Title 17. Electrostatics Easy 2.pdf ✅

1. The radius of a metallic sphere if its capacitance is 1 / 9 F , is (a) m 6 10 (b) m 7 10 (c) m 9 10 (d) m 8 10 2. The ratio of charge to potential of a body is known as (a) Capacitance (b) Conductance (c) Inductance (d) Resistance 3. If the capacity of a spherical conductor is 1 picofarad, then its diameter, would be (a) m 3 1.8 10 −  (b) m 3 18 10 −  (c) m 5 1.8 10 −  (d) m 7 18 10 −  4. A parallel plate air capacitor is charged to a potential difference of V. After disconnecting the battery, distance between the plates of the capacitor is increased using an insulating handle. As a result, the potential difference between the plates (a) Decreases (b) Increases (c) Becomes zero (d) Does not change 5. A 10 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor (a) J 8 1.25 10 −  (b) J 7 2.5 10 −  (c) J 5 3.5 10 −  (d) J 2 4.5 10 −  6. Two protons A and B are placed in space between plates of a parallel plate capacitor charged upto V volts (See fig.) Forces on protons are FA and FB , then (a) FA  FB (b) FA  FB (c) FA = FB (d) Nothing can be said 7. If a slab of insulating material m 3 4 10 −  thick is introduced between the plates of a parallel plate capacitor, the separation between plates has to be increased by m 3 3.5 10 −  to restore the capacity to original value. The dielectric constant of the material will be (a) 6 (b) 8 (c) 10 (d) 12 8. When a dielectric material is introduced between the plates of a charged condenser then electric field between the plates (a) Decreases (b) Increases (c) Remain constant (d) First (b) then (a) 9. A parallel plate capacitor has a plate separation of 0.01 mm and use a dielectric (whose dielectric strength is 19 KV/mm) as an insulator. The maximum potential difference that can be applied to the terminals of the capacitor is (a) 190 V (b) 290 V (c) 95 V (d) 350 V 10. Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance C, a potential V, and a charge q, then the capacitance of the bigger drop will be (a) C (b) 4C (c) 16C (d) 64C 11. A 700 pF capacitor is charged by a 50V battery. The electrostatic energy stored by it is (a) J 8 17.0 10 −  (b) J 9 13.6 10 −  (c) J 9 9.5 10 −  (d) J 7 8.7 10 −  12. A variable condenser is permanently connected to a 100 V battery. If the capacity is changed from 2 F to 10  F , then change in energy is equal to (a) J 2 2 10 −  (b) J 2 2.5 10 −  (c) J 2 3.5 10 −  (d) J 2 4 10 −  13. A 12 pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor (a) J 8 1.5 10 −  (b) J 7 2.5 10 −  (c) J 5 3.5 10 −  (d) J 2 4.5 10 −  14. The capacity of a parallel plate condenser is 15 F , when the distance between its plates is 6 cm. If the distance between the plates is reduced to 2 cm, then the capacity of this parallel plate condenser will be (a) 15 F (b) 30  F (c) 45  F (d) 60 F 15. When we touch the terminals of a high voltage capacitor, even after a high voltage has been cut off, then the capacitor has a tendency to (a) Restore energy (b) Discharge energy (c) Affect dangerously (d) Both (b) and (c) 16. In a capacitor of capacitance 20  F , the distance between the plates is 2mm. If a dielectric slab of width 1mm and dielectric constant 2 is inserted between the plates, then the new capacitance is (a) 2 F (b) 15.5 F (c) 26.6 F (d) 32 F 17. The capacity of a parallel plate capacitor with no dielectric substance but with a separation of 0.4 cm is 2 F . The – – – – – A B + + + + +
separation is reduced to half and it is filled with a dielectric substance of value 2.8. The final capacity of the capacitor is (a) 11.2F (b) 15.6F (c) 19.2F (d) 22 .4F 18. Two insulated metallic spheres of 3F and 5F capacitances are charged to 300 V and 500V respectively. The energy loss, when they are connected by a wire is (a) 0.012 J (b) 0.0218 J (c) 0.0375 J (d) 3.75 J 19. Two conducting spheres of radii 5 cm and 10 cm are given a charge of 15 C each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is (a) 5 C (b) 10 C (c) 15 C (d) 20 C 20. In a parallel plate capacitor of capacitance C, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is half of the separation between the plates. The capacitance will be (a) 2 C (b) 4 3C (c) 4C (d) 2C 21. While a capacitor remains connected to a battery and dielectric slab is applied between the plates, then (a) Potential difference between the plates is changed (b) Charge flows from the battery to the capacitor (c) Electric field between the plates increases (d) Energy store in the capacitor decreases 22. A body of capacity 4  F is charged to 80 V and another body of capacity 6  F is charged to 30V. When they are connected the energy lost by 4  F capacitor is (a) 7.8 mJ (b) 4.6 mJ (c) 3.2 mJ (d) 2.5 mJ 23. The capacity of the conductor does not depend upon (a) Charge (b) Voltage (c) Nature of the material (d) All of these 24. A solid conducting sphere of radius R1 is surrounded by another concentric hollow conducting sphere of radius R2. The capacitance of this assembly is proportional to (a) 1 2 2 1 R R R − R (b) 1 2 2 1 R R R + R (c) 1 2 1 2 R R R R + (d) 2 1 1 2 R R R R − 25. Two spherical conductors A and B of radius a and b (b > a) are placed in air concentrically B is given charge + Q coulomb and A is grounded. The equivalent capacitance of these is (a) b a ab − 4 0 (b) 4 ( )  0 a + b (c) b0 4 (d) b a b − 2 0 4 26. The capacity of a parallel plate condenser is 10  F , when the distance between its plates is 8 cm. If the distance between the plates is reduced to 4 cm, then the capacity of this parallel plate condenser will be (a) 5  F (b) 10  F (c) 20  F (d) 40  F 27. A capacitor is used to store 24 watt hour of energy at 1200 volt. What should be the capacitance of the capacitor (a) 120 m F (b) 120  F (c) 24  F (d) 24 m F 28. The mean electric energy density between the plates of a charged capacitor is (here q = charge on the capacitor and A = area of the capacitor plate) (a) 2 0 2 2 A q  (b) 2 2 0 A q  (c) A q 0 2 2 (d) None of the above 29. A charge of 40  C is given to a capacitor having capacitance C = 10  F . The stored energy in ergs is (a) 6 80 10 −  (b) 800 (c) 80 (d) 8000 30. Work done by an external agent in separating the parallel plate capacitor is (a) CV (b) C V 2 2 1 (c) 2 2 1 CV (d) None of these 31. A parallel plate capacitor has an electric field of 10 V /m 5 between the plates. If the charge on the capacitor plate is 1 C , the force on each capacitor plate is (a) 0.5 N (b) 0.05 N (c) 0.005 N (d) None of these 32. A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V0. The charging battery is disconnected and the plates are pulled apart to three times the
initial separation. The work required to separate the plates is (a) d AV 2 3 0 0  (b) d AV 2 2 0 0  (c) d AV 3 2 0 0  (d) d AV 2 0 0  33. The electric field between the plates of a parallel plate capacitor when connected to a certain battery is E0 . If the space between the plates of the capacitor is filled by introducing a material of dielectric constant K without disturbing the battery connections, the field between the plates shall be (a) KE0 (b) E0 (c) K E0 (d) None of the above 34. If the distance between parallel plates of a capacitor is halved and dielectric constant is doubled then the capacitance (a) Decreases two times (b) Increases two times (c) Increases four times (d) Remain the same 35. Putting a dielectric substance between two plates of condenser, capacity, potential and potential energy respectively (a) Increase, decrease, decrease (b) Decrease, increase, increase (c) Increase, increase, increase (d) Decrease, decrease, decrease 36. A thin metal plate P 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 (a) C (b) C/2 (c) 4C (d) None of these 37. If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to (a) CV (b) 2 2 1 nCV (c) 2 CV (d) 2 2 1 CV n 38. If n drops, each of capacitance C, coalesce to form a single big drop, then the ratio of the energy stored in the big drop to that in each small drop will be (a) n : 1 (b) n 1/3 : 1 (c) n 5/3 : 1 (d) n 2 : 1 39. A conducting sphere of radius 10cm is charged 10C . Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the sphere are separated, then surface density of charges, on the spheres will be in the ratio of (a) 1 : 4 (b) 1 : 3 (c) 2 : 1 (d) 1 : 1 40. 64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is (a) 1 : 64 (b) 64 : 1 (c) 4 : 1 (d) 1 : 4 41. Capacitance (in F) of a spherical conductor with radius 1m is (a) 10 1.1 10 −  (b) 6 10 − (c) 9 9 10 −  (d) 3 10 − 42. A condenser has a capacity 2 F and is charged to a voltage of 50 V. The energy stored is (a) 25  105 Joule (b) 25 Joule (c) 25  10 erg (d) 25  103 erg 43. The energy required to charge a capacitor of 5  F by connecting a d.c. source of 20 kV is (a) 10 kJ (b) 5 kJ (c) 2 kJ (d) 1 kJ 44. The capacitance of a parallel plate capacitor is 12  F . If the distance between the plates is doubled and area is halved, then new capacitance will be (a) 8  F (b) 6  F (c) 4  F (d) 3  F 45. A capacitor of capacitance 6 F is charged upto 100 volt. The energy stored in the capacitor is (a) 0.6 Joule (b) 0.06 Joule (c) 0.03 Joule (d) 0.3 Joule 46. A parallel plate air capacitor is charged and then isolated. When a dielectric material is inserted between the plates of the capacitor, then which of the following does not change (a) Electric field between the plates (b) Potential difference across the plates (c) Charge on the plates (d) Energy stored in the capacitor 47. Capacitance of a parallel plate capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/2 is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is (a) 8 (b) 4 (c) 6 (d) 2
48. A 10 micro-farad capacitor is charged to 500 V and then its plates are joined together through a resistance of 10 ohm. The heat produced in the resistance is (a) 500 J (b) 250 J (c) 125 J (d) 1.25 J 49. The unit of electric permittivity is (a) Volt/m2 (b) Joule/coulomb (c) Farad/m (d) Henry/m 50. The work done in placing a charge of 18 8 10 −  coulomb on a condenser of capacity 100 micro-farad is (a) Joule 32 32 10 −  (b) Joule 32 16 10 −  (c) Joule 26 3.1 10 −  (d) Joule 10 4 10 −  51. 64 drops of mercury each charged to a potential of 10V . They are combined to form one bigger drop. The potential of this drop will be (Assume all the drops to be spherical) (a) 160 V (b) 80 V (c) 10 V (d) 640 V 52. Two identical capacitors are joined in parallel, charged to a potential V and then separated and then connected in series i.e. the positive plate of one is connected to negative of the other (a) The charges on the free plates connected together are destroyed (b) The charges on the free plates are enhanced (c) The energy stored in the system increases (d) The potential difference in the free plates becomes 2V 53. The condensers of capacity C1 and C2 are connected in parallel, then the equivalent capacitance is (a) C1 +C2 (b) 1 2 1 2 C C C C + (c) 2 1 C C (d) 1 2 C C 54. A parallel plate capacitor is made by stacking n equally spaced plates connected alternately. If the capacitance between any two plates is C then the resultant capacitance is (a) C (b) nC (c) (n −1)C (d) (n +1)C 55. Seven capacitors each of capacity 2F are to be so connected to have a total capacity F 11 10 . Which will be the necessary figure as shown (a) (b) (c) (d) 56. Four plates of equal area A are separated by equal distances d and are arranged as shown in the figure. The equivalent capacity is (a) d 2 0 A (b) d 3 0 A (c) d 3 0 A (d) d  0A 57. The capacitor of capacitance 4 F and 6F are connected in series. A potential difference of 500 volts applied to the outer plates of the two capacitor system. Then the charge on each capacitor is numerically (a) 6000 C (b) 1200 C (c) 1200 C (d) 6000 C 58. A parallel plate capacitor with air as medium between the plates has a capacitance of 10 F . The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant k1 = 2 and 4 k2 = . The capacitance of the system will now be (a) 10 F (b) 20 F (c) 30 F (d) 40 F 59. Three capacitors are connected to D.C. source of 100 volts shown in the adjoining figure. If the charge accumulated on plates of 1 2 C , C and C3 are qa qb qc qd qe , , , . and f q respectively, then (a) qb qd qf C 9 100 + + = A B k1 k2 2F a b 3F c d 4F e f