A capcitor is a divice which stores electric energy. It is also named as condenser.

Transcription

1 PITNE PITNE. capcitor is a ivice which stores electric energy. It is also name as conenser. When charge is given to a conuctor, its potential increases in the ratio of given charge. The charge given to the conuctor is irectly proportional to its potential. v or = cv where is a constant calle electrical capacitance of the conuctor. If V= volt, then = ; i.e., the electrical capacitance of the conuctor is equal to that amount of charge which increases the potential of the conuctor by a unit amount. The electrical capacitance of the conuctor epens upon the following: (a) The size of the conuctor: The capacitance is irectly proportional to the area of the surface of the conuctor, i.e., (area) (b) The meium aroun the conuctor: If a conuctor is place in a meium other than air or vacuum, its capacitance will increase. meium K airor vacuum where K is a constant calle ielectric constant of the meium. This constant is always greater than. Theoretically the charge can be given to any isolate conuctor upto an infinite amount. When a very large amount of charge is given to the conuctor, its potential increases to such an extent that ielectric breaks own an the charge starts leaking from the object an electrical ischarge takes place between the conuctor an nearby objects or earth. This ecreases the potential of the conuctor. Unit of apacitance: (a) In M.K.S. system unit of capacitance is fara. coulomb fara volt Dimensions of the capacitance are 4 M L T (b) If a charge of one coulomb given to a conuctor increases the potential by one volt, then its capacitance is one fara. (c) In practice, submultiples of fara are use as units of capacitance. 6 micro fara = F 0 F nano fara = 9 nf 0 F () micro-micro fara or pico fara = F pf 0 F Electrostatic unit of electrical capacitance is stat fara. fara = 9 0 statfara

2 PITNE. When a charge is given to a spherical conuctor of raius R, then The potential of the surface of the spherical conuctor will be V 4 0 R Electrical capacitance of spherical conuctor in M.K.S. system will be 40 R V / 4 R In.G.S. system, 0 R because K = (in.g.s unit) R The electrical capacitance of a spherical conuctor is irectly proportional to its raius i.e., R The electrical capacitance of a spherical conuctor oes not epen on the charge given to a conuctor. 3. P PP PP P PP P P PP P PP PP P PP PP P PP PP PP P PP PP PP PP PP P P P PP PP P The work one in charging a conuctor is equal to its potential energy or the store energy. This energy resies in the form of energy of the electric fiel create. The potential energy of a charge conuctor: 0 U Vq qq or U Unit of U is joule 0 V V Energy store in the conuctor epens upon the given charge, its potential an its capacitance. Store energy epens upon the capacitance of the capacitor an the given charge or the potential ifference. It oes not epen upon the shape of the capacitor. If the area of the plates are an the thickness of ielectric constant is, then energy store per unit volume i.e., energy ensity of the meium will be u E 0r E where E is the electric fiel. The energy of the charge capacitor resies in the electric fiel between its plates. Note : In charging a capacitor by battery half the energy supplie is store in the capacitor an remaining half energy V is lost in the form of heat. 4. RRRRRRRRRRRRRR RR RRRRRR RR RRRRRRR RRR RRRRRRR RRRRRRRRRR RRR RRRRRR RRRR When two charge conuctors are joine together by a conucting wire of negligible capacity, the charge flows from higher potential to lower potential. When the potentials of both conuctors become equal, the flow of charge stops. Law of conservation of charge hols goo in the process i.e., total charge on the two conuctors will be same after reistribution. Let the amounts of charge on the conuctors be an an their electrical capacitances be an respectively. If their potentials are V an V, then

3 V an V Total charge V V V Total capacitance On joining the conuctors, the common potential becomes V, then PITNE V V V V The charge on the conuctors after joining them will be V ' ' V V V V V harge transferre V V ' V ( ((( ( ( ' V The ratio of the amounts of charge after reistribution ' ' In the process of reistribution of charge some work is to be one. Total amount of charge remains constant in this process but their total potential energy ecreases i.e., there is loss of energy. This loss of energy is ue to transformation of electrical energy into heat in the connecting wire an in electrical ischarge. Energy loss ue to reistribution of charge U U initial U final V V, which is always positive. (a) If V V, then U 0 that is, there is no loss of energy. Hence no loss of energy occurs in joining the conuctors of equal potentials. (b) If V V or V V, then V will remain positive. Thus energy will be lost, i.e., there is always V loss of energy in joining the conuctors at unequal potentials.

4 EEEEEEE EEEEE EE EEEEEEE EEEEEEEEEE EEE EEEEEE EEEE EE EEEEEEEEEEEEEE PITNE Ex. 0 capacitor is charge to potential of 500V an then connecte in parallel to another capacitor of capacity 0 F. If the potential of 0 F capacitor is 00 volt then the common potential of two will be [] 00 V [] 00 V [3] 300 V [4] 400 V V Sol. V = V = 400 V Hence the correct answer will be (4) 5. (i) Parallel plate capacitor : It consists of two parallel plates separate by a small istance with a ielectric material in between. If is area of each plate, is the istance between the plates an r is the ielectric constant of the material place between the plates, then the capacitance of parallel plate capacitor will be 0 (for air or vacuum as meium) r where F / m an 0 r (for meium of ielectric constant r ) Note : (i) If two plates are place sie by sie then three capacitors are forme. One between istant earthe boies an the first face of the first plate, the secon between the two plates an the thir between the secon face of the secon plate an istant earthe objects. However the capacitances of the first an thir capacitors are negligibly small in comparison to that between the plates which is the main capacitance. The capacitance of a capacitor epens upon the following: (a) rea of the plates : The capacitance is irectly proportional to the area of either plate, i.e.,. (b) Distance between the plates : The capacitance of a capacitor ecreases as the istance between the plates increases i.e., (c) Dielectric meium between the plates : If any meium other than air or vacuum is between the plates, the capacitance of the capacitor increases by constant of the meium. r times where r is calle relative permittivity or ielectric On keeping the ielectric meium between the plates, the charge on the plates remains unchange but the potential ifference between the plates ecreases. Note : (ii) It is a very common misconception that a capacitor stores charge but actually a capacitor stores electric energy in the electrostatic fiel between the plates. The energy ensity of the fiel u = E

5 PITNE (iii) Two plates of unequal area can also form a capacitor because effective overlapping area is consiere. (iv) The istance between the plates is kept small to avoi fringing or ege effect (non-uniformity of the fiel) at the bounaries of the plates. Dielectric Meium an Dielectric onstant: Note : (v) Dielectrics are insulating (non-conucting) materials which transmits electric effect without conucting we know that in every atom, there is a positively charge nucleus an a negatively charge electron clou surrouning it. The two oppositely charge regions have their own centres of charge. The centre of positive charge is the centre of mass of positively charge protons in the nucleus. The centre of negative charge is the centre of mass of negatively charge electrons in the atoms/molecules. () Type of Dielectrics : Dielectrics are of two types - (i) Polar ielectrics : Like water, lcohol, O, NH 3, (ii) Non polar ielectric : Like N, O, Benzene, Hl etc. are mae of polar atoms/molecules M et h a ne e t c. a r e m a e o f no n - po la r atoms/moelcules. In non-polar molecules, when no In polar molecules when no electric fiel is applie electric fiel is applie the centre of positive charge centre of positive charges oes not coincie with the coincies with the centre of negative charge in the centre of negative charges. molecule. Each molecule has zero ipole moment in its normal state. O 05º P = 0 H P H polar molecule has permanent electric ipole moment (p) in the absence of electric fiel also. But a polar ielectric has net ipole moment is zero in the absence of electric fiel because polar molecules are ranomly oriente as shown in figure. - In the presence of electric fiel polar molecules tens to line up in the irection of electric fiel, an the substance has finite ipole moment. P When electric fiel is applie, positive charge experiences a force in the irection of electric fiel an negative charge experiences a force in the irection opposite to the fiel i.e., molecules becomes inuce electric ipole. E Note : In general, any non-conucting, material can be calle as a ielectric but broaly non conucting material having non polar molecules referre to as ielectric because inuce ipole moment is create in the non polar molecule.

6 PITNE () Polarization of a ielectric slab : It is the process of inucing equal an opposite charges on the two faces of the ielectric on the application of electric fiel. Suppose a ielectric slab is inserte between the plates of a capacitor, as shown in figure. E i Inuce electric fiel insie the ielectric is E, hence this inuce electric fiel ecreases the main fiel E to E E i i.e., New electric fiel between the plates will be E = E E i. (3) Dielectric constant : fter placing a ielectric slab in an electric fiel. The net fiel is ecrease in that region hence. E If E = Original electric fiel an E = Reuce electric fiel. Then E E' = K where K is calle ielectric constant K is also known as relative permittivity (e r ) of the material or SI (specific inuctive capacitance) The value of K is always greater than one. For vacuum there is no polarization an hence E = E an K = (4) Dielectric breakown an ielectric strength : If a very high electric fiel is create in a ielectric the outer electrons may get etache from their parent atoms. The ielectric then behaves like a conuctor. This phenomenon is known as ielectric breakown. The maximum value of electric fiel (or potential graient) that a ielectric material can tolerate without it s electric breakown is calle it s ielectric strength. S.I. unit of ielectric strength of a material is V m but practical unit is kv mm. On the basis of electrical behavior there are three types of meium: (a) conuctor (b) semiconuctor (c) insulator Free charge carriers o not exist in insulators an their conuctivity is of the orer of 6 0 mho/metre or resistivity of the orer of 6 0 ohm-m. In insulators there is microscopic local isplacement of charges uner the influence of electric fiel. Such materials are calle ielectrics. Electrical behaviour of a ielectric meium is represente by a imensionless constant calle ielectric constant. Dielectric constant Permittivity of meium Permittivity of vacuum or free space r 0 Dielectric constant is also calle relative permittivity or specific inuctive capacity of that meium. Dielectric constants are ifferent for ifferent meia. Following effects are observe when a ielectric meium is place between the plates of the capacitor. (a) The capacitance of the capacitor increases while the potential ifference between the plates ecreases.

7 (b) The capacitor can be charge upto a higher potential than without the ielectric. PITNE (c) Electrostatic potential energy of the capacitor ecreases. () The plates of the capacitor can be place very close to each other without touching each other. The capacitance, electric fiel E, potential ifference V an the charge q are effecte ue to introuction of ielectric meium as follows (a) 0 r (b) E 0 E for a given charge r (c) V 0 V for a given charge () q' r q for a given potential ifference. r (a) If capacitor is partially fille with ielectric between the plates, then 0 t r where t is the thickness of the ielectric meium. (b) If several slabs of ielectrics of ifferent thicknesses are place between the plates, then t t t t 3 = 3 0 t t t r r r3... r (a) r r r3 (b) (c) If a slab of metal r of thickness t is place between the plates, then 0 t Example base on apacitance of apacitors of Different Shapes Ex. Two ielectrics of equal size an of constant an 3 respectively fill up space between two plates of a conenser. The ratio of capacities in two possible arrangements will be 4 [] 5 5 [] 4 [3] 5 4 [4] 4 5 Sol. = KK [K K ] = [ K K ] 4 KK = (K K ) or = = 5 Hence the correct answer will be ()

8 PITNE Ex.3 The capacity of a parallel plate capacitor in air is 50 F an on immersing it into oil it becames 0 F. The ielectric constant of oil is [] 0.45 [] 0.55 [3].0 [4].0 Sol. K = 0 K = 0 = = Hence the correct answer will be (4) Ex.4 parallel plate capacitor with air between the plates has a capacitance of 8 pf. What will be the capacitance if the istance between the plates is reuce by half, an the space between them is fille with a substance of ielectric constant 6? [] 86 pf [] 96 pf [3] 90 pf [4] 80 pf Sol. For parallel plate capacitor = K 0, with K = for air If istance between plates is reuce to half an K = 6, the new capacitance is ' = 8 pf = 96 pf Ex.5 In a parallel plate capacitor with air between the plates, each plate has an area of m an the istance between the plates is 3 mm, in the capacitor a 3 mm thick mica sheet of ielectric constant = 6, is inserte between the plates, while the voltage supply remains connecte. What is the charge on each plate now 8 8 [].08 0 oulomb [].08 0 oulomb [3] oulomb [4] oulomb 8 8 Sol. If ielectric is inserte, the capactiance becomes = K 6 8 pf The charge on plates is = V = = coulomb Ex.6 parallel plate conenser is charge to a certain potential an then isconnecte. The separation of the plates is now increase by.4 mm an a plate of thickness 3 mm is inserte into it keeping its potential constant. The ielectric constant of the meium will be [] 5 [] 4 [3] 3 [4] Sol. s charge an potential of the conenser both are constant in two cases, hence its capacity must also remain constant

9 PITNE 0 = or 0 = 0 ' t K or = t K or ( ) = t K or = K or K = 0.8 or 0. K K = 5 Hence the correct answer will be () (ii) Spherical apacitor: It consists of two concentric spheres. The space between the spherical surfaces is fille by a ielectric. (a) When outer sphere is earthe an inner is given the charge, then R 4 0 r RR R R O R R R r (b) When inner sphere is earthe an outer one is given the charge, then 4 R R 0 r 4 0 R R R () (B) In orer to increase the capacitance of a spherical capacitor: () both spheres shoul be very close to each other i.e., R R shoul be small. () meium between the spheres shoul be such that its ielectric constant is high. (3) the raii of both spheres shoul be large. (iii) ylinrical capacitor : It consists of two coaxial cyliners with the space between them fille by a ielectric. If R an R are the raii of inner an outer cyliners respectively an is the length of the cyliner, then 0r l R loge R l log 0 r R R

10 PITNE (iv) apacitance of two parallel transmission lines: If the raius of each wire is r, is the istance between them ( > > r) an is the length of the wires, then 0r l loge r 0r l. 3log0 r s meium between the wires is usually air so r wire 0 l loge r (v) Multiplate capacitor an capacitance of a variable capacitor : If n is the number of plates, is the area of each plate, r is the ielectric constant of meium an is the istance between two successive plates, then n 0 r In orer to obtain signals of a esire frequency in electronic instruments such as raio, T.V. etc., a parallel resonance circuit is use. In this circuit a special type of parallel plate capacitor calle gang conenser is connecte in parallel with an inuctance coil. It consists of two sets of semi circular plates. The plates of one set are stationary an the plates of other set are rotate by means of a knob. By changing the common area of the plates, the resultant capacitance can be change. 6. apacitors can be combine in two ways: (a) (b) (a) Series combination Parallel combination Series combination: ombination of capacitors on series is shown in following iagram 3 mount of charge is same on each capacitor, i.e., V V 3V3... V V V 3.. V Potential ifference across each capacitor will be ifferent an is inversely proportional to its capacitance. V,V, V 3 3 In this combination the potential ifference between the plates of the capacitor of least capacitance is maximum. The potential ifference applie in this combination is the sum of potential ifferences on iniviual capacitors. V V V V3... If is the equivalent capacitance of this combination, then

11 PITNE 3... That is, if several capacitors are connecte in series,then the reciprocal of the capacitors equivalent capacitance is equal to the sum of the reciprocals of capacitances of the iniviual capacitors. On combining the capacitors in series, the total capacitance of the circuit ecreases an the equivalent capacitance is less than the lowest capacitance connecte in series. If n ientical capacitors each of capacitance are connecte in series, then the equivalent capacitance will be : ' n This combination is use when: (a) a capacitance less than the lowest value of the given capacitance is neee, (b) a high voltage is to be ivie on several capaacitors. (b) Parallel combination : ombination of capacitors in parallel is shown in the iagram given: v v v 3.. V The potential ifferance across each capacitors is equal to the applie potential ifference in the circuit. The amount of charge is ifferent on each capacitor an the charge is irectly proportional to the capacitance of the capacitor. V, V,3 3V... Total charge in the circuit : 3... or V V V... 3 If is equivalent capacitance of this combination, then: 3... That is, the equivalent capacitance of the capacitors connecte in parallel is equal to the sum of their capacitances. On combining the capacitances in parallel the equivalent capacitance of the circuit increases. If n ientical capacitors each of capacitance are connecte in parallel, then equivalent capacitance will be : = n This combination is use when : (a) The capacitance in the circuit is to be increase. (b) Higher capacitance is require at low potential.

12 EEE EEEE E EEEE E E PITNE Ex.7 Three capacitors of same capacitance are connecte in parallel. When they are connecte to a cell of volt, total charge of.8 is accumulate on them. Now they are connecte in series an then charge by the same cell. The total charge store in them will be [].8 [] 0.9 [3] 0.6 [4] 0. Sol. If the capacitance of each capacitors is, then equivalent capacitance on joining them en parallel will be 3. Store charge = 3V = = 3 3V Let be the equivalent capacitance on joining them in series, then ' ' = 0. F Now = V = 0. = 0. nswer will be (4) Ex.8 In the ajoining figure, if the capacitance of each capacitor is F, then the equivalent capacitance between Sol. an B will be [] F [].5F [3] 4.5F [4] 5F If equivalent capacitances of the rows of capactors are,, 3..., then B = F = F 3 = 4 F 4 = 8 F etc. Equivalent capactance between an B = = 4 8 This is a geometric series whose first term is a = an common ratio r = = a r = F nswer will be ()

13 PITNE Ex.9 The effective capacitance between points an B is F. What is the capacitance of? [].39F [].46F 8F F 6F 4F [3].3F F Sol. [4] None of the above The circuit is equivalent to fig, Thus, given ata implies that F F B (3 9) = ( 3/9) = 3/3 =.39 F The correct answer is () Ex.0 Four inentical capacitors are connecte in series with a battery of emf 0 V. The point X is earthe. Then the potential of point is [] 0 V 0 V [] 7.5 V [3] 7.5 V [4] 0 V X B Sol. The equivalent capacitance of the circuit is /4 an the charge on each capacitor is = V = Thus potential ifference acros each capacitor is V =. 5 volt. Starting, from groune point X, we go to point, with change in p. of V across each capacitor. Thus V V X = 7/5 V since V x = 0, thus V = 7.5 volt. The correct anser is () Ex. The equivalent capacity between the points X an Y in the following circuit will be Sol. [] 6F [] F [3] 4F [4] 3F Because the brige is balance, hence the central capacitance between Z an T is ineffective. X 6F 6F 6F 6F 6F Y an are connecte in series, hence their resultant = = 3F 3 an 4 are connecte in series, hence their resultant = Now the two branches are connecte in parallel 3F eq = 3 3 = 6F Hence the correct answer will be ()

14 PITNE Ex. Five similar conenser plates, each of area, are place at equal istance apart an are connecte to a source of e.m.f. E as shown in the following iagram. The charge on the plates an 4 will be [] [3] 0 0, 0 V 3 V, 0 [] [4] 0 V V, 0 0 V 4 V, E Sol. Equivalent circuit iagram charge on first plate = V = 0 V charge on fourth plate V ' V - s okate 4 us reoeate twice, hence charge on 4 will be = Hence V ' 0 Hence the correct answer will be () Ex.3 Four conensers of equal capacity are connecte as shown in the figure. If the capacity of the system between P an is F then the capacity of each conenser will be [] F [] F [3] 3 F [4] 4F P Sol. ll the four conensers are connecte in series between P an an capacity of each is say. Hence resultant capacity of the combination = 4 But = f = f Hence the correct answer will be () Ex.4 Two conensers are joine as shown in the figure. Their central rigi part is movable. The capacity of the combination will be [] 0 a b [] 0 a b [3] 0 a b a b [4] 0 b a

15 Sol. For the first conenser PITNE = 0 For secon conenser = 0 a (b ) an are connecte in series = = 0 = 0 a (b ) 0 0 a (b ) 0 (a b) Hence the correct answer will be (3) 7. UUU UU UUUU UUUU UU (a) In storing charge. (b) In storing energy. (c) () (e) In electronic evices for tuning. In electrical appliances as circuit elements, for smoothing rectifie current, in timing circuits etc. In scientific stuies. 8. (i) harging process: (a) When a capacitor of capacitance connecte in series with a resistance R is charge from a source of voltage V 0, then the voltage across the capacitor increases from zero to the maximum value.the voltage at any time t is given by v t = v 0 ( e t/r ) (b) In charging, initially the current is maximum. fterwars the current ecreases exponentially with time as : I I 0 e t / R where I 0 = maximum current V 0 K R V 0 = R (c) The charge on the capacitor at time t is q e t / R In charging a capaciator the voltage an the charger rise exponentially whereas the current ecreases exponentially. When t, the current becomes zero an the potential ifference across the capacitor becomes equal to the voltage of the applie voltage source.

16 PITNE R is calle time constant of the circuit. Time constant is the time in which the charge on the capacitor an the voltage across the capacitor become equal to 0.63 or 63.% times their final values,i.e., at t=r V 0.63V 0 an q 0.63 Time constant is also the time in which the current in the circuit reaches a value 0.37 or 37% of its initial maximum value i.e., at t =R I 0.37I 0 In charging, the variation of voltage an current with time are shown in the following figures: V 0 I 0 V I t t (ii) Discharging process: (a) In ischarging the potential ifference ecreases exponentially with time as : V V 0 e t / R (b) The charge also ecreases exponentially with time as : q e t / R (c) In ischarging the current ecreases exponentially from maximum with time, as I I 0 e t / R V 0 In ischarging the variation of the voltage an the current with time are shown in the following figure: V I t I 0 EXMPLE BSED ON HRGING ND DISHRGING OF PITOR THROUGH RESISTNE Ex.5 capacitor of capacity 0 F is charge through a resistance of 00 k by a c source of volts. The potential ifference across the capacitor after sec will be [].0 V [].73 V [3].5 V [4].0 V Sol. Time constant of the R circuit = R = = sec During the process of charging V = V 0 ( e t/r ), (e =.78) = ( e / ) = ( 0.35) = =.73 volts nswer will be ()

17 PITNE Ex F capacitor is charge through a K resistor by a V.c. source. What is the voltage across the capacitor after 5 sec? [] 0.38 volt [].38 volt [3].38 volt [4] 3.38 volt Sol. The time constant of the circuit is = R = =.5 sec For charging V = V 0 ( e t/r ) put t = 5 sec, an r =.5 sec, then V = ( e ) = ( 0.35) = = 0.38 volt 9. SSSS SSSSSS SSS SSS SSS SS SSSSSSS SSSSSS SSSS n arrangement of conuctors in which capacitance can be increase without changing the size of the conuctor is calle conenser or capacitor. It has two conuctors, one is charge an other is earthe. suitable ielectric material may be place between them. There are several types of capacitors base on the ielectric such as paper capacitor, electrolytic capacitor, ceramic capacitor etc. Similarly there are several types of capacitors base on the shape of the conuctors such as parallel plate capacitor, spherical capacitor, cylinrical capacitor etc. lternating current flows easily through a capacitor while irect current oes not flow through the capacitor. Both plates of the charge capacitor have equal an opposite charges. Force of attraction acts between these plates an it is equal to: F E If is the capacitance of the capaacitor,v is the potential ifference an is the istance between the plates, then the attracative force between the plates: V F The relation between the voltage an the current is : V i V t t t Following conclusions can be rawn from the above relations. (a) Since V, therefore voltage is irectly proportional to the charge but not current. (b) apacitor has the ability to accumulate charge, therefore it has the capability to store information. (c) There can be potential ifference across the capacitor even when current is not flowing through the capacitor.

18 PITNE () apacitor acts as an open circuit for irect current. Instantaneous current flows uring charging or ischarging of the capacitor. (e) In the above relation V t, that is, the rate of change of voltage is inversely proportional to the capacitance of the capacitor. If rate of change of voltage is less, then will be more. Thus the voltage in the capacitor oes not change suenly. omparison of the energy of charge capacitor an the potential energy of the spring: (a) omparing the relation for energy U q of the capacitor an the energy of the spring U kx, the charge q is equivalent to isplacement x. (b) The reciprocal of the capacitance of the capacitor is equivalent to the force constant k of the spring. (c) The potential ifference between the plates of the capacitor of the spring. q V is equivalent to the restoring force F kx Metallic plate can not be use as a ielectric in the capacitor because it will short circuit the plates. The ielectric constant of a metal is infinite. 0. P P P P P P P P P P P P P P P P P apacity or apacitance of a onuctor :, V Unit is fara = coulomb volt F = 0 6 F, pf = 0 F apacitance of a spherical conuctor : = 4 0 R, 0 is permittivity of vacuum. m = 4R = r (4 0 R) is permittivity of meium an r is ielectric constant of the meium. Work one in charging or energy store : U V V ommon potential when two charge conuctors are connecte : =, = = V V ommon potential V V V harge transferre (V V )

19 PITNE Energy loss U (V V ) apacitor or conenser : n arrangement of conuctors for increasing the capacitance. It has two conuctors place nearby, one is charge an the other is earthe. apacity of a conenser = V Parallel plate capacitor : 0 0, m r r If a ielectric of thickness t is place in between, then 0 t t r If slabs of thicknesses t, t, t 3... t n of ielectric constants r,,... are place in between r rn t r t 0 t... n r rn an t t... tn Spherical conenser : When outer spherical shell is earthe 4 0 r RR R R When inner sphere is earthe 4 ylinrical capacitor : R R 0r 4 0 R R R 0r log (R /R ) e r.303log (R 0 0 Multiplate capacitor : /R ) = (n ) 0 r

20 Energy store in a capacitor : PITNE U V V This energy resies in electric fiel. Energy ensity of electric fiel U E ombination of capacitors : Series combination :... n,... Parallel combination :... n,v V... V harging an ischarging of a capacitor through a resistance : hargingq = (q e t/r ) V = V 0 ( e t/r ) I I t / R V0 e, I0 R 0 Discharging q e t / R Time constant : V = V 0 e t/r I = I 0 e t/r = R, time in which q = 0.63, V = 0.63 V 0 an I = 0.37 I 0, while charging, q = 0.37, V = 0.37 V 0, I = 0.37I 0 while ischarging. Force of attraction between the plates of a capacitor : F E V

21 SSSSSS SSSSSSS PITNE Ex. 8 similar charge rops combine to form a bigger rop. The ratio of the capacity of bigger rop to that of smaller rop will be Sol. bigger rop = ( small rop )n /3...() bigger rop small rop...() Ex. Two charge metal spheres of raii R an R are temporarily place in contact an then separate. t the surface of each, which sphere has the greater value for the following (a) charge, (b) charge ensity, (c) potential an () electric fiel? Sol. (a) In sharing, charge ivies in proportion to capacity so q q R R R R i.e. smaller sphere has greater charge ensity (b) harge ensity, = q/(4r q R R ) so q R R i.e, smaller sphere has greater charge ensity (c) In case of spherical conuctor, V S = q/(4 R) so V V q R R q R R i.e., both the sphere are at same potential E q R R () In case of spherical conuctor, E S = q/(4 R) E q R R i.e., file at the surface of smaller sphere has greater value Ex.3 Sol. Two uniformly charge spherical rops at potential V coalesce to form a large rop. If capacity of each smaller rop is then fin capacity an potential of larger rop When rops coalesce to form a larger rop then total charge an volume remains conserve. If r is raius an q us charge of smaller rop then = 4 an q = V Equating volume we get R r = 3 3 /3 apacitance of larger rop = 4 0 R = /3 harge on larger rop = q = V Potential of larger rop V' ' V / 3 / 3 V

22 PITNE Ex.4 capacitor is mae of a flat plate of area an a secon plate having a stair-like structure as shown in figure. If the area of each stair is an the height is, fin the capacitance of the arrangement 3 /3 /3 /3 Sol. The given arrangement of flat plate an the starilike structure is equivalent to the parallel combination of three capacitors, an 3. The plate area of each of the three capacitors is /3, while the separation between the plates of the three capacitors is, an 3 respectively. RE = 0 3 / = 0 ; 3 = 0 / 3 = 0 6 ab 3 / Ex.5 Equivalent capacitance, = 3 = If capacitors, 3, 5... in one network an, 4, 6... in another network are connecte in series. If the effective capacitance of first network be an that of network secon be then equal to Sol. For first network, For secon network, = = [log e ( x) = x 3 = X x x... ] = loge( ) 3 4 Ex.6 Sol. loge log In the given figure the resultant capacity will be e First n capacitor are connecte in sereis so, their resulte capacity = /n up to n up to n B secon n capacitor are connecte in parallel so, their resultant capacitance = n Now an are in series, so resultant capacity = n n n ' ' n n n (B) = V an = ' = V () The total energy store in parallel combination of two capacitors is U = U U = V V = V ( )

23 Ex.7 In the following circuit, the resultant capacitance between an B is F. Then value of is PITNE Sol. F an 6 F are in series an again are in parallel with 4F 6 Therefore resultant of these three will be = 4 = 8F 6 8F F 6F 4F Equivalent of 8F, F an F = F () B F FF () an () are in parallel an are in series with 8 8 = an 9 eq = F Ex.8 Sol. The capacitance of a parallel plate capacitor is 400 pico fara an its plates are separate by mm in air (i) What will be the energy when it is charge to 500 volts, (ii) What wil be the potential ifference with the same charge if plate separation is ouble?, (iii) How much energy is neee to ouble the istance between its plates? Here = 400 pico-fara = fara an = mm = 0.00 meters (i) The capacitor is charge to a potential V = 500 volts. The energy W of the capacitor is given by W V (400 0 ) (500) = joules (ii) We know that the capacity of parallel plate conenser = 0 /. When is ouble, the new capacity. becomes halve i.e. ' fara harge on the capacitor q = V = = coul. Let the new potential ifference be V then for the same charge q, we have q = V = or 00 0 V = V = 3000 volts (iii) The energy require to ouble the istance between the plate = final energy initial energy = ' V' V = (00 0 ) (3000) ( ) = = joules

24 PITNE EXERISE #. The capacitance of a spherical conuctor is proportional to [] R [] R [3] R [4] R. Store energy in a charge conuctor is [] V [] V [3] [4].3 If the two plates of the charge capacitor are connecte by a wire, then [] potential will become infinite [] charge will become infinite [3] capacitor will get ischarge [4] charge will become ouble that of earlier one.4 The capacity of a parallel plate capacitor is 0.5mF. When a mica sheet is place between the plates the potential ifference reuces to 8 of the previous value. The ielectric constant of mica is [].6 [] 5 [3] 8 [4] 40.5 Unit of capacitance is [] coulomb [] volt [3] henry [4] fara.6 The capacitance of a capacitor is [] irectly proportional to the ielectric constant of the meium between the plates [] inversely proportional to the ielectric constant of the meium between the plates [3] proportional to the square of the ielectric constant of the meium between the plates [4] inepenent of the ielectric constant of the meium between the plates.7 If the energy of a capacitor of capacitance F is 0.6 joule, then its potential ifference will be [] 800 V [] 400 V [3] V [4] 4 60 V.8 The capacitance of a parallel plate capacitor is F. If the istance between its plates is reuce to half an the area of plates is ouble, then the capacitance of the capacitor will become [] 4 F [] F [3] 6 F [4] 48F.9 capacitor of 6 F is charge to such an extent that the potential ifference between the plates becomes 50 V. The work one in this process will be [] J [] J [3] J [4] 3 30 J.0 The raius of the circular plates of a parallel plate capacitor is R. ir is ielectric meium between the plates. If the capacitance of the capacitor is equal to the capacitance of a sphere of raius R, then the istance between the plates is [] 4 R [] R [3] R [4] R

25 PITNE. capacitor of capacitance 500 F is charge at the rate of 00 / s. The time in which the potential ifference will become 0 V, is [] 00 s [] 50 s [3] 0 s [4] 0 s. The capacitances of spherical iron, copper an alluminium conuctors of same raii are, an 3, then [] 3 [] 3 [3] 3 [4] 3.3 Eight rops of mercury of same raius an having same charge coalesce to form a big rop. apacitance of big rop relative to that of small rop will be [] 6 times [] 8 times [3] 4 times [4] times.4 64 rops each charge to a potential of 00 volt, coalesce to form a big rop. The potential of the big rop will be [] 6400 volt [] 300 volt [3] 600 volt [4] 800 volt.5 Two spheres of capacitances 3 F an together. The common potential will be 5 F are charge to 300 V an 500 V respectively an are connecte [] 400 V [] 45 V [3] 350 V [4] 375 V.6 The equivalent capacitance between an B of the combination, shown in the figure, will be [].5 F [] 3.0 F F F 3 F B 6 [3] F [4] 6F.7 The potential of earth is zero because it is [] unchange [] an object of zero capacitance [3] an object of infinite capacitance [4] having infinite charge.8 In the combination shown in the figure, the voltmeter reaing will be 8 [] 4.5 V [] V F V 3F 6 F [3] 3 V [4] V 6V.9 If a thin metal foil of same area is place between the two plates of a parallel plate capacitor of capacitance, then new capacitance will be [] [] [3] 3 [4] 4.0 On charging a capacitor of 0 F upto 500 V an a capacitor of parallel, their common potential will be 0 F upto 00 V, they are connecte in [] 500 V [] 400 V [3] 350 V [4] 50 V

26 . Two capacitors of capacitances F an PITNE F are connecte in series an this combination is charge upto a potential ifference of 0 V. The potential ifference on the capacitor of F will be [] 40 V [] 60 V [3] 80 V [4] 0 V. To reuce the capacitance of a parallel plate capacitor, the space between the plates is [] fille with ielectric material [] reuce an area of the plates is increase [3] increase an area of the plates is ecrease [4] increase an area is increase relatively.3 The effective capacitance between an B is [] F F F [] F [3].5F F B [4].5F.4 In the figure given, the effective capacitance between an B will be [] [] B [3] [4] 3.5 In the given circuit, the equivalent capacitance between an B is [] [] [3] 3 [4] 4.6 In the circuit shown in the figure the equivalent capacitance between an B will be [] [] 9 [3] [4] In the given figure, the equivalent capacitance between a an b will be B [] F a l 6F 6F [] 4F [3] 6F 4F 4F 6F [4] 6F b l 6F 6F

27 .8 In the given figure the capacitance between an B will be PITNE [] [] [3] 3 [4] 4.9 The vertical plates of a parallel plate capacitor are just in front of each other an the capacitance is. If the plates are shifte relatively, then capacitance [] will remain [] will be more than [3] will be less than [4] nothing can be sai.30 Three capacitors of same capacitance are connecte accoring to the following figures. For which combination the equivalent capacitance will be maximum? [] in an [] in an D [3] in B [4] in D.3 In the above question, in which combination the energy store will be maximum? [] in B an [] in D [3] in an D [4] in an B.3 Three capacitors of capacitances F each are available. The minimum an maximum capacitances, which may be obtaine from these are [] F,36F [] 4 F, F [3] 4 F,36F [4] 0F, F.33 n apacitors each having capacitance an breakown voltage V are joine in series. The capacitance an the breakown voltage of the combination is [] an V [] n an nv [3] n an n V [4] n an nv.34 The SI unit of 0 is [] fara [] fara/metre [3] henry/metre [4] none of the above.35 apacitors are use for [] smoothing rectifie current from power supplies [] elimination of sparking in switches [3] storing large quantities of charge for use in research such as nuclear fusion [4] all of the above.36 Five capacitors of 0 F capacity each are connecte to a D.. potential of 00 volts as shown in figure. The equivalent capacitance between the points an B will be equal to [] 40 F [] 0 F [3] 30 F [4] 0F

28 PITNE.37 parallel plate air capacitor is connecte to a battery. the quantities charge, voltage, electric fiel an energy associate with this capacitor are given by 0,V0, E0 an U 0 respecitvely. ielectric slab is now introuce to fill the space between the plates with battery still in connection. The corresponing quantities now given by, V, E an U are relate to the previous ones as [] 0, U U 0 [] V V0, 0 [3] E E0, U U0 [4] V V0, E E0.38 For the section B of a circuit shown in figure, F, F, E 0V an the potential ifference V VB 0 volt. Then, the charge on capacitor is - B E 0 [] 0 [] 3 40 [3] 3 [4] none of the above.39 Two spherical conuctors an B of raii a an b b a are place concentrically in air. is given a charge while B is earthe. Then the equivalent capacitance of the system is [] 4 0 ab b a [] 4 0b a [3] b [4] b b a.40 Force acting upon a charge particle kept between the plates of a charge conenser is F. If one of the plates of the conenser is remove, force acting on the same particle becomes [] 0 [] F [3] F [4] F.4 For the circuit shown in figure, the equivalent capacitance of the combination is 30 [] 3 F [] F 3 54 [3] F 0 [4] F.4 For the circuit given above, the charge on 4 F capacitor is [] 30 [] 40 [3] 4 [4] Two capacitors, 3 F an 4 F, are iniviually charge across a 6V battery. fter being isconnecte from the battery, they are connecte together with the negative plate of one attache to the positive plate of the other. What is the common potential? 6 [] 6V [] V 7 3 [3] V [4] V

29 PITNE.44 In the above question what is the final charge on the 3 F capacitor? [].57 [] 3.43 [3] 6.45 On charging a capacitor, the energy store in it will be [4] none of the above [] kinetic [] magnetic [3] potential [4] thermal.46 The capacitance between terminals an B is 9 [] 36 F [] F 4 7 [3] F [4] F 4.47 The capacitance between terminals x an y is [] [] 5 5 [3] 6 [4] zero.48 4 F capacitor is charge to 400 volts an then its plates are joine through a resistor of resistance K. The heat prouce in the resistor is [] 0.6 J [] 0.3 J [3] 0.64 J [4].8 J 0.49 Seven capacitors each of capacitance F are to be connecte to obtain a capacitance of F. Which of the following combination is possible [] in parallel 5 in series [] 3 in parallel 4 in series [3] 4 in parallel 3 in series [4] 5 in parallel in series.50 We wish to obtain a capacitance of 5 F, by using some capacitors, each of of capacitors require is F. Then the minimum number [] 3 [] 4 [3] 5 [4] not possible.5 apacitance of a conucting sphere will be F if its raius is approximately []. km [] km [3] 0. mm [4] 9 km.5 0 V battery is connecte to two capacitors an an a resistor R. When the capacitors are fully charge, then the potential ifference across the resistor will be [] 0 V [] 5 V [3] 3.33 V [4] zero.53 In the above question, when the capacitors are fully charge, then the potential rop across the capacitor will be 0 [] zero [] volt 3.54 In the above question the potential of point is 0 [3] volt 3 [4] 0 volt [] 3V [] 6V [3] 9V [4] Zero V

30 .55 The capacitance of the capacitors of plate areas an ( < ) at a istance is PITNE [] 0 [] 0 0 ( ) [3] [4] 0.56 parallel plate capacitor has separation t an capacitance 00 pf. If a metallic foil of thickness t/3 is introuce between the plates, the capacitance woul become (in pf unit) [] 3 00 [] (3/) 00 [3] 00 [4] (/3) F conenser is charge to 400 volts an then its plates are joine through a resistance of k. The heat prouce in the resistance is [] 0.6 J [].8 J [3] 0.64 J [4] 0.3 J.58 Two capacitors F an 4 F are connecte in parallel. thir capacitor of 6 F capacity is connecte in series. The combination is then connecte across a V battery. The voltage across F capacity is [] V [] 6 V [3] 8 V [4] V.59 s shown in the figure, a very thin sheet of aluminium in place in between the plates of the conenser. Then the capacity - [] will increase [] will ecrease [3] Remains unchange [4] May increase or ecrease.60 Work one by an external agent in separating the parallel plate capacitor is - [] V [] V [3] V [4] None of these.6 If the istance between parallel plates of a capacitor is halve an ielectric constant is ouble then the capacitance - [] Decreases two times [] increase two times [3] increases four times [4] Remain the same.6 capacitors is use to store 4watt hour of energy at 00 volt. What shoul be the capacitance of the capacitor [] 0 mf [] 0 mf [3] mf [4] 4 mf.63 soli conucting sphere of raius R is surroune by another concentric hollow conucting sphere of raius R. The capacitance of this assembly is proportional to - [] R R R R [] R R R R [3] R R R R [4] R R R R NSWER KEY EXERISE # us ns us ns us ns us ns us ns. 3 4

31 EXERISE # PITNE. capacitor of capacitance 0 F is charge to a potential of 00 V. Now connecting it in parallel with an uncharge capacitor, the resultant potential ifference becomes 40 volt. The capacitance of this capacitor is [].5 F [] 5 F [3] 0 F [4] 5F. Three capacitors of same capacitance are connecte in parallel. When they are connecte to a cell of volt, total charge of.8 is accumulate on them. Now they are connecte in series an then charge by the same cell. The total charge store in them will be [].8 [] 0.9 [3] 0.6 [4] 0..3 large number of metal plates an mica sheets are given. If a mica sheet is place between two metal plates, then it becomes a capacitor of capacitance. How many such plates will be require to make a capacitor of capacitance 5 [] 5 [] 6 [3] 9 [4] 0.4 In the arrangements shown in figure, ielectric constant K an K 3. If the capacitances are an respectively, then will be K K K K [] : [] : 3 [3] 9 : 5 [4] 5 : 4.5 fter charging a capacitor the battery is remove. Now by placing a ielectric slab between the plates [] the potential ifference between the plates an the energy store will ecrease but the charge on plates will remain same [] the charge on the plates will ecrease an the potentaial ifference between the plates will increase [3] the potential ifference between the plates will increase an energy store will ecrease but the charge on the plates will remain same [4] the potential ifference, energy store an the charge will remain unchange.6 The istance between two neighbouring plates of a gang conenser is 0.5 cm an the effective area of overlap of ajacent plates is 6 cm. Its capacitance will be [].06 pf [] 3.8 pf a b [3] 6.36 pf [4].7 pf.7 In the circuit given, charge (in ) on each capacitor in steay state will be [] [] 0 [3] 8 [4] 6 3F 3F 0V 4 ^v^v^v 4 ^v^v^v 4 ^v^v^v ^v^v^v 3F 3F

32 PITNE.8 In the figure given, the potential ifference between an B in steay state will be 3F B l [] 0 V 3F [] 5 V F F [3] 75 V [4] 00 V l 0 ^v^v^v^v F 00 V ^v^v^v l 0.9 In the above question, the potential ifference between B an in steay state will be [] 0 V [] 5 V [3] 50 V [4] 75 V.0 In the given figure, the equivalent capacitance between P an will be P l [] zero [] infinite [3] 0.6 [4].6 l. Four plates are arrange as shown in the iagram. If area of each plate is an the istance between two neighbouring parallel plates is, then the capacitance of this system will be [] 4 0 [] 3 0 [3] 0. If four plates each of area are arrange accoring to the given iagram with istance between neighbouring plates then the capacitance of the system will be [4] 0 [] 4 0 [] 3 0 [3] 0.3 n air capacitor is charge upto a potential V. It is connecte in parallel to anientical uncharge capacitor fille with a ielectric meium. fter reistribution of charge if the potential ifference of this combination is V, then the ielectric constant of the substance will be [] V V V [] V V V [3] V V V [4] 0 V V [4] V

33 PITNE.4 s shown in the figure an insulating material of ielectric constant K is inserte into half of the space between the plates. If initial capacitance of the capacitor was, then its new capacitance will be [] K [] K [3] K [4] K.5 Two parallel plate capacitors of capacitances an are connecte in parallel an charge to a potential ifference V. If the battery is isconnecte an the space between the plates of the capacitor of capacitance is completely fille with a material of ielectric constant K, then the potential ifference across the capacitors will be come [] 3VK K [] 3V 3V [3] K [4] 3 K V.6 Three parallel plates are arrange as shown in figure. The area of each plate is an the istance between two neighbouring parallel plates is. If upper an lower plates are connecte by a wire, then the capacitance of this system will be [] 4 0 [] 3 0 [3] 0 [4] 0.7 parallel plate capacitor of plate area an separation is fille with two materials each of thickness an ielectric constants an respectively. The equivalent capacitance will be 0 [] [] 0 0 [3] [4] 0.8 In the given figure cm, mm,k 5.0,K 5. 5 an K 3.. The capacitance of the system will be a K K K 3 b [] 0.44 pf [] 0.88 pf [3].77 pf [4].0 pf

34 PITNE.9 Four ientical metal plates each of area (on one sie) an each separate by a istance are connecte as shown in figure. The capacitance of the system between points an B is [] 0 [] 3 0 [3] 0 3 [4] Four ientical metal plates each of area on one sie an each separate by a istance are connecte as shown in figure. The capacitance of the system between points an B is [] 0 [] 3 0 [3] 0 3 [4] 3 0. apacitor of capacitance microfara an capacitor of capacitance microfara are separately charge fully by a common battery. The two capacitors are then separately allowe to ischarge through equal resistors at time t = 0 onsier the statements (a) the current in each of the two ischarging circuits is zero at t = 0 (b) the currents in the two ischarging circuits at t = 0 are equal but not zero (c) the currents in the two ischarging circuits at t = 0 are unequal () capacitor loses 50% of its initial charge sooner than loses 50% of its initial charge. Then, the correct statement (is) are [] (a) an () only [] (b) an () only [3] () only [4] none of the above. The time constant of charging of the circuit shown in fig. is [] R 3 3 [] R [3] 3 R [4] R.3 Time cosntant of a -R circuit is secon. apacitor is ischarge at time t = 0. The ratio of charge on the ln() capacitor at time t = s an t = 6s is [] 3 : [] 8 : [3] 4 : [4] :.4 In the circuit shown in fig. switch S is close at time t = 0. Let i an i be the currents at any finite time t then the i ratio i [] is constant [] increases with time [3] ecreases with time [4] first increases an then ecreases

35 PITNE.5 In the circuit shown in fig. charge store in the capacitor of capacity 5 F is [] 60 [] 0 [3] 30 [4] zero.6 Two inentical capacitors an connecte in series to a battery as shown in fig. apacitor contains a ielectric slab of ielectric constant k as shown. an are the charges store in the capacitors. Now the ielectric slab is remove an the corresponing charges are an. Then E [] ' k k [] ' k [3] ' k k [4] ' k.7 The plates of a parallel plate capacitor are charge upto 00 volt. mm thick plate is inserte between the plates, then to maintain the same potential ifference, the istance between the capacitor plates is increase by.6m.m. The ielectric constant of the plate is [] 5 [].5 [3] 4 [4].5.8 capacitor of capacitance F withstans a maximum voltage of 6 kv, while another capacitor of capacitance F, the maximum voltage 4 kv. If they are connecte in series, the combination can withstan a maximum of [] 6 kv [] 4 kv [3] 0 kv [4] 9 kv.9 In orer to obtain a time constant of 0 secons in an R circuit containing a resistance of 0 3 the capacity of a conenser shoul be [] 0 F [] 00 F [3] 000 F [4] 0,000 F.30 Two ientical capacitors, have the same capacitance. One of them is charge to potential V an the other to V. The negative ens of the capacitors are connecte together. When the positive ens are also connecte, the ecrease in energy of the combine system is [] (V V ) [] (V V ) [3] 4 4 (V V ) [4] 4 (V 4 V ).3 parallel plate capacitor carries a charge q. The istance between the plate is ouble by application of a force. The work one by the force is - [] zero [] q [3] q [4] q 4.3 parallel plate capacitor has an electric fiel of 0 5 V/m between the plates. If the charge on the capacitor plate is m, the force on each capacitor plate is - [] 0.5N [] 0.05N [3] 0.005N [4] none of these.33 conucting sphere of raius 0cm is charge 0m. nother uncharge sphere of raius 0cm is allowe to touch it for some time. fter that if the spheres are separate, then surface ensity of charges on the spheres will be in the ratio of - [] : 4 [] : 3 [3] : [4] :