# 13. In the circuit shown the amount of charge on the plates of capacitor is 5 V

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1 CAPACITORS 1. A parallel plate air capacitor consists of two circular plates of 2m 2 area separated by 1mm. If the gap between plates is doubled then its capacitance will be 1. Halved 2. Doubled 3. 4 times 4. 6 times 2. A parallel plate capacitor is charged by connecting to a battery, After charging the battery is disconnected.which of the following increases when plates of capacitor are moved apart 1. Charge 2. potential 3. capacitance 4.electric field 3. A parallel plate capacitor is connected across a battery.a dielectric slab is introduced between the plates, the battery being still connected to the plates, which of following remains constant? 1. charge 2. capacitance 3. electric field 4.Energy stored 4. In a charged capacitor the energy is stored in 1. the electric field between the plates 2. the edge of the capacitor 3.positive charges 4. both in positive and negative charges. 5. Two capacitors of capacitances C 1 and C 2 are connected in parallel. If a charge Q is given to the combination the charge gets shared. The ratio of the charge on capacitor C 1 to the charge on capacitor C 2 is 1. C 1 C 2 2. C 2 / C 1 3. C 1 + C 2 4. C 1 / C 2 6. The effective capacity of two capacitors in series and parallel is 2/3 and 3 respectively. The value of individual capacitance is 1. 2/3 and and and and 3 7. If C s and C p are the effective capacitances of C 1 and C 2 when connected in series and parallel then 1. C s C p = C 1 C 2 2. C s + C p = C 1 C 2 3. C s C p = C 1 + C 2 4. C s +C p = C 1 + C 2 8. In a parallel plate capacitor of capacitance C a metal plate is inserted between the plates parallel to them. The thickness of plate if half of the separation between the plates. The capacitance now is 1. 2C 2. C 3. 4C 4. C/ identical water droplets charged to same potential V coalesce to form a bigger drop. The potential of the new drop will be

2 10. Five identical plates are connected as shown in figure to a battery. If the charge on plate 1 is +q, then charges on the plates 2, 3, and 4 are 1. -2q, +2q, -2q 5 2. q, +q, -q, 4 3. q, +2q, -2q q, -2q, +q Four metal plates each of area A are arranged as shown. If the separation between the plates is d,the equivalent capacitance between A and B is 2. A B C 12. The effective capacity between A and B in the figure is 1. 7C/4 2. 3C/4 3. 2C/ C/7 A C C C C B 13. In the circuit shown the amount of charge on the plates of capacitor is µ C 5Ω 2. 6 µ C 3. 4 µ C 4µF 4 Ω 4. 8 µ C 14. How many condensers of 2 µf, 250 V, are required to make a condenser of 10 µf, 1000 V, A 15 µf capacitor is charged to 50 V and a 10µF is charged to 100 V. The net charge stored in the two capacitors when they are connected in parallel is µc µC µC µc 16. Three identical capacitors of capacitance 6µF each are connected in the form of a triangle and a battery of 5V is connected between two of the vertices of triangle. The charge stored in the system is 5 V

3 1. 40 µc µc µc µc 17. The insulation property of air breaks down when the electric field is 3MV/m. The maximum charge that can be given to a sphere of diameter 10 m is approximately mc 2. 2 m C mc mc 18. If the charge on a body is increased by 2 µc the energy stored in it increases by 21%. The original charge on the body is µc µc µc µc 19. A parallel plate capacitor is charged to 60µC. The plate looses charge at the rate of 3.6 x10-8 C/S. The magnitude of displacement current is x 10-8 C/s x 10-8 C/s x C/s x C/s 20. Four identical capacitors are connected in series with a 20 V battery as shown. The point N is earthed. The potentials at points A and B are V, 0 V V, -2.5 V 20V V, -5 V V, 2.5 V A N B 21. A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed v. If x is the separation between the plates, then the time rate of change of the electrostatic energy of the condenser is proportional to X 22. The time in seconds required to produce a potential difference of 50 V across a capacitor of capacitance 100 µf when it is charged at the steady rate of 500 µc/s is The equivalent capacitance of the system of plates each of area A in the figure is d d A 3A

4 24. The equivalent capacity between A and B in the figure is A B 25. In the figure point C is grounded and the point A is at 4000 V. The point B will be at 10µF 10µF V V A B C V 5µF V 10µF 26. A capacitor is charged to 10V & it stores 10-3 C of charge. The capacitance of Capacitor is pf pF 3. 10x10-6 F F 27. The energy stored in a capacitor of capacity 2nF where pd is 400V is 1. 16x10-5 J 2. 16x10-6 J 3. 32x x drops of water of radius 1cm each carrying a charge of 10-3 C combine to form a single drop. By how many times the capacitance of the combined drop increases compared to that of smaller drop Two metal spheres of radii R 1 and R 2 are charged to the same potential. The ratio of charge on the two spheres is 1. R 1 /R 2 2. R 2 /R 1 3. R /R 1 4. R / R Two capacitors having capacitance 10 pf and breakdown voltage 50 V are connected in series. The capacitance and breakdown voltage of combination will be 1. 5 pf, 50 V pf, 50 V 3. 5 pf, 100 V pf and 100 V 31. A conducting sphere of radius 10cm is charged with 10µC.Another uncharged sphere of radius 20 cm is allowed to touch it for enough time. After two are separated the ratio of the surface charge density is 1. 4 : : : : 1

5 32. Two capacitors 2 µf and 3 µf are connected in series across 100 V. The p.d across 3 µf is V V V V 33. A condenser having a capacity 2 µf is charged to 200 volts and then the plates of capacitor are connected by a resistance wire. The heat produced is J J J J 34. If Q denotes charge on the plates of a capacitor of capacitance C. The dimensional formula for Q/C is 1. M 1 L 1 T M 1 L 2 T M 1 L 1 T -1 4.M 1 L 2 T -3 A A plane metallic sheet is given a potential of 10 V. Another plane and earthed plate of equal area is brought very close to it. The effective potential of charged plate is nearer to 1. Zero V V V 36. The electric field between the plates of a capacitor with air as dielectric is E. If a dielectric of dielectric constant 4 is placed between plates then field becomes 1. E 2. E/2 3. 2E 4. E/4 37. Total capacity of the system of capacitors shown in the figure between A and B is 1. 1 µf A 2µF 2. 2 µf 1µF 3. 3 µf 1µF 2µF 4. 4 µf B 2µF 38. A parallel plate capacitor consists of two metal plates each of area 1m 3 separated by 0.2 cm in a dielectric of constant 4. If the capacitor is connected to a battery of 500 V, the electric field between plates is KVm K V m KVm K V m A parallel plate capacitor is filled with dielectrics of dielectric constants K 1 and K 2 respectively. The area of each plate is A and the separation between plates is d. the capacitance of capacitor is given by K 1 K 2

6 40. Four capacitors each of capacitance 50 µf are connected as shown in figure. If the DC voltmeter reads 200 V, the charge on each plate of capacitor is V 1. 2 x 10-3 C 2. 5 x 10-3 C mc mc 41. Two identical parallel plate capacitors are connected in series to a battery of emf 200 V. A dielectric slab of dielectric constant 3 is inserted between the plates of second capacitor The p.d. across the capacitors now is V, 20 V v, 75 V V, 50 V V, 150 V 42. A parallel plate capacitor of capacitance 4 µf if fully charged using a battery of 20 V. It is then disconnected from the battery and connected in parallel with an uncharged capacitor. If the common potential difference is 8 V, the capacitance of second capacitor is 1. 6 µf µf µ F µf 43. If all the capacitors have capacitance C then the A equivalent capacity between A and B is B C Three capacitors 3 µf, 10 µf and 15 µf are connected in series to a voltage source of 100 V. The charge on 15 µf capacitor is µc µc µc 4. (200/3) µc 45. When two capacitors of capacitances 5µF and 25 µf are connected in parallel and charged using a battery, the total charge stored is 400 µc. The charge stored in 25 µc is µ C µc µc µc 46. Two capacitors of 3µF and 6µF are connected in series and a P.d. of 5000V is applied across the combination. They are then disconnected and reconnected in parallel. The P.d. across the combination is

7 V MV V MV 47. A capacitor of capacitance 4 µ F is charged to 80 V and another capacitor of capacitance 3 µf is charged to 60 V. When they are connected in parallel, the energy lost by 4 µf capacitor is mj mj mj mj 48. In a parallel plate capacitor the distance between the plates is d= 0.2 mm. The medium between the plates is air. The maximum potential difference which can be applied to the capacitor is ( dielectric strength of air = 3 M V /m) 1. 3 MV V 3. 3 x V V 49. Four capacitors with capacitances C 1 = 1µF, C 2 = 1.5 µf, C 3 = 2.5 µf and C 4 = 0.5 µf are connected as shown and are connected to a 30 V source. The potential difference between points A and B is C 1 C V A 2. 9 V V C 3 B C V 50. A parallel plate capacitor with plate area A and separation d is filled with two dielectric materials as shown in figure. The dielectric constants are K1 and K2. The capacitance will be d/2 K1 K2 51. A capacitor of capacitance 4µF withstands a maximum voltage of 6KV, while another capacitor of capacitance 2µF withstands 4 KV. If they are connected in series the combination can withstand a maximum of 1. 6 KV KV KV 4. 9 KV 52. Two capacitors 2µF and 4µ are connected in parallel. A third capacitor of 6µF is connected in series. The combination is connected across a 12 V battery. The voltage across 2µF capacity is 1. 2 V 2. 6 V 3. 8 V 4. 1 V

8 53. Three plates A,B,C each of area 50cm 2 have separation 2 mm between A and B and 2 mm between B and C. The energy stored when the plates are fully charged is 1. 2 µj µj A 3. 5 µj µj B C 1 V 54. A thin metal plate is inserted half way between the plates of a parallel plate capacitor of capacitance C in such a way that it is parallel to the two plates. The capacitance now becomes 1. C 2. C/2 3. 4C 4. 2 C 55. Five identical capacitors when connected in series produce equivalent capacitance of 10 µf. Now these capacitors are connected so as to produce maximum value of equivalent capacitance.the maximum value will be µf µf µf µf 56. Two capacitors of capacitances 3 µf and 6µF are charged to a potential of 12 V and 15 V respectively. They are now connected to each other, with the positive plate of each joined to negative plate of other. The potential difference across each will be 1. 4 V 2. 6 V 3. zero 4. 3 V 57. A parallel plate capacitor having capacitance C has two plates of same area A and thickness t. Figure shows the charge available on four surfaces of the plates. The potential difference V between the two plates is given by q 1 q 2 q 3 q A parallel plate capacitor has plate area A and charge Q. The force on one plate due to the charge on the other is (if σ is the surface density of charge) σ A

9 59. Capacitance in farad of a spherical conductor having radius 2m is x x x A capacitor C 1 = 4 µf is connected in series with another capacitor C 2 = 5µF. The combination is connected across A.C. source of 200 V. The ratio of potential difference across C 1 and C 2 is 1. 5 : : : :1

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