Capacitors Questions and Answers

Initially charged two capacitors and a battery of 100 V are arranged as shown in the figure Now the switch S is closed List I P Final charge on 1uF capacitor Q Final charge on 2 F capacitor R Charge flown through switch S Total work done by battery during the process magnitude A P 1 Q 4 R 1 S 2 3 R 1 8 4 P 90V HE 1 F H 100V 40V DE 2 F List II 1 20 2 2000 3 60 4 70 B P 4 Q 3 R 1 S 2 D P 4 0 4 R 1 S 3

Three capacitors each of capacity 4 microfarad are to be connected in such a manner that the effective capacitance is 6 microfarad This can be done by 4 Hisal a Galdi uka 6 OPTIONS MARK FOR REVIEW CLEAR SELECTION All the three are connected in series A AU FUGA All the three are connected in parallel BA D BHAR HUIG OC n DI Two are connected in parallel and then connected in series with the third capacitor Red de fe der Huika ug Auf HYGG Two are connected in series and thon

A R C circuit is shown in figure Each resistor is having a resistance R and capaci tance of capacitor is C and initial charge on capacitor is zero At t 0 switch S i closed ww R www E A In steady state current through the battery is 5R CE B In steady state charge on the capacitor is A CE D Charge on capacitor as function of time is www C The total energy stored in the capacitor in steady state me 191 SRC 82

The graph between capacitance of a parallel plate capacitor and charge on a capacitor is charge is within breakdown limit of capacitor a atenkai aur unka u de OPTIONS MARK FOR REVIEW CLEAR SELECTION Straight line inclined to charge axis A B C B OC Straight line parallel to charge axis DE FRE Straight line parallel to capacitance axis CERERE

Capacitance of a sphere A is 4 F while for another sphere B it is 8 uF If on sphere A there is a charge 2 C and on 8the charge is 4 C then the ratio o potentials of the spheres is Batra 8 F A r 2 C Gi ri a BYR 4 C Gi r a t c faya 351 3FUID OPTIONS MARK FOR REVIEW CLEAR SELECTION OA 6 1 B 1 1 OC 4 1 OP 2 1

xiii A potential difference of 300V is applied between the plates of a plane capacitor spaced 1cm apart A plane parallel glass plate with a thickness of 0 5cm and a plane parallel paraffin plate with a thickness of 0 5cm are placed in the space between the capacitor plates find a intensity of electric field in each layer b the drop of potential in each layer c the surface charge 2 density of the free charge on the plates Given that k paraffin 6 k glass a 1 55 x 104V m 4 5 x 104V m b 75V 225 V c 8 10 7C m

9 An uncharged parallel plate capacitor filled with a dielectric constant k is connected to an air filled identical parallel plate capacitor charged to potential V If the common potential is V then the value of k is 1 V V V V V 2 V V V V E

1 Two identical capacitors are charged to different potentials then they are connected to each other in such a way that the sum of charges of plates having positive polarity remains constant Mark the correct statement at na Afya For far far for at de Ad de fa any a Sum of charges of plates having negative polarity remains constant 3 b Mean of individual final potentials is different from mean of individual initial potentials 3fm fanati fant sted c Total energy stored in two capacitors in final state may be equal to that in initial state 3 3 ta en fed ut 1 d Heat dissipation in the circuit could be zero uffger H

For the circuit shown in figure a battery of voltage Vo is applied across AB Match the entries in column I with entries in column II C 2 2C 3 A C 1 2C C 4 Column l Q1 Potential across capacitor 1 Q2 Potential across capacitor 2 Q3 Potential across capacitor 3 Q4 Potential across capacitor 4 C Column II A1 A2 A3 A4 6 7V 12 3 B Vo 4

Consider a system of four large thin metal plates of plate area A each arranged parallel to each other as shown in steady state Now the key is closed so that the system again reaches steady state Work done by the cell after the key is closed is key

A certain capacitor is rated at 13 nF Currently it uses paper as a dielectric which has K 3 7 If the capacitor is made with the same dimensions but using glass as dielectric which has K 5 6 what will the new capacitance be C nF What if we double the thickness of the glass what will the new capacitance be C nF

In nanofarads What is the capacitance of a parallel plate capacitor with metal plates each of area 0 29 m separated by 1 00 mm of air C nF What charge in nancoulombs will be stored on each plate when attached to a 5 4 Volt power supply Q nC

These three capacitors are attached in series to a 9 Volt battery Their capacitances are C1 17 F C2 55 F and C3 115 F Find the equivalent capacitance of the circuit the total charge the charge on each capacitor and the voltage across each capacitor Ceq QT Q1 Q C3 Q3 V V V3 HC UF HC HC C V V V

A 48 F Capacitor is attached to a 10 9 Volt power source After the capacitor is fully charged what will be the charge on the positive side of the capacitor unit q What is the charge on the negative side unit q

Three capacitors C 80 F and C 160 F and C3 120 F are combined as shown What is the equivalent Capacitance the system of capacitors shown UF Capacitance

The charge on one plate of a capacitor is 40 nC and the charge on the other plate is 40 nC If the potentia difference between the plates is 200 Volts what is the capacitance of the capacitor pay attention to units Capacitance Farads

What is the Voltage across a 11 6 F capacitor with 100 C of charge on each plate V unit How much energy is this capacitor storing U unit

Problem Find the equivalent capacitance of the circuit below Please show work for credit Please Show Work 30 points 15 00 uF 4 00 F HH 6 00 uF 3 00 uF 12 00 uF 3 00 uF 7 00 F

Consider the series RC circuit shown below for which R 40 0 k2 C 47 0 F and E 17 0 V Find the following C S R a the time constant of the circuit b the charge on the capacitor one time constant after the switch is closed

The circuit in the figure below contains a 9 00 V battery and four capacitors The two capacitors on the left and right both have same capacitance C 11 60 uF The capacitors in the top two branches have capacitances of 6 00 uF and C 5 60 uF 6 00 F UF 9 00 V a What is the equivalent capacitance in uF of all the capacitors in the entire circuit b What is the charge in uC stored by each capacitor right 11 60 F capacitor C left 11 60 F capacitor C 5 60 F capacitor C 6 00 uF capacitor C c What is the potential difference in V across each capacitor Enter the magnitudes right 11 60 F capacitor V left 11 60 F capacitor 5 60 F capacitor 6 00 uF capacitor V V V

a How much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is 6 00 cm Assume air has a dielectric strength of 3 00 x 106 V m and dielectric constant of 1 00 nC b Find the maximum charge if nylon is used between the plates instead of air Assume nylon has a dielectric strength of 14 0 x 106 V m and dielectric constant of 3 4 nC

n air filled parallel plate capacitor has plates of area 3 00 cm separated by 1 70 mm The capacitor is connected to a n 22 0 V battery a Find the value of its capacitance pF b What is the charge on the capacitor pC c What is the magnitude of the uniform electric field between the plates N C

a A physicist connects a 8 50 V battery to the plates of a capacitor After waiting a while the capacitor reaches a maximum amount of 32 0 C of stored charge What is the value of the capacitance in uF UF b The capacitor is disconnected from the battery discharged and then connected to a 17 5 V battery Again jong enough time is waited for the capacitor to fully charge How much charge in uC is stored now Assume the capacitor can handle this new voltage without failing C

4 In the shown circuit involving a resistor of resistance R 2 capacitor of capacitance C farad and an ideal cell of emf E volts the capacitor is initially uncharged and the key is in position 1 At t 0 second the key is pushed to position 2 for to RC seconds and then key is pushed back to position 1 for to RC seconds This process is repeated again and again Assume the time taken to push key from position P 1 to 2 and vice versa to be negligible 6 K 1 The charge on capacitor at t 2RC second is A CE B CE 1 2 A www R B E 5 The current through the resistance at t 1 5 RC seconds is A 1 1 e R C C CE 2 Then the variation of charge on capacitor with time is best represented by M mor C 3 D CE 1 e D D VER 1 1 m

deviation angle of the prism and angle of VI Answer any THREE of the following questions 3x5 15 33 A parallel plate air capacitors of two plates each of area 0 01 sq m separated by distance of 0 1 mm Calculate its capacitance If capacitor is charged to a potential 50 volt find the charge on the capacitor

2 Capacitance of a parallel plate capacitor depends on a Electric charge stored b Potential difference applied b Electric field between the plates d Electrical permittivity of the medium between the plates Brospectively B

An insulator plate is passed between the plates of a capacitor Then current 1 A B 1 Always flows from A to B 2 Always flows from B to A 3 First flows from A to B and then from B to A 4 First flows from B to A and then from A to B

Q2 A parallel plate capacitor with air as medium between its plates has a capacitance of 10 uF The capacitance becomes 60 F when a dielectric medium is introduces between its plates The relative permittivity of the dielectric medium is a 10 b 6 c 60

Five plates each of area A are arrange in the diagram If the spacing between two consecutive plates is d 1 equivalent capacitance between a and a Only one correct answer i b

D6 4 Figure 6 9 shows the cross section of two circular cylinders at potential of 0 and 60 V The axes are parallel and the region between the cylinders is air filled Equipotentials at 20 V and 40 V are also shown Prepare a curvilinear square map on the figure and use it to establish suitable values for a th capacitance per meter length b E at the left side of the 60 V conductor if it true radius is 2 mm c ps at that point Ans 69 pF m 60 kV m 550 nC m V 0 V 60 V

127 Find equivalent capacitance between A and B 1 w 0 2 3 3C 4 20 A B 2 the sa 4 R Th ch A A po R TH wh 3 A A of R TH of A E p

Four identical plates 1 2 3 and 4 are placed parallel to each other at equal distance as shown in the figure Plates 1 and 4 are joined together and the space between 2 and 3 is filled with a dielectric of dielectric constant k 2 The capacitance of the system between 1 and 3 2 and 4 are C and C respectively The ratio A 5 C C is B 1 C 5 D 3 5 4

The space between the plates of a parallel plate capacitor is filled with two dielectrics of thickness d and d and relative permittivities and 2 respectively If a single dielectric of the total thickness d d is to replace the two effectively to get the same capacitance then its relative permittivity should be A d d B d d e d d C d d d d e D d d d d

b How would your answer differ if the sphere was solid A plane parallel capacitor consists of two metallic plates of area A 2 m2 each separated by a d 0 5 mm of air Assuming that a spark occurs if the electric field is larger than 106 V m Break down field how much charge can be stored in the plates 3 Two concentric metallic shells of radius R1 and a Find the charges in the inner and the outer CAL

12 A particle of charge q is placed at the inner surface of a hemisphere of radius R directly above the c symmetrically Calculate the flux through the outer curved surface of the hemisphere 13 In the circuit shown in figure C 6uF Find the charge stored in the capacitor of capacitance C

Q 125 A capacitor is charged by a battery The battery is removed and another identical uncharged capacitor is connected in parallel The total electrostatic energy of resulting system 1 decreases by a factor of 2 2 remains the same 3 increases by a factor of 2 4 increases by a factor of 4 3 6i 5j 2k 4 2i 3j k Q 125 fan va tet saferer fazen feteater AN a wire fau en ferger 1 m 2 1 after f 2 3 2 4 4 ft et f

2 170 In the circuit shown both capacitors are Q 170 identical Now the plates of capacitor 1 are moved further apart then 1 2 1 Charge on capacitor 1 will become less than that on capacitor 2 2 Potential difference across capacitor 1 increases 3 Potential difference across capacitor 1 decreases 4 Potential difference across capacitor 2 does not change f 1 at et un ren tat 1 1 a 2 go ETIT al Exa 2 3 f 1 ft a 4 na 2 a fet a TE ST 1 a feret afavareren fer tran fare ufada

The 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 11 2C 2kV HH DU JAZ

5 6 Following figure shows the initial charges on the capacitors After the switch S is closed find The charge on capacitor C A 0 C The charge on capacitor C A 0 C The work done by the battery A 50 J B 5 C B 5 C B 100 J 10 C 10 C 1 uF C 1 uF 00 10 V C 10 C C 10 C C 150 J D None of these D None of these D Zero

The outer sphere of a spherical capacitor is earthed For increasing its capacity 1 Vacuum is created between two spheres 2 The space between spheres is increased 3 Earthing of outer sphere is removed 4 Dielectric spheres material is material is filled between two

Example 61 In the circuit shown in Fig 2 75 if the point Cis earthed and point A is given a potential of 1200 V find the charge on each capacitor and the potential at the point B C HI 4 F C3 1200 V A C HI 3 F O B V 0 C

A certain series R C circuit is formed using resistance R a capacitor without dielectric having a capacitance C 2 F and a battery of emf E 3 V The circuit is completed and it is allowed to attain the steady state After this at t 0 half the thickness of the capacitor is filled with a dielectric constant k 2 as shown in the figure The system is again allowed to attain a steady state What will be the heat generated in joule in the capacitor between t 0 and t o Kd 2 K A B K 2 3 LO 5

A 2 F capacitor is charged to a potential of 200 V and a 1 F capacitor is charged to 100 V The capacitors are then connected in parallel with plates of opposite polarity joined together The common potential will be 500 3 V 100 V O 200 v V 3 O 150 Y

Figure shows two identical parallel plate capacitors connected to a battery with the switch S closed The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of K 3 Find the ratio of the total electrostatic energy stored in both the capacitors before and after the introduction of the slab S EC 2105 C 3 1 2 A S B 4 0 8

A parallel plate capacitor is charged to 50 C at 150 V It is then connected to another neutral parallel plate capacitor of capacitance 4 times of charged capacitor Find the loss in energy in mJ Answer 00 01 8 01 02 03 04 05 06 07

A parallel plate capacitor with a glass slab of dielectric constant k between the conducting plates is charged to a potential V The connecting wires are then disconnected and the glass slab is removed The potential difference between the plates is A KV B V C V k D zero 199

surface d there must be charges inside the surface The graph shows the variation of voltage Vacross the plates of two capacitors A and B versus increase of charge Q stored in them Which of the capacitors has higher capacitance for VB bob VA CHERTLI AR B AC Q A 160 W zi laba a Capacitor A Ju b Capacitor B c Both have same capacitance Q MIL

Before filling with dielectric a parallel plate capacitor has a capacitance of 6 F It is filled by dielectric and connected to a battery as shown in the circuit diagram The electrostatic energy stored in the capacitor is k 8 k 12 a 0 3 J b 0 6 J c 0 9 J d 1 2 J 100V

Two identical metal plates are given positive charges Q and Q Q respectively If they are now brought close together to form a parallel plate capacitor with capacitance C the potential difference between them is a Q1 Q2 2C b Q1 Q2 C c Q1 Q2 C d Q1 Q2 2C

30 A point charge q is surrounded by eight identical charges at distance r as shown in figure How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity 1 Zero 8q 4Teor 9 q q 9 0 9 9 Eor d q 9 2 9 3 Electrostatics of Conductors Dielectrics and Polarization Capacitors and Capacitance 8q 4Teor 31 1000 small water drops each of capacitance C join together to form one large spherical drop The capacitance of bigger sphere is 1 C 2 10 C 3 100 C 4 1000 C 32 Two similar conducting balls having charges q and q are placed at a separation d from each other in air The radius of each ball is r and the separation between their centres is d d r Calculate the capacitance of the two ball system 64q 4Teor 1 4TE 2 2 3 4rloge 4 4rloge The Parallel Plate Capacitor Effect of Dielectrics on Capacitance Combination of Capacitors 33 Two parallel plate capacitors have their plate areas 100 cm and 500 cm respectively If they have the same charge and potential and the distance between the plates of the first capacitor is 0 5 mm then the distance between the plates of the second capacitor is 1 0 10 cm 2 0 15 cm 00 34 A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacitor carrying charge q The induced charge q on the surface of slab is given by q 1 q q 2 q q K 4 d a 1 1 0 05 36 3 q q 35 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 mhm 1 2AEok q A ok ka edice IIT JEEF 3 5 A d 3 4 Zero The following arrangement consists of five identical metal plates parallel to each other Area of each plate is A and separation between the successive plates is d The capacitance between P and Q is 4 EA 3 d q K 1 K fig A 1 2d 3 2 3d 2 3 3d 4 k www smooth q 2 4A ok 2 A Q 37 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 5 EA d fig B d