AB, The length ofa cylindrical capes in tripled Ry what fretor must ‘change for the new eapacitance to he equal tothe ori nal capacitance * [am (mf AS Acytindrical capacitor hax two co-axial cylinders, each ‘of Yength 18 om and radii 1.8 em and 14cm, The outer cextinder is earthed and the inner eylinder is given charge of 3.8 4xC. Determine the capacitance of the: system and potential of the inner cylinder, Neglect end effects Le. bonding of ines at the ends, (Ana, 1.2 «10-1 F, 2.9 x 10V) 34 A co-xial cable used in transmission line has inner radius of 0.1 mm and an outer radius of 0.6 mm. Calculate the capacitance per metre of the cable. {Ans 71.5 pF m!] Type D—Based on Combination of Capacitors ‘Formulae used: C=C, +C,+0,+ - 2 Four capacitors of values 12 uF, 12 nF, 12 iF and 4 uF are connected to a 12 V battery as shown in Fig. 4.78. Determine the (i) equivalent capacitance of the net- ‘work, (i) the charge on each capacitor. uF 12uF aH Low 4, oN i Fig. 4.78 [CBSE 2010 Compt.) sos. i) 8 uP (ii) 48 WC, 48 uC, 48 WC and 48 C] Pind the capacitance of the network of capacitors in Pig. 4.79 (a) and (b) PRB Talay a) ww Pig. 4.79 (Ans. (a) 3 (b) Cl 17. A capacitor in made of a ~ flat plate of area A and fa plate having stair like shape as shown in Fig 4.80. The width of [4 tench stair ia A/D and the hight iad. Caleulate Fig. 4.80 the capacity of the tapacitor. ame, 251¢04)] l @ | 18, Caleulate the eapacitance of 1 uF and a 2uF capacitor connected (a) in parallel and (6) in series. If a 9 V battery i connected across the series combination, what is the potential difference across (c) the 1 uP capacitor and (d) the 2 uP capacitor ? (Ana, (a) 3 uP (6) 087 uF (c)6 V(d) VI Four identical capacitors connected between Aand Bis 1 uF, Determine the capacitance of each capacitor. Fig. 481 (Ans. 4 uF] 20. What is the effective capacitance of two conductors of capacitances 3 uF and 4 uF when connected in (i) series (ii) parallel ? (Kerala 1992] (Ans. (3) 1.7 wP (az) 7 uF) wee Go ¢ caleulate the approximate A°—| ‘equivalent capacity of the network, shown in Fig. 4.82, & Tetmeen points Aand Bg [CBSE Sample Paper} °° {TF (Ans. 1 pF 22. Find the charge on each ne oz capacitor in Fig. 483. (Ame, 24 uC. 36 uC Calculate the charge on each of the three capacitors shown in Fig. 4.84. 4nF Our i 1 | : 1+ bel | oe * Le Pig. 83 Fig. 4.84 Wn, A: 24 uC, Bs 24 uC, C48 uC),448 (Calculate the charge on the 12 : 90, Calculate the equivalent capacitorin the circuit shown = -—{t—ww¥— capacitance of the combination pi 7a shown in Fig. 4.88 tans 18 uc) |S _ 4a (Ans aoe WA 6a /n the circuit shown in a Cone cnt toe me 4.86, er hw 4h 7 ine ae Poa te .as a capacity of 3 uP. tance between A and B. aa quantity of 4 8 B. ov Goes on the charge on each capacitor. 14 capacitors. Ans 12 uc) | tr [Ans (i) 6 uF (ii) Charge - on 2 uF is 48 uC, 2V — charge on 12 uF and wv 6 uF is 96 uC] ae Fig. 405 $2 The capacities of three capacitors are in the rai 26. The effective capacitance of two capacitors are 3 uF 1:2:3. Their equivalent capacitance when formed ‘and 16 uF when they are connected in series and parallel is greater than that when in series by 5 = yp parallel respectively. Calculate the capacitance of each vt a capacitor. [Karnataka 1991S) [Ans 12 uP, 4 uFl oo oe 27. A capacitar of fixed capacitance 0.005 uF is combined $3. Caleulate : in series with a capacitor whose capacitance can be ate {| ‘varied from 0.00009 uF to 0.001 uF. What is the range ity of the eur — a. FT rk TAns. 884 x 10+ uF to 8.33 x 104 uF) tion of ca- 12H | F DF A network of four 10 uF Cee Our cepacitors is connected to a 500 a Fig 490. Fig. 4.90 F . ‘V supply as shown in Fig. 487. ror capacitances of the combination ? What char Determine the (a) equivalent 77% 7 ‘capacitance of the network and © 34. Six 3 uF capacitors are connected first in series wi it then in parallel. What are the respective joint v- appears on each capacitor in each case when the and y. (Ans. 2 uF) ‘Note. The charge on 2 capacitor is ae Sere See e es group is connected to 600 V battery ? charge on the plate with lower potential tans. 83.3 oF ; 3.0 uF ; 50 xC ; 90040 35. A 0.500 uF capacitor is placed in parallel with « OSGERE Selved Beenie] 0.750 uF capacitor and the group is joined to a 100 (Ans. (a) 13.3 pF, (b) on.C,,C, and ‘de source. What charge is taken from the source ? Whst ,:157 x 10°C; on C, :5.0107C) are the charges on each capacitor ? 29. Three capacitors made of paper have capacitances of (Ans. 125 uC ; 50 uC ; 75 x0 0.15 uF, 0.20 uP and 0.40 pF. If they are arranged in Five capacitors of capaci- G parallel and are charged to a potential difference of ec atg wP,C,= 200 V, then (a) what is the charge on each capaci- «= 2 uP are connected \ tor? (b) what is the total capacitance ? (c) what is ae boss Fig. 495 From the given c Fig 426, find St} 77 the value of the = € [41 capacitance Cif the equivalent wera | EGCG? 2 and B is to be Ee Fig. 4.96 are 139 uF Me (Ans. ite circuit formed by FFind the capacitance of an infinite aires the repetition of the same link consisting of two dential capacitors each with capecitance C. (Fig. 497] a - c - c = oe ee Fig. 497 [Ans 0.616 C] A cscs sacnaiy unenamssen ene network shown in Fig. 498. lar 2a yr = T F aie Fig. 498 (Ans. 2 uF) Fig. 4.99 shows an infinite network of capacitors, each of capacity 1 uF. Calculate the equivalent capacity of the network between A and B. (Ans. 2 uF)450 49. Two capacitors, each having ca a ing capacitance C and breakdown voltage V, are joined in series. What is the breakdown voltage of the combination? (Ans. 2 V) 150. Ifthe capacitors in the previous question are connected in parallel, then what will be the breakdown voltage of the combination ? Ans. VI 51. A capacitor of capacitance C, = 1.0 uP withstands the ‘maximum voltage V, = 6.0 kV while a capacitor of capacitance C, = 2.0 uF, the maximum voltage V,=4.0 kV. What voltage will the system of these two capacitors withstand if they are connected in series? (Ans. 9 kV} falculate the Sur capacity between thay the points A and B eave: are eae tion of capacitors is shown in fig. 4.100 Su 2001} Fig. 4.100 (Ans. 2.5 uF] . Find the capacitance of ele ‘a system of identical |B capacitors between = A HAF points A and B shown in Fig. 4.101. lAns.C, +C,+C,) Fig. 4.101 Calculate the equiva- lent capacity between Sur og the points A and Bin. ¢4}-4}4}-4p+ the combination shown * SpF| 10pF | 30uF in Fig. 4.102. [HSEB 2001 ; Fig. 4.102 CBSE 2000, 1997] tAns. 15 uF] SuF . Calculate the ef- (eae fective capaci- opel 10uF tance between A »—1 Sizanoe QV= 5 CV#= 35 av = Siva + CVe C1+C2 Uniteused: 1. Uinjoule 2. Qin coulomb 3. C in farad 4. V in volt KK 57, Refertothearrangement in fig. 4.105. | ?#F SuF How much work is done by the battery in charging the arrangement ? te (Ans. 7.97 x 10 J} e 58. How much work must be done to L4y,__ ‘charge @ 24 pF capacitor, when the sv potential difference between the Fig. 4.105 plates is 500 V? [HSEB 2006, 2002) (Ans. 3 J ‘A capacitor of capacitance 50 MF is charged toa potential of 1000 V. Calculate the energy stored inthe capacitor [HSEB 2005, 2004] Ans. 25 J 60, A 20 uF capacitor is charged by a 30 V de supply ané then connected across an uncharged 50 HF eapacter Caleulate (i) the final potential difference across the combination, and (i) the initial and final energies, How ‘will you account for the difference in energy ? {CBSE 2005) Ans, (i) 857 V (tt) 9 m J, 2.67 mJ, Loss is 6.43 my) ‘A capacitor is charged through a potential difference ‘of 200 V, when 0.1 C charge is stored in it. How much energy will it release, when it is discharged ? [ISC Exam. 1998] (Ans. 10) 662, What chould be the capacitance of a capacitor capable of storing one joule of energy when used with a 100 de supply ? {SC Exam. 1996] (Ans. 0.2 nF} wee capacitors are connected in parallel to a 100¥ battery as shown in Fig. 4.106. What is the total energy stored in the combination of capacitors ? ao 61. Fi 10 pF Lowe | “Yofrenn-4 100 V Fig. 4.106 {ISC Exam. 1994] [Ans. 03)CONDUCTORS, CAPACITANCE AND DIELECTRICS G4, Twocapacitors of capacities 5 uF and 10 uF are charged to 16 volt and 13 volt respectively. What is the common potential, when they are connected in parallel ? Find the ratio of the potent applied across the (i) parallel (i) series combination of two identical capacitors so that the energy stored in the two cases becomes the same. {CBSE 2003 8} {Ans. 1: 2) Fig. 4.107 shows a series 30F GF combination of two capaci- ; bE tors connected across 1000 V. ali ae i Calculate : (i) the effective capacitance of the combina- tion, (ii) the magnitude of the charges on the capacitors, (iii) the potential difference across the capacitors, and (iv) the energy stored in the eapacitors (Ans. (1) 2 pF (ii) 2 nC (it) 666.7 V, 333.3 V Gin) 1 yd} 67, A parallel plate capacitor of 300 uF is charged to 200 V. If the distance between its plates is halved, what will be the potential difference between the plates and what will be the change in energy stored in it ? (PSEB 1999] [Ans. 100 V, 33) ‘A capacitor of capacitance 20 uF is charged to a potential of 300 V, Calculate the energy stored in the capacitor. (CBSE 1995} [Ans. 09 J} 69. A LAF capacitor has a voltage of 100 V acros its plates, ‘The battery is removed and another 1 uF capacitor is placed in parallel. Find the voltage across the capacitors now. Has the stored energy changed ? Ifso account for the change. (Ans. 50 V, Initial energy = 0.02 J, Final energy 90026 J, The energy loss appears as heat in the ‘onnecting wires. {A400 pF capacitor is charged by a 100 V battery. (a) How much electrostatic energy is stored by the capacitor ? (b) The capacitor is disconnected from the battery and connected to another 400 pF capacitor. ‘What is the electrostatic energy stored by the system ? (HSEB 1999S ; PSEB 1991] (Ans. (a) 2 J (6) 1u] 71, 4.900 pF capacitor is charged by 100 V battery. (a) How ‘much electrostatic energy is stored by the capacitor ? (6) The capacitor is disconnected from the battery and connected to another 900 pF capacitor. What is the ‘electrostatic energy stored by the system ? INCERT Solved Example] [CBSE 1995] (Ans. (a) 4.5 uJ (6) 2.25 yu) 72. A 0.2 HF capacitor is charged to potential of 600 V. After disconrecting the battery, it is connected in 13, 1, 15. 76. a 451 parallel to a 1 uF capacitor. What will be the new otential of the capacitor ? tAns. 100 V) 4 uF capacitor is connected to a 400 V supply. It is then disconnected and connected to an uncharged 2 uP capacitor. Find the common potential after the capacitors are connected together. (Kerala 1992] (Ans. 266.67 V] AB UF capacitor is charged to 120 volt. The charging battery is then removed and the capacitor is connected in parallel to an uncharged 4 uF capacitor. (a) What is the potential difference across the combination ? (b) What is the energy stored before and after the switch is closed ? (Ans. (a) 80 volt (b) 5.76 x 10°? 5 ; 3.84 x 10-7 J) ‘Two square metal plates, each of side 10 em, are separated by 1 em and connected to a 10 V, 1.0 ampere-hour battery. Calculate (a) the electric field between the plates, (b) the capacitance of the plates, (c) the charge stored on the plates, (d) the energy stored in the battery, (c) the energy stored in the capacitor. (Ams. (a) 10° Var (b) 8.85 * 10-8 F (c) 8.85 «10! C (d) 3.6 « 10* J (e) 4425 « 10° J]. Calculate the quantities mentioned in exercise 75 assuming that there is an insulator of dielectric constant 2.0 between the plates. (Ans, (2) 500 Vin") 1.77 « 10-" Fe) L77 «107 C (d) 3.6 x 10* J (e) 8.85 x 10 J ‘Two insulated metallic spheres of capacitances 3 uF and 5 uF are charged to potentials of 300 V and 500 V respectively. They are connected by a wire. Calculate the common potential, charge on each sphere and the loss of energy. (Ans. 425 V, 1275 mC, 2.125 mC, 37.5 mJ) ‘A spark passes in air when the potential gradient at the surface of a charged conductor is 3 « 105 V ax! Determine the radius of an insulated metal sphere which can be charged to a potential of 3 million volt before sparking inthe surrounding air. Also determine the energy stored immediately before sparking occurs. (Ams. 1 m, 500) ‘The capacitance ofa parallel plate capacitor is 400 pico- farad and its plates are separated by 2 mm of air. (@ What will be the energy when itis charged to 1500 volt ? (i) What will be the potential difference with the same charge if plate separation is doubled ? Gi) How much energy is needed to double the distance between its plates ? Ana. (2) 45 10+ joule, ti) 3000 V, (Wi) 45 = 10+ joule! A horizontal capacitor is filled with two dielectrics of ‘the same dimensions but of dielectric constants 2 aodan CAPACITANCE AND DIELECTRICS introduced between the plates with its faces parallel to them and the distance between the plates is s0 changed that capacitance of the capacitor remains un- changed. What is new distance between the plates ? (Ans. 0.028 ml 95. A parallel plate capacitor with plate separation § mm is charged up by a battery. The battery remaining con- nected, a mica sheet 2 mm thick is introduced. The capacitor now draws 25% more charge, Calculate the electrical permittivity and electrical susceptibility of mica. Ans. 2, 1) 98, Two circular plates of a parallel plate capacitor are each 0.08 m in diameter and 0.015 m apart. An ebon- ite slab of thickness 5 mm is introduced between them, Calculate its capacitance, What would be the capacity. ifthe slab were made of copper ? Given : dielectric con- stant of ebonite = 2.8, n = 3.14. (Ans. 3.8 pF, 4.45 pF] 97, The area of parallel plates of an air capacitor is 0.20 m? and the distance between them is 0.01 metre. The potential difference between the plates is 3000 V. When 8.0.01 metre thick sheet of a dielectric material is put between the plates, the potential difference reduces to 1000 V. Find (a) capacitance of the capacitor before putting the sheet ; (b) charge on the each plate ; (c) dielectric constant of sheet material ; (d) capacitance of capacitor after putting the sheet ; and (e) permituivity € of the dielectric medium, (Ans. (a) 177 pF (b) 0.53 uC (c) 8 (d) 581 pF (€) 26.55 pF m) the capacitor shown in Fig. 4.110. The plate area is A and the plate separation isd. Different dielectric slabs in K, la the Fig. 4.110 are of the same thickness and the entire gap between the plates is filled with dielectric slabs. three different dielectric materials as shown. ‘What is the capacitance between terminals P and Q? 100. 101. 102, 103. 104, 453 ‘A parallel plate condenser consists of two metal plates of area A and separation d. A slab of thickness t and dislectric constant K is inserted between the plates with, its faces parallel to the plates and having the same surface area as that of the plates. If K = 2, for what t 3 value of 4 will the capacitance of the system be > (Ans, 2/3) A dielectric of dielectric constant 3 fills up only three- fourth of the space between the plates of a charged parallel plate capacitor. What. percentage of total energy is stored in the dielectric? Ans. 60%) ‘The plates of a parallel plate capacitor are 1m apart and 2 m* in area. A potential difference of 6000 volt is applied across the capacitor. When a sheet of dielec- tric is inserted between the plates, the potential dif. ference decreases to 2000 volt. Calculate (i) the origi- nal capacitance Cy ; (i) the charge Q on each plate (iii) the capacitance after insertion of the dielectric (iv) the dielectric coefficient K of the dielectric ; (0) the permittivity e of the dielectric ; (vi) the induced charge Q,0n each face of the dielectric ; (vii) the original elec- tric intensity E, between the plates ; (vii) the electric intensity E after the insertion of the dielectric. times that of the air condenser alone? (Ans. (i) 1.77 x 10° farad ; (i) 1.062 x 10° coulomb ; (ili) 5.81 « 10° farad ; (iv) 8 ; (v) 26.55 x 10" C2 N+ m= (vi) 7.08 x 10° coulomb ; (i) 6 x 10 Vm ; (viii) 2 x 10° V mt] A parallel plate capacitor has an area of 100 cm?, a plate separation of 1.0 em and is charged initially to a potential of 100 V [eall this V;). The supply is disconnected and a slab of dielectric, 0.5 em thick and of dielectric constant 7, is then placed between the plates. Calculate : (a) the capacitance C, before the slab is inserted. () the charge Q on the plates. (c) the electric field strength in the gap between the plates and the dielectric. (d) the electric field strength within the dielectric. (e) the potential difference between the Plates ater the dielectric is inserted. () the capacitance when the dielectric has been inserted. Ans, (a) 8.85 pF ; (b) 8.85 x 10°C; () 104 Vn"? ; (d) 1.4 kV mr"; (e) 87 V; (f) 15.5 pF ‘The distance between the parallel plates of a charged condenser is 2% 5 cm and the intensity ofthe field E = 800 V em”*. A slab of dielectric constant K = 5 and lem wide is inserted parallel to the plates. Determine the potential difference between the plates, before and af- ter the slab is inserted, (Ans. 1500 V ; 1260 VI