential is reached 4 charge flows from A to B till charges on them are equal

MATCH LIS nswer questions 1 2 by appropriately matching the list based on the information given in th aragraph All identical capacitor plates each of area A are arranged such that adjacent plates are at d distance apart Plates are connected to a source of emf V volts as shown in figure dielectric constant in each shaded region is k 2 Then 1 II IV Charge on plate 3 is List 1 10 AV Kd value of K is The heat rejected by the system is 26 AV Then the value of Kis Kd Equivalent capacitance between AB is III 26A Then the value of K is Kd Potential difference between the plates 4 and 7 is KV Then the Then the value of K is 5 Which of the following is correct Options A I U II Q III P IV Q B I T II P III Q IV U C I U II T III Q IV P D P R Q 3 S S A zero U T 6 13 5 26 5 10 3 3 6 8 10 12 2 4 5 7 9 11 F List Il B

A parallel capacitor has some dielectric between its plates and it is charged by using a battery The battery is now disconnected and then the dielectric is removed Explain the changes if any that occur in the values of i energy stored and ii electric field Justify your answer

In the circuit shown there is steady state with the switch closed The switch is opened at t 0 Choose the incorrect option Given 24V C 3F and C 2F 30 962 1 The voltage across C before the switch is open is 12V 2 The voltage across C after a long time after the switch is open is 12V 3 The voltage across C after a long time after the switch is open is 24V 4 The voltage across C before the switch is open is 8V

Resistance of each side of the cube is R 10 If switch Sis closed at t 0 then E 4 volt R A Switch R R C 1F R R R R E R R 2R 2R Initial current I will be 2 A Initial current I will be 1 A 4 1 07 c Charge on the capacitor Cat time twill be 41 e

Two conducting spheres A and Bhaving equal charge Qeach placed at large distance are connected with each other as shown If at t 0 key K is closed then C 4T oa Q 2a7 A Charge on sphere A at time tis 3t 1 e 2C Qt Q ww R 192 9 Initial current through resistance Ris Q 8 aR Total heat dissipated in resistance Ris B Q 4 a 4Q

In a parallel plate capacitor with air between the plates each plate has an area of 6 x 10 m and the distance between the plates is 3 mm Now this capacitor is connected to a 100 V supply Now supply is disconnected and a mica sheet of dielectric constant 6 is inserted between the plates Find the voltage across capacitor 1 100 V 2 600 V 100 3 V

4 depend on internal resistance of the cell 5 Two identical plates of a parallel plate capacitor are given charges q and 3q If o and o are the charge densities on outer and inner faces of the first plate then 1 a a 3 9 a 2 22 4 0 0

and 2C are connected in parallel and charged to a potential difference V Now the battery is disconnected and the region between the capacitor plates of capacitance C is completely filled with a dielectric of dielectric constant K The potential difference across the capacitors now becomes 1 3K 1 3V K 2 2V K 4 2K 1

A cumulonimbus cloud is 5 km long and 2 km wide and has its base 1 km above the surface of the earth as shown here Conside the cloud and earth to be a parallel plate capacitor with air as the dielectric Then the capacitance of the cloud earth combination is 1 8 8 F Cumulonimbus cloud 35 Earth Lightning Strike 2 8 08 F

A capacitor of capacitance 10 uF is charged to 40 V and a second capacitor of capacitance 15 F is charged to 30 V If they are connected in parallel with identical polarity The amount of charge that flows from smaller capacitor to higher capacitor is O 320 C O 200 C O 60 C O 20 C

A slab of material of dielectric constant 3 has the same area plates of parallel plate capacitor and thickness where d is plate separation The new capacity when slab is inserted between the plates is O Unchanged OTwice the original value O Thrice the original value O Four times the original vale

For the circuit shown in the figure determine the char of the capacitor in steady state 3 a 4 C 102 3V www 6V b 6 C 152 202 www 1 F 3V 102 www c l C 10V 50 d Zero

The capacitance of spherical capacitor is 1 uF If the separation between the two spherical shells is 1 mm The radius of outer shell is nearly 30 cm 60 cm 02m 03m

20 The capacities and connection of five capacitors are shown in the adjoining figure The potential difference between the points A and B is 60 volts Then the equivalent capacity between A and B and the charge on 5 F capacitance will be respectively 5 va a en fara 60 HR I A R 12 F 10 F a 44 F 300 C C 15 uF 200 G 5 F 9 F 8 F A B b 16 F 150 C d 4uF 50 G

3 Two condensers of capacities 1 F and 2F are connected in series and the systemis charged to 120 volts Then the P D on 1F capacitor in volts will be 1 F 2F ER 120 ale fara a fa FR 14FR a 40 b 60 c 80 d 120

9 Four condensers are joined as shown in the adjoining figure The capacity of each is 8uF The equivalent capacity between the points A and B will be 4 HR T ETA A 8 F A Rai JTV B

W 3 If at t 0 the switch S is closed then the charge on capacitor in the given circuit initially uncharged when the current through battery becomes 50 of its maximum value is assume battery is ideal S 6 37R t 0 ft Safar y a f fer R a C 3 3 RR 50 T 4 Fra den C b CE 2 Sw R www R www c Ca 4 d Cs

4 Four capacitors of each of capacity 3 F are connected as shown in the adjoining figure The ratio of equivalent capacitance between A and B and between A and c will be R R THER 3F ART BCfargait a 4 3 b 3 4 HH B C c 2 3 d 3 2

5 The capacities of two conductors are c and c and their respective potentials are v and v If they are connected by a thin wire then the loss of energy will be given by at an af afte a C C V V 2 C C c C C V V 2 C C b GC V V 2 C C d C C V V C C v S

dielectric having dielectric constant as shown in the figure Find the force acting on a unit surface of the plate from the dielectric 58 WHITR Centar Ridea Audi fagur SARRI BRI a E V 2d c 2d 1 b d e 1 V 2d x 8 1 s V 2d

7 In the figure shown P and P are two conducting plates having charges of equal magnitude and opposite sign Two dielectrics of dielectric constant K and K fill the space between the plates as shown in the figure The ratio of electrical energy in 1st dielectric to that in the 2nd dielectric is fra P en P de fa face STAITI de factu quaya fag K K A Kat B P P vi

In the given circuit all the capacitors are initially uncharged After closing the switch s for a long time suddenly s is also closed and kept closed for a long time Total heat produced after closing s will be fear S age to an events fan vaan at dia a MY C 2 CRO

In the given circult all three capacitors are initially uncharged It a battery of emf E is connected between the points A and B the potential difference across the capacitor of capacitance 2C at steady state becomes O O 20 b

some charges on them as shown Find the charge flown through switch after closing the switch 3Qnc 8Q Q A cl 8 moit nertons 3 or no one awolt tana 1 1 4Q towards earth 2 2Q towards earth

of energy Five identical plates of dimension 5 cm x 8 m are placed at separation of 8 85 mm from each other If they are connected through a battery which provides constant potential difference of 20V as shown then find the total charge given by battery 1 8 10 C 3 4 x 10 C 20V 2 16 10 C 4 12 x 10 C

1 2 3 5 Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere The ratio of their radii would be R 2 www 2n A conducting solid sphere is joined in an electrical circuit as shown in figure 2R 2n 1 n 1 6 Two imaginary points A and B are taken inside the sphere For given conditions 2 V V 7 4 Data insufficient 1 V V 3 V V In the given circuit R 202 R 302 r 152 s 6V C 1 F and C 2 F In steady state the ratio of energy stored in the capacitors C and C is RO 1 6 9 3 8 9 4 9 9 2 9 6 There are 8 drops of a conducting fluid Each has radius r and they are charged to potential 1 volt They are then combined to form a bigger drop Find potential of big drop 1 1 V 2 4 V 3 2 V 4 8 V A B C D E and F are conducting plates each of area A and any two consecutive plates are separated by a distance d The net energy stored in the system after the switch S is closed is 1 3 ob 1000 2d Va 1 C 2 C 3 C 2 SE A 12d 2d When an additional charge of 2C is given to a capacitor energy stored in it is increased by 21 The original charge of the capacitor is 1 30 C 2 40 C 3 10 C 4 20 C Three capacitors C C and C are connected to a battery as shown in figure The three capacitors have equal capacitances Which capacitor stores the most energy V 1 8 x 10 C 3 4 x 10 C 4 All three capacitors store the same amount of energy Five identical plates of dimension 5 cm x 8 m are placed at separation of 8 85 mm from each other If they are connected through a battery which provides constant potential difference of 20V as shown then find the total charge given by battery 201 2 16 x 10 C 4 12 x 10 C

When three capacitors of equal capacities are connected in parallel and one of the same capacity is connected in series with its combination The resultant capacity is 3 75 F The capcity of each capacitor is A 5 F B 6 F C 7 F D 8 F

Question 2 Three capacitor C 2 F C2 3uF and C3 4 F are separately charged with battery of potential difference 40V 30V and 10V respectively and then disconnected After the they are connected to each other as shown in figure 1 C LJ Options a Final charge on capacitor C b Final charge on capacitor C2 C c Final charge on capacitor 800 13 800 13 380 13 C C HC

What is the voltage across capacitor in steady state 6V 792 30 A www www 10 C D www 622 E 120 2 2 V B at higher potential O 2 2 v B at lower potential O 4 4 v B at higher potential O 4 4 v B at higher potential

Three capacitors C 12F C 6F and C3 8F are separately charged with battery such that charge on capacitors are 48 coulomb 18 coulomb and 56 coulomb respectively and then disconnected with the battery After they are connected in a circuit along with two uncharged capacitors C4 2F and C5 8F and a battery of emf 8 V as shown in figure C 36 J 8V C5 C B Answer Now the switch S is closed Choose the correct option s A B C D A Your Attempt C4 Correct answer Final charge on the capacitor C4 is 8 coulomb Final charge on the capacitor C3 is 48 coulomb Potential difference between A and B is 9 V Amount of charge flown in the circuit is 8 coulomb Rate this questic V

Q15 Two capacitors of capacitances C and 2C are charged to potential differences V and 2V respectively These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other The final energy of this configuration is Sep 05 2020 1 a 2cr b cv c Zero

Illustration 10 The plates of the capacitor formed by inserting four dielectric slabs as shown have an area equal to S Find the equivalent capacitance between A and B if 2 k 2 k k k 5 SOLUTION A K 1 4 1 4 K 1 2 KI d 2 d 2

urrent comes out from positive terminal of battery energy is supplied by the battery to external circuit In this process e inside cell moves from higher potential to lower potential Work against the field inside the cell is done at the cost of chemical potential energy Net energy output from battery is also called work done by battery If AQ charge flows through battery then work done by battery is equal to AQ V Where V is potential difference between two electrodes 1 F 2 F 1uF 12 V 2 F S Energy stored in capacitors is U when S is open If S is closed the charge passed through S is Q Now total energy stored in capacitors is U Choose the correct answer 1 What is the value of U U 1 Zero 2 20 kJ

A variable capacitor is initially adjusted to its lowest capacitance Co and is connected with a source of constant voltage Vo for a long time Resistance of connecting wire is R After that at t 0 its capacitance starts to increase so that a constant current starts to flow through the circuit Choose the correct answer 1 At any instant t the rate of increase of electrostatic energy stored in capacitor is 1 VI PR 3 2 VI PR VI PR 2 4 VI PR

1 A capacitor of capacitance 400 F is charged upto a potential of 100 volt and another capacitor of capacitance 600 F 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

4 Find the equivalent capacitance between point a and b in the following arrangement of plates Each plate has the area A and separation between the plates is d 1 3 2 A 3 d 2AE d ps 2 4 a 3 AE 2 d 3A d etska 20 00

Four capacitors and a switch are connected in the circuit as shown in the figure Initially switch S is open Now if switch S is closed then charge flown through switch in C 6 F 200V 3uF B Write an answer 3 F S 6 F V 0

An uncharged capacitor C resistances R R and R 2R cells of emf E E and E E are connected as shown in the figure First switch S is connected to terminal 1 for a long time H is heat energy lost through the resistor R up to the steady state and U is energy stored in the capacitor at steady state Now the switch is connected to terminal 2 for an another long duration H is heat energy lost through the resistor R up to the steady state and U2 is energy stored in the capacitor at steady state Choose the correct statement s HARC fate R RR 2R E E E Efs and farger gerne Her er en af U 3 Raa R fa 2 i 3 R en U 1 515 A U 1 www R wwwwww R B 14 TH E E S 2 C H 2H D H CE

There are five large conducting plates of equal area A connected such that potential of plates 1 and 4 is same 2 and 5 is same then find equivalent capacitance between 1 and 5 2 3 B C 5 A 2 d A d EA 5d 5A

d The driving for 12 When an AC voltage of 220 V is applied to the capacitor C a the maximum voltage between plates is 220 V b the current is in phase with the applied voltage c the charge on the plates is in phase with the applied voltag power delivered to the capacitor is zero

In a circuit shown in figure resistances R and R are known as well as emfs E and Ez The internal resistances of the sources are negligible At what value of the resistance R will the thermal power generated in it be the highest ALSO he EU 0 in the circus shown in tale SWAILLES A R1 R B R R www www LE Reclar C R R D low rmyn R R R R

Two identical capacitors A and B charged to the same potential 5V are connected in two different circuits as shown below at time t 0 If the charge on capacitors A and B at time t CR is QA and QB respectively then Here e is the base of natura logarithm R HE A R www B

Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant K The charge on each capacitor is q Find the extension in the spring at equilibrium JEL1 13 q 2A k q k smooth 2 A 151 q 4A k Zoro

A parallel square plate capacitor of side a is connected to a cell of emf 3 volt A dielectric of mass m 0 1 kg and dielectric constant K initially completely fills the space between plate of parallel plate capacitor The dielectric is connected to a solid cylinder of mass m 0 1 kg through the string Cylinder is pulled by a tangential force F 1 N and acting on top of cylinder The surface between cylinder and horizontal surface is enough rough to prevent slipping The distance between plate is d The graph between the current through the cell V S time t is a straight line till dielectric leaves the capacitor Find the slope of straight line a K 1 d 3V E Given F 1N 9

4 A 900 pF parallel plate capacitor is charged by 100 V ideal battery The space between the plates is 1cm How much electrostatic energy is stored per unit volume of empty NCERT Pg 82 space of capacitor 1 4 42 10 4 Jm 3 2 8 85 10 6 Jm 3 3 2 21 10 7 Jm 3 4 6 2 10 6 Jm 3

A slab of material of dielectric constant 3 has the same are 3 A as the plates of parallel plate capacitor and thickness where d is plate separation The new capacity when slab is inserted between the plates is Unchanged Twice the original value Thrice the original value Four times the original vale 4

Minimum number of capacitors each of 8 F and 250 V used to make a composite capacitor of 8 F and 1000 V is 6 8 16 32