Capacitors Questions and Answers

9 A conductor carries a certain charge When it is connected to another initial uncharged conductor of finite capacity then the final energy of combined system is 1 More than that of the first conductor 2 Less than that of the first conductor 3 Equal to that of the first conductor 4 More or less depends on the shape of the conductor

3 a 9 A capacitor of capacitance C is charged by a battery to a potential difference V Now it is disconnected from this battery and connected to another battery of potential difference 2V so that positive plate of capacitor is connected to positive terminal to the battery and negative plate of the capacitor is connected to the negative terminal of the battery The heat produced in the circuit is 1 CV 2 CV 2

50 Capacitance C 2C 2C3 and potential ons A difference across C C and C3 are V V and V3 respectively then C C IF V 1 V V V3 2 2 V 2V 2V3 1 3 2V V V3 2 4 2V 2V V C Au Au 0010 PACITOR 02 EXERCISE P65

Two capacitances C and C are connected in series assume that C C The equivalen capacitance of this arrangement is C where 1 1 C C 2 2 C 2 C C 3 C C C 4 C Mosse

7 The effective capacitance between the points P and Q of the arrangement shown in the figure is loq to leitaston IT V 2 F P HH 2 F VO 1 1 2 UF HH 5 F 2 F 1 F HH HH HH 2 F 1 F 2 1 F Q Shuning

Five identical conducting plates 1 2 3 are fixed parallel to and equdistant from each other see figure Plates 2 5 are connected by a conductor while 1 3 are joined by another conductor The junction of 1 3 and the plate 4 are connected to a source of constant e m f Vo Find the effective capacity of the system between the terminals of the source 1 5 A 3 d A 5 4 3 2 2 2 A 3 d 5E A

Initially both the capacitors are uncharged in the shown circuit If switch is closed at t 0 then charge on capacitor C at time t is ww R 2C HH HH C E C 2R www www 2R Switch

4 a On what factors capacitance of a capacitor depend b Two capacitors of capacitances 2 F and 4 Fare connected in parallel A 300 volt potential differen is applied across the terminal Find out the energy stored in the combination

The resistance of the galvanometer G in the circuit is 2592 The meter deflects full scale for a current of 10mA The meter behaves as an ammeter of three different ranges The range is 0 10A when the terminals O and P are taken The range is 0 1A between 0 and Q The range is 0 0 1A between O and R The value of R3 is 0 R ww 10 A P R ww 1A R 0 1A

9 Consider the two long cylindrical conductor separated by a distance de form a capacitor Cylinder 1 has charge density A and radius b and Cylinder 2 has charge density A and radius b Show that the capacitance per unit length is given approximately by C TEO In Teo In where b is the geometric mean LL 71

lo max 20 voo op E 0 i 739 200 Z max ooo N O 000 pi day 9 q da vi ooo Palla La 2020 71 000 7 voo B E E Oscillating Accelerated Charge Oscillating charge Oscillating Electric Field Produces an Oscillating Magnetic Field htt 1 0 L C Osallations t Wave propogating abng x E and B are in same phase X Self Propogating den

What happens to the capacitance of a parallel plate capacitor if the area of its plate is tripled Options The capacitance of a parallel plate capacitor is tripled 2 3 4 The capacitance of a parallel plate capacitor is doubled The capacitance of a parallel plate capacitor is quadrupled The capacitance of a parallel plate capacitor does not change

A point object O is placed between two plane mirrors as shown in M 10mm M figure If object is moved toward M with speed u then relative speed between first images of M and M is A Zero B u D 2u u C 17 7 2 NE A point obiect in pla O

A finite ladder is constructed by connecting several section of 3 F 6 F capacitor combinations as shown The value of C such that the equivalent capacitance of ladder between the points A and B become independent of number of sections in between 6 F A 3 F Bo 3 F 6 F HH 3 F 6 F 16 C

A perfect insulator is filled between the plates of a capacitor For practical purposes this insulator is assumed to be perfect when its resistance is taken to be very large or infinite Due to this if a capacitor is connected to a battery no current flows through it in steady state However an insulator pl So due to the must have some finite resistance which can be calculate by using the relation R A finite value of the resistance a non zero current must pass through the resistance This small non zero current is called leakage current Consider a leaky parallel plate capacitor is filled completely with material having dielectric constant K 18 and its resistivity is 47x10 22m The charge on the plate at instant t 0 is 2 C Based on the above facts and the data provided answer the following questions Charge on the capacitor at t 2 s is in uc WANAWA

A condenser of capacity C is charged to a potential Vo The electrostatic energy stored in it is U It is connected to another uncharged capacitor C in parallel The energy dissipated in the process is O O C C C U C U

Two capacitors C 3 F and C 6 F in series are connected in parallel to a third capacitor C3 4 F This arrangement is then connected to a battery of emf 30 V as shown The energy lost by battery in charging the capacitor 3 F HE 4 F 6 F

36 Take the breakdown voltage of the zener diode used in the given circuit as 6 V For the input voltage shown in the figure below the time variation of the output voltage is Graphs drawn are schematic and not to the scale A V 0 10 V M 10 V Vin R ww

A capacitor is charged to 500 V and then its plates are joined together through a resistance of 10 2 If the heat produced in the resistance is 1 25 J then the capacitar will be a 1 F d 0 F b 10 uF c 100 F

A parallel plate capacitor made of circular plates each of radius R 6 0 cm has a capacitance C 100 pF The capacitor is connected to a 230 V AC supply with an angular frequency of 300 rad s The amplitude of B at the point 3 cm from the axis between the plate is 0 0 1 1 12 x 10 11 q 2 2 01 x 10 2 T 3 1 63 x 10 7 4 1 01 x 10 12 T

Three identical large metal plates each of area S are at distance d and 2d from each other as shown Metal plate A is uncharged while metal plates B and C have charges Q and Q respectively Metal plates A and C are connected by a conducting wire through a switch K The electrostatic Find the value of N energy lost when the switch is closed is Q d NE S 2d A B 2 352 Q 2 6 plates capaci 45 2 3 AAG

cuit shown here C 6 F C 3 F and battery B 20 V The switch S is first closed It is then opened and Es S is closed What is the charge on C C 6 F 3 F S

An air capacitor has capacitance 70 F with a separation between plates 20 mm Now distance between plates is doubled and dielectric of k 2 thickness 10 mm is inserted between the plates of capacitor then its capacitance becomes A 35 F 40 F 50 uF

24 Initially switch remains in position 1 for long Now it is turned to position 2 Find amount of charge flow from point P in indicated direction 10 V 1 Zero 3 12 UG 2 5 F 0 P 2 25 C 4 125 G 15 V

the given capacitance circuit all the capacitors are uncharged Find the charge flown through the battery as the switch S is closed 1 F 1 F 2 F HH 1 F 2 F 130 V Options 1 135 C S 0 5 F 0 5 F

91 Two identical metallic plates are given positive charges Q and Q Q Q If these plates are brought together to form a parallel plate capacitor then potential difference between them will be 09 a Q Q 20 Consider b W li le C G le C G l 2C

93 Each of two identical capacitors has capacitance C one of them is charged to a potential V and the other to a potential V The negative terminals of capacitors are connected together When their positive terminals are also connected together then energy loss of whole system is a C V V b C V V c C V V d C V V

which these parameters belong Column I A Work done by external agent is negative B Electric field between plates increases C Energy of capacitor decreases D Force between plates remains constant Shows tha ange Column II P Dielectric is being removed slowly from a charged capacitor Q Dielectric being introduced slowly while battery is connected th R Dielectric is being introudced slowly in a charged capacitor dh S Plates of capacitor are being slowly moved closer to T Plates of capacitor are being moved slowly in a charged capacitor

1 70 The capacitance of a capacitor becomes times its original value if a dielectric slab of thickness t d is introduced in between the plates where d is the separation between the plates The dielectric constant of the slab is a 144 b 11 11 d 11 8

43 On reducing potential across a capacitor its capacitance a decreases c remains constant 44 A charge 0 is supplied to 110 b increases d first increases then decreases TITE

8 Two identical capacitors joined in parallel are charged to a common potential V 2 Th battery is disconnected Now the capacitors are separated and joined in series For the ne combination a Energy and p d both will remain unchanged b Energy will remain same p d will become l c Energy and potential both will become 2 times d Energy will become 2 times p d will remain I

The capacitance of C and C shown in the diagram is C C is initially uncharged and C is given a charge 2C as shown Which of the following graph represents charge on plate B of capacitor C as a function of time A CE 2 2CE 2CE B CE C 3CE 2 2CE D 2CE 9

3 If the potential of a capacitor having capacitance 6 uF is increased from 10 V to 20 V th increase in energy is a 9 x 10 J c 12 x 10 J b 4 5 x 106 J d 2 25 x 10 J

8 A wire of a certain material is stretched slowly by ten per cent Its new resistance and specific resistance become respectively AIPMT Prelims 2008 1 1 1 times 1 1 times 2 1 2 times 1 1 times 3 1 21 times same

Solution Initial energy of capacitor E CV av 2c0 2 V At steady state the potential across capacitor is equal to battery Thus Final charge on capacitor becomes CV For 2CV 2CV e ee e DI

2 There is a distance d between two parallel conductive plates each of which has a surface area of S and the upper plate and the bottom plate are kept at VO and 0 potential respectively A non omic piece is placed in the space between the plates Accordingly a Find the total resistance between the plates b Find the surface charge densities on the plates c Find the volumetric charge density and total charge between the plates

A 914 m long interconnect wire has a resistance per unit length of 0 2 02 m and a capacitance per unit length of 0 9fF um I this wire drives a 47fF load what is the delay through this wire in picoseconds

A parallel plate capacitor with no dielectric has a capacitance F The space between the plates is then fixed with equal amount of two di electric of di electric constance 2 and 3 In the two arrangement as shown one by one find the ratio of capacitances C and C II HASI KEK 13 I I

Three capacitors C 20 pF C 10 pF and Cy 30 F are connected to a potential difference of AV 14 Vas thewn in the figure Find the voltage in Vall C C 10 F HH G C 20 F H C 30 uF

A variable capacitor is connected to a 200 V battery If its capacitance is changed from 2 F to X F the decrease in energy of the capacitor is 2 x 10 2 J The value of X is a c 1 F 3 F b d 2 F 4 F

Solve for i t in circuit as shown in Fig 4 in which 3 F capacitor is initially charged to 20V the 6F capacitor to 10V and the switch is closed at t 0 Also draw the transformed circuit 5 20V 3F 2 t 0 102 i t Fig 4 www 10 10V 6F

the circuit given below all capacitors have identical capacitance of 10 pF The equivalent capacitance of the combination between P and Q is C C a 10 F b 5 F c 15 F d 20 F C C H C

A parallel plate air capacitor of capacitance Cis connected to a cell of emf Vand then disconnected from it A dielectric slab of dielectric constant K which can just fill the air gap of the capacitor is now inserted in it Which of the following is incorrect The charge on the capacitor is not conserved The potential difference between the plates decreases K times The energy stored in the capacitor decreases K times The change in energy stored is 1 cv 1 1

2 b Solve for i t in circuit as shown in Fig 4 in which 3 F capacitor is initially charged to 20V the 6F capacitor to 10V and the switch is closed at t 0 Also draw the transformed circuit 5 20V3F t 0 meto 10 i c Fig 4 www 10 10V 6F

3 A part of circuit in steady state along with the current flowing in the branches with value of each resistance is shown in figure 2 A ZA 3Q 192 3Q 4 F 1 A 522 www www 292 19 www 422 1 A The energy stored in the capacitor is x 10 4 J Find r

Five plates each of area A are arranged as in the diagram If the spacing between any two consecutive plates is d then equivalent capacitance between a and b is a Only one correct answer b

Two parallel plate air condensers have same dimensions A glass plate and an identical mica plate relative permittivity of glass is greater than that of mica have been introduced between the plates in each condenser new capacities become Cg and Cm respectively then the ratio of becomes Only one correct answer A Greater than 1 B Less than 1 C Equal to 1 Cm Cg

Two capacitors of capacitances C and 2C are charged to potentials 2V and V respectively and then these capacitors are disconnected from the charging batteries Now capacitors are connected together such that their opposite polarity plates are connected together The loss in potential energy of the system is Only one correct answer A CV B CV2 C CV D 3CV

A parallel plate capacitor consists of two square plates of side length a 6 cms There is dielectric slab in the shape of a cylinder of parabolic cross section between the plates as shown in figure The dielectric constant of the material is K 2 The length of latusrectum of the parabola is equal to the side length of the plate Then the capacitance is given by 4E N 10 farad then fin d the value of N K

A parallel plate capacitor with plate area A and separation d has charge Q A slab of dielectric constant k is inserted in space between the plates almost completely fills the space IfE and C be the electric field and capacitance before inserting the slab then E A the electric field after inserting the slab is k B the capacitance after inserting the slab is k C C the induced charge on the slab is Q D the energy stored in the capacitor becomes U being the energy of the capacitor before