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VIDYA MaKmarks Electrostatic Potential and, Capacitance, , 28 PHYSIcs | CLASS12, , Competency Based Questionss, , Ans. (C) In (i), , changes., (D) decreases, , Choice Questions, , Multiple, , 1. Two capacitors of capacitances, , C, , and, , 1 Mark, , C2 a r e, , Ans., , because, , the, , charge, , opposite to the electic field., the charge, , because, (C) decreases, the electric field., , moves, , move, , charge, the capacitor C, to the charge on C willIbe, , Explanation: Equipotential surface is, , Foreign 2017, Set VIVII), , electric field.Positive charge experiences the, , always perpendicular to the, , direction of, , force in the direction of electric field. When, a (+)ve charge is released from uniform, , electric field, its velocity increases in direction, and, of electric field. So, K.E., decreases by conservation of law of energy., , increases, , As C and C2 are connected in parallel, so the, potential will be same for both capactiors., , Thus, Q, , CV and Q2 = C,V, , 2. A capacitor of 4 uF is connected as shown, in the figure given below. The internal, resistance of the battery is 0-5 2. The amount, of charge on the capacitor plates will be:, 4 uF, , PE, , 4. Equipotential at a great distance from, collection of charges whose total sum is not, zero are approximately:, , Explanation, , 102, ww, , (C) paraboloids, , Ans. (A) spheres, 5. The electric potential of earth is taken to be, zero because earth is a good:, (B) conductor, (A) insulator, (C)semi-conductor (D) dielectric., Ans. (B) conductor., , Explanation: Earth is considered to be the, of, storehouse, infinite negative charge. So,, most points are at (+)ve potential w.rt. it., a battery as shown in the figure. Consider, , two situations:, , -(, w, 22, , (A) 0, (C) 14 C, Ans. (D) 8 HC, , Explanation:, , V remains, , same, , and hence Q, , Explanation:, The battery maintains, the potential diference across connected, capacitor in every circumstance. However,, capacitor remains conserved., 8. 100 Joule of work is, performed in carrying, a charge of- 5C from, infinity to a particular, , (B) 4 C, , 11, , Since, , 1, , is positive. Hence, VA - VB is, , 2, , positive, 11. In the given circuit, with steady current, the, charge stored across the capacitor is:, 6V, , point in an uniform electrostatic field. The, , potential of this point is :, (A) 100 V, , (B)5 V, , C)-20 V, , (D) 20 V, , B, , I2 V, , Ans. (C)-20 V, , Explanation: Charge q = -5C, Work done,, , W, , 100Joule, , Let V be the potential, then, , (B) planes, (D) ellipsoids, , (A) spheres, , 7. A parallel plate capacitor (C) is connected to, 2.5 V, , :, , charge stored by disconnected charged, , along, , connected in parallel. If a charge Q is given, to the combination, the ratio of the, on, , Ans. (A), , 29, , D) In (i): Q and V both remains same, , =qx V, 100=-5 x V, V, , = -20V, , 9. A hollow metal sphere of radius 5 cm is, charged so that the potential on its surface is, , w, 22, , (A) 10 C, , (B)-10uC, , (C) 12 C, , (D) None of these, , Ans. (A) 10 uC, , Explanation: Potential on each point of, equipotential surface is constant., In ACDFA,, , I=14=2A, , Current,, , 10 V. The potential at the centre of the sphere, , VAFBE, , is:, , (A) 0V, (B) 10 V, (C) Same as at point 5 cm away from the, surface, (D) Same as at point 25 cm away from the, , 6+2 6 + Ve, V. =, , Charge,, , 2V, , Q= CV,=, , 2V, 12. In the given circuit, with steady current, the, drop across the capacitor in terms, , 5uF, , x, , =, , 10 4C, , potential, , surface, , ofEVis:, , Ans. (B) 10 V, , 5V, , Explanation:, , 22, , potential inside, , the, Since,, hollow sphere is same as that on the surface., 10. A point charge +Q is placed at point O, as shown in the figure. The potential, difference Va-V» is :, , 5V, , (D) 8 uC, , 4 uF, , 10V, D, , os-8C, , A positively charged particle is released, from rest in a uniform electric field. The, electric potential energy, of the charge:, (A) remains a constant because the electric, field is uniform, (B) increases because the charge moves, along the electric field, (C) decreases because the charge moves, along the electric field, , (i) Key, kept closed and plates o, capacitors (C) are moved apart using, insulating handle., i) Key Kis opened and plates of capacitors, K is, , (C) are moved apart using insulating, handle., Choose the correct, option (s)., (A) In (i) : Q remains same but C changes., (B) In (ii): V remains, C changes, , same but, , (C) In (i): V remains same and hence, , changes., , (A) Positive, , (A), , (B) Negative, , (C), , (C) Neither postive non negative, , (B) 2V, D) 4, , 3V, , Ans. (B) 2v, , (D) None of the above, Explanation: In steady state, BE is ignored., , Ans. (A) Positive, , 10-5, , equipotential surface is constant., Let OA =, , and OB =r2, , =1A, , 3+2) 5, , Explanation: Potential on each point of, , =1A, , For EBCDE, by Kirchoffs second law, , -V-5, , +, , 10 -3, , x, , 1, , =, , 0, , V+10-8 =0, V.= 2V

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30 PHYSIcs, , CLASS 12, the, , given circuit, with steady current, the, potential drop across the capacitor and, ICBSE 20161, charge stored in it is:, , 13. In the, , VIDYA MaXmdtkS Electrostatie Potential and, Capacitance, For series combination, Ans. (A) 200 pC, 300 pC, 400 pC, 1C2, C, C+C2, Explanation, , CC2, Ca C+C2, Cx4C, , 22, , 4 5, , 45C, , 91CV, , =2, , C 5 uF, , w, , 42, , Charge on C, , 4C = 20 uF, , 42CV, = 3 x 10.x 100, , 15. In a Van de Graff type generator, a spherical, , 42 300 pC, , metal shell is to be a 15 x10° Velectrode. The, , B) V,0.3 uC, , A)V,1.33C, )V,13.33 HC, , (D) None of these, , Ans. (C)V,13.33 HC, Explanation: In the loop ACDFA,, , (A) 3m, , (B) 0.30 m, , (C) 0.03 m, , (D) None of these, , and,, , 4, , 93, , x 10x 100, , 400 pC, , (C) 15J, , D) 60J, , Ans. (A) zero, 19. The work done by an agency to carry a -10C, charge from infinity to a point in electrostatic, , Q=CV, , Charge,, , Ot,, , Q, , 10 x, , 15X10, 5x 10, , 13.33uC, , =3, , x, , 101, , field is 50J.The potential at that point is:, , =0.30 m, , 16. If three capacitors each of capacitance 9 pF, 14. Two parallel capacitance X and Y have the, same area of plates and same separation, between them. X has air between the plates, while Y contains a dielectric medium of, s,=4. Calculate capacitance ofeach capacitor, if equivalent capacitance of combination is 4, , are connected in series, the total capacitance, , of the combination is :, (B) 2 x 10-12 F, (A) 3 x 1017F, , (C) 4x 10-12 F, , (D) None of these, , Ans. (A) 3 x 10-12 F, , Explanation:, , Let,, , Cx=, C, , Cyd, =, , Ce4 uF, , =3pF =3 x 10-1, , (D) -10 uF, 17. Three, , are, , =C, , =4C, , (D)-500v, , (C) - 5V, , 20. The electrostatic potential energy of a charge, of 5 C at a point in the electrostatic field is, 50 J. The potential at that point is:, (A) 0.1 V, , (B) 5V, , (C) 10V, , (D) 250 V, , (D) None of these, , Ans. (B) Normal to it, , (B) 10 uF, , Explanation: Capacitance of two capacitors, , (C)-5V, , (C Be inclined, , 15 V, , Ans. (A) 20 uF, , (B) 5V, , 21. What is the direction of the lines of force at, any point on the equipotential surface ?, (A) Parallel to it, (B) Normal to it, , Total capacitance,, , (C)-20uF, , (A) 0.2 V, , Ans. (C) 10 V, , CC2=C3=9pF, , (A) 20 pF, , Ans., , capacitors of capacitance. 2 p, 3 pf and 4 p¥ are connected in, paralle, then the charge on each, capacitor, , the combination, 100 V supply is, , is, , connected, , (A) 200 pC, 300 pC, 400 pC, , (B) 100 pC, 300 pC, 200 pC, , (C) 400 pC, 200 pC, 200 pC, (D) 400 pC, 200 pC, 300 pC, , tod, , 22. The work done in displacing a charge of 2C, through 0.5 m on an equipotential surface, (A) zero, , (C) 4J, Ans. (A) zero, , For Detailed Solutions Scan, , (B) 2Tq J, (D) zero, , Ans. (D) zero, 25. A charged spherical conductor has potential, its radius is 2 m. The electric, of 6 V, intensity at its centre is :, , 18. Work done in carrying 2C charge in a circular, path of radius 3m around a charge of 10C is:, (A) zero, (B) 6.66J, , V41Teo, E =, , (A) 1J, (C), , and, , Scan Yourself, , Ans. (B) 0.30 m, , V., , Ans. (D) E is directed in the direction of decreasing, V., 24. A circle has been drawn round a point, positive charge (+9) on its centre. The work, done in taking a unit positive charge once, round it is:, , 93 CV, , radius of the spherical shell required is, , Explanation:, 4-2x -4-V, , Charge on C, , dielectric strength of the gassurrounding, , the electrode is 5 x 10' Vm". The minimum, , VAFVBE, , x 1012x 100, 200 pC, , 41, , C 5 uF, Cy, , The capacitance are in, , parallel combination., So, charge on Cy, , 31, 23. E=-dVldr. Here negative sign signified, that:, (A) E is opposite to V, (B) E is negative, (C) E increases when V decreases, (D) E is directed in the direction of decreasing, , (B) 1J, (D) none of these, , Ans., , (A) zero, , (B) 3NC, , (C) 12 NC, , (D) None of these, , (A) zero, , 26. The potential of a spherical conductor of, radius 3 m is 6 V. The potential at its centre, is, , (A) zero, , B) 2V, , (C)6V, , (D) 18 v, , Ans. (C) 6V, 27. A charge is moved against electric repulsion, in an electric field. Which of the followingis, Correct ?, , (A) Work is done by the electric field, (B) The potential energy of the charge, decreaseS, (C) The strength of electric field decreases, (D) None of the above, Ans. (D) None of the above, 28. What is the angle between maximum value, of potential gradient and the equipotential, surface ?, , (A) zero, , (B) T/4, , (C) t/2, Ans. (C) /2, 29. Two, , (D) T, , small spheres, 1, , each, , carrying a charge, , The electric force, between them is F. If one sphere is taken, around the other. The work done is :, (B) 21tF, (A)I, (D) Zero, (C) F/ 2t, , 9, , are, , placed, , Ans. (D) Zero, , m, , apart.

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32, , VIDYA ManKmarks, , PHYsIcs | CLASs 12, , 30. A solid conducting sphere having a charge, , Qis surrounded by an uncharged concentric, conducting spherical shell. The potential, , difference between the surface of solid, now, sphere and the shell is V. The shell is, given a charge -3Q. The new potential, difference between, , the, , same surfaces will, , be, , low potential point to a, , (A) It increases, , O1/2, , (A) r/2, (C) / 1, , (B) It decreases, , (D) (r2/r), , (C) It will remain the same, , Ans. (B) 72/1, proton and an electron are released, , (B) 2V, , infinite distance apart and are attracted, , (C) 4V, , (D)-2V, , towards each other. Which of the following, statement about their kinetic energy, , copper sphere of diameter 1 m, , carries a, , true?, , charge of 200 uC. A test charge of 2u0, taken from a point P to a point Q on the, , (A) Kinetic energy of electron is more than, , opposite sides of the sphere. Both points are, , (B) Kinetic energy of electron is less than, , at a distance of 1 m from the centre of the, , sphere. What is the work done?, , 32. An electron carrying charge " - e"is, , located, , at O and another charge q is located at P., , The electron is moved from O to Q such that, OPQ is an equilateral triangle. What is the, work done in doing so?, , (C), , eg, 47TE 0Q, , 2, , (4TtE O, , 47tEg 00, , Ans. (A) Zero, 33. A test charge go is released from rest at a, distance r from a source charge 4. What will, the maximum value of the kinetic energy, , that may be acquired by the test charge?, , (A) 4TE0, , 940, , (B), , energy, , of, , electron, , =, , kinetc, , 1, 47Te0, , (D) Nothing definite can be predicted, Ans. (A) It increases, 42. Two equal positive charges are kept at, points A and B. What will be the change in, potential if one moves from A to B along the, line joining these charges?, (A) Potential will continuously decrease, (B) Potential will continuously increase, (C) Potential will decreases first and then, increase, (D) Potential will increase first and theen, , decrease, increase, , Ans. (A) Kinetic energy of electron is more than, that of proton, 37. Two protons are released ata distance of 0.1, nm from each other. What is their kineti, energy infinite distance apart ?, , (A) 23 x 10°J, , (B) 23 x 10-1°J, , (C) 11.5 x 10J, , (D) 11.5 x 10-1 J, , 43. A small circle is drawn with the centre at, , the origin cutting the axes at points A, B, C,, D having co-ordinates, (0, -a) respectively in a region uniformly, , (a, 0); (0, a):(-a, 0);, , surrounded at the origin by the electric field, along the x-axis as shown in the figure. Then,, , the potential is minimum at which point?, , conducting spheres, , electric field on their surfaces. The ratio, the electric potential at their centres is:, , (A) h/, , (B) 2, , ()/, , (D) n, , E, , 4TEg, , (D) None of these, , 940, Ans. (A) 4TE0T, 34. How does the maximum potential (V) that, can be given to a, spherical conductor vary, with its radius R?, , A) VR, (C) V «R, Ans. (C) vcR, , (B) V, (D) V«R2, , 46. Two positively charged conductors are put, in contact. The final value of which of the, following quantities of both the conductors, will be less than the initial value of one of, the conductors ?, , (A) Capacitance, , (B) Charge, , (C) Potential, , (D) None of these, , Ans. (C) Potential, , to, , of, , a, 47. A soap bubble is charged, potential, 16 V. Its radius is then doubled. The potential, , of the bubble now will be :, (A) 16 V, , C)4V, Ans. (B) 8V, , B) 8V, (D) 2V, , 48. If the radius of a soap bubble is doubled, its, capacitance will be :, (A) doubled, , (B) unchanged, , (C)halved, , (D) increases by 50%, , Ans. (A) doubled, 49. The capacitance of a conductor in vacuum, is 10 E. If it is put in a medium of relative, permittivity 5, the capacitance will be., , (A) unchanged, D) 9x 10x 5x 10 F, Ans. (C) 50F, , o, (A) P, , (B)Q, , (C)R, , D) S, , Ans. (A) P, 44. Which of the following options is correct for, the isolated conductor shown in the figure, , below having potentials Ve, Ve VR and Vs at, points P, Q, R and S respectively?, , Ans. (B) 1/2, , charge +50 e., , If the, , protor, , 50. A number of charged liquid drops coalesce., Which one of the following quantities doess, , not change?, (A) Charge, , (B) Capacitance, , (C) Potential, , D) Electrostatic Energy, Ans. (A) Charge, , is at a distance 104 m from the nucleus ther, , (9, , (D) F= Cvi, , (C) 50F, , and, the same, , of radii r,, , are charged such that they have, , 39. A tin nucleus has, , (B) F=C1Hv, , (C)F=Cv1, , (B) 2F, , Ans. (D) 11.5 x 10-9J, 38. Two, , (A) F= CV, , Ans. (D) F = CV1, , Ans. (C) Potential will decreases first and then, , D) None of the above, , Ans. (D) Zero, , (B), , that of proton, energy ot proton, , (D) Zero, , (A) Zero, , that of proton, , (C) Kinetic, , (B) 1.85, , (A)33.6J, (C)0.93J, , high potential point, , (B) 2/1, , (A) V, , A, , 33, , 41. What is the change in the electric potential, energy if a positive charge is moved from a, , of charges be o , and o, respectively the, , 36. A, , Ans. (A) V, 31., , Electrostatic Potential and Capactance, , 35. The spheres of radii ri and r are at th, same potentials. If their surface densitio, , 51. Which of the following factors does not, , the potential V at this position is, , affect the capacitance of a capacitor ?, , (charge on proton =1.6 x 10" C), , (A) Distance between the plates, , (A) 14.4x 10* volts, , (B) 7.2 x 10 volts, , (C) 7.2 x 10 volts, , (D) 14.4 x 10 volts, , Ans. (B) 7.2 x 10 volts, 40. Which of the, following is, across the charged, , (A) Vp=Vo> Vx > Vs, , discontinuou", , conducting surface?, , (A) Electric field, (B) Electric potential, , (B) Vs> VR > Vo =Vp, (C) Vs> VR> Vo > Vp, (D) Vs = VR = Vo = Vp, , Ans. (D) Vs= VR= Vo = VpP, , (C) Both, , (D) Nothing definite, Ans. (A) Electric field, , (B) Material of the plates, , can, , be, , predicted., , 45. Which of the following is the correct relation, between the units of capacitance, potential, and charge ?, , (C)Area of the plates, (D) Curvature of the plates, Ans. (B) Material of the plates, 52. If n drops each charged to potential V, , coalesce to form a single droP, the potential, , ofsingle drop is, (A) V/n, (C) nsv, Ans. (D) nsy, , B), , nV, , (D) ny

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34, , vIDYA MayKmarks, , PHYsics | CLASS 12, , C, (C)Q remains unchanged,, and E decrease, , 53. If n drops each of capacitance C coalesce, , single, , drop,, , the, , of the, , capacitance, , single, , drop is:, , (A) Cn, (C)C, Ans. (C) c, , (B), , Cn, , (B) distance between the plates, , C) relative permittivity of the medium, (D) permittivity of the medium., , QR=QR2, , (B) 0R OR, (D) QR=QR, , Ans. (B), 56. A parallel plate capacitor is charged, connectin8 to a battery. After charging,, , Q1R =Q,R1, , the battery is disconnected. Which of the, , following increases, when the plates of the, capacitor moved apart?, (B) Potential, (A) Charge, (C) Capacitance, (D) None of these, Ans. (B) Potential, 57. Which of the following is blocked by the, capacitor ?, , (D) None of these, , Ans. (D) None of these, 59. An air capacitor C, is connected to, a, battery, of emf V. It, a, acquires, and energy, charge, Q, E. The, is, then, capacitor, disconnected from, the battery and a dielectric slab is, between the plates. Which of theintroduced, following, is true ?, V&, (A), Q decrease but E & C, , increase, , V remains, increase, , unchanged, , but, , Q E and, , C, , Ans. (D) None of the above, 67. The dielectric strength of a medium is, 2k V mm. What is the maximum potential, , (A) charge gradient, (B) potential gradient, , difference that can be set up across a 50 um, , (C) electric field gradient, , specimen without puncturing it ?, (A) 10 V, (B) 100 V, , (D) capacitance gradient, , (C) 1000 V, , Ans. (D) capacitance gradient, 62. How does the electric field (E) between the, plates of a charged cylindrical capacitor vary, the distance (r) from the axis of the cylinder, , (B) E, , A)E, ), , Ecr2, , D) Exr, , 50 uF is, to 10 volts. Its energy is equal to, 2.5, , x, , 10 joules, , charged, , (B) 2.5 x 10 joules, , (D) 1.2 x 10d joules, Ans. (A) 2.5 x, joules, 64. A parallel plate, capacitor has a capacitance, 45 uF in air and 100, pf when immersed in an, oil. The dielectric constant K of the oil is, (A) 0.45, (B) 0.55 (C) 1.10, (D) 2.22, Ans. (D) 2.22, 65. A parallel plate air, is, , capacitor connected to, battery of e.m.f. E volts. The electric field, between its plates will, G) not be affected if we change the distance, , between the plates, (i) decrease if we insert a block of a, , dielectric, , between the plates, ii) increase if we connect another similar, capacitor in parallel to it., Mark, (A) If (i) is correct, (B) If (i) is correct, (C) If (ii) is correct, , (D), Ans. (D), , Ans., , (D) 9000 VV, , (A) 10 V, , 73. The electric potential V (, y, z) in space is, , givenby:, V 41 volt. What is the electric field ae the, point (1, 0, 2)?, , (A) 8 Vm, , along - x axis, , B) 8 Vm, , along - z axis, , (C) 8 Vm along + z axis, , (D) 8 Vm along+ x axis, Ans. (A) 8 Vm' along x axis, 74. Aparallel plate capacitor is made by stacking8, n similar metallic plates equally spaced from, one another. The capacitance of, the, , capacitor, , formed by any two neighbouring plates is, , charge that can be stored on a copper sphere, of diameter 2m?, , (A) 1C, , (B) 10 uC, , (C) 100 C, , (D) 1 mC, , will be, , (A) C/n, , (B) nC, , (C) (n-1)C, , (D) (1 + 1)C, , Ans. (C) (n -1)C, 75. Two capacitors of capacitances C and, , C,are, , connected in parallel across a battery. If Q1, , and Q respectively be the charges on the, capacitors, then Q/ Q2, , from a source charge is 600 V and electric, , capacitor of capacitance, , (A), , (B) 90 V, , 10 V, , (C) 1000 V, , C. The total capacitance of the combination, , (B) 100 V, , 68. The insulating property of the air break, down is 9 x 10 V/m. What is the maximum, , 69. The electric potential at a certain distance, , Ans. (B) E, 63. A, , Ans., , (D) 10,000V, , Ans. (A) 11C, , 10, , (D) Neither A.C. nor D.C., Ans. (B) D.C., 58. Introduction of a slab of which of the, following will decrease the capacitance of a, capacitor ?, (A) Zinc, (B) Copper, , (B), , (D) +Q and +Q, , (C)+Q and +Q, Ans. (A) +Q and -Q, , to the sphere and the other terminal is, , earthed, (C) By placing 2C charge on the sphere, (D) None of the above, , and - Q, , (C) 5 x 10 joules, , (A) A.C., B) D.C., (C) Both A.C. and D.C., , (C) Aluminium, , (B) +, , (A) +Qand-Q, , 61. The unit of permittivity is same as that of, , Ans. (B) distance between the' plates, 55. Two insulated charged spheres of radi, R and R, are given charges Q and Q, respectively. They are connected to each, other with a wire No loss of energy takes, place when:, , (B) One terminal of a 2V battery is connected, , 60. If the area of the parallel plates ofa capacitor, is not equal, then the charges on the plates, , will be:, , (A), , sphere, , 66. A potential of 2V is to be given to a, of capacitance 2F. In which of the following, can it happen ?, (A) A battery of emf 2V is connected across, , increase., , 54. Which of the following is correct?, The capacitance of parallel plate capacitor, varies inversely as the:, (A) area of plates, , 35, , Electrostatlc Potentlal and Capacitance, , V, , V& E decrease, (D) Q & Cincrease but, Ans. (B) V remains unchanged but Q, E and c, , (D)C, , (A) 0,R, = Q,R, , increases,, , If none of these is, correct, If none of these is, correct., , field strength at that point is 150 N/C. What, is the distance of the observation point from, the source charge ?, (C) 4m, D) 6 m, (A) 2m, (B) 3 m, Ans. (C) 4m, 70. When a proton is accelerated from rest, through a potential difference of 500 volt, its, kinetic energy is, , (A), , 1840, , x, , 10, , electron volt, , (B) 1840 electron volt, , Ans. (B), and, 76. Two capacitors of capacitance, are connected across a 120 V battery in, series with each other. What is the potential, difference across the 4uF capacitor?, (A) 40 V (B) 48 V (C) 60V, (D)72V, , 4uF, , 6uF, , Ans. (D) 72 V, , (C) 1840 x 10* electron volt, , (D).None of the above, Ans. (D) None of the above, 71. A hollow metallic sphere of radius 10 cm, is given a charge of 3.2 x 10, coulomb,, electrical potential at a point 4 cm from, , 77. Two, , (B) 288 x 10 volt, , (C) 28.8x 107 volt, , (D) zero, , Ans. (C) 28.8 x 10 volt, 72. A charge 3 coulomb experiences a force, 3000 N when placed in a uniform electric, field. The p.d. between two points separated, by a distance of 1 cm along the field lines is, , capacitors, , are, , joined, , in, , are then separated and connected in series, with the +ve plate of one connected to the, , -ve of the other. Which of the following, statements is true?, (A) Charge on the plates connected together, , centre is, , (A) 9x 10 volt, , identical, , parallel and charged to a potential V. They, , reduces to zero., , (C) Charge on the free plates increases., (C) Potential drop across the combination, , is, , zero., , drop, , across, , the combination is, , 2V, Ans. (D) Potential drop, 2V, , across, , the combination is, , (D), , Potential

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VIDYA MaKmarks, 36, , IPHYsIcs | CLASs 12, , 0., , 1 F, , conductors, each of capacitance, and 6 V, charged to potential of 10 V, then, are, joined together., respectively. They, Two, , (C), (D), , are, , Their, , common, , potential will be :, 8V, , (A) 16 V, , (B), , (C) 4V, , (D) 1V, , a source of constant negative potential and, , (C) less than 102, , 80. Two parallel plates are separated by 2 cm. If, , the potential difference between them be V,, then electric field between them is:, (B) 200 NC(A) 100 NC, , (C)1000NC-1, , 91. A dipole is placed in a uniform electric field., potential energy will be minimum when, , Its, the angle between its axis and field is :, , remain the same, , (B) 10 m, , (A) 9 km, , (D) 1.11 cm, , (C) 1.11 m, Ans., , air is:, , (C) 30 x 10° V/m, (D) 0.3 x 10 V/m, , (B) Equidistant planes parallel to XY-plane., , (C) Equidistant planes parallel to XZ-plane., radii, (D) Coaxial cylinders of increasing, , (A) 90° always, (B) 0 always, (C) 0° to 90 always, Ans., , (C) get out and be flat on the ground, the nearest electric, , pole, , If the, , rotating, , itby 180° is:, , (Diksha), , (A) 2 W, (C) 4 W, , (B) the potential difference increases, Ans., , (C) 4W, , (Diksha), , (B) 3W, (D) W/2, , (Diksha), , (C) 10 v, , (D) 10 v, , Ans. (C) 10° V, 100. The electric potential at the surface of an, atomic nucleus (Z = 50) of radius 9.0 x 10, , cm, , (B) 8x 10 volt, (C) 80 volt, (D) 9 volt, (D) 9 volt, , Vat, , a, , (A) 90° always, , (C)q/r, , (D), , and, , Vc, , denote the, c, , =, , distantr, (Diksha), , a, , potentials, +b,, , we, , Ans. (C) q/r, 102., , have, , from the negative to the, terminal of a 9V battery?, , (Diksha), , (Diksha), , (B) 54 x 10°J, , (C) 54x 10J, (D) 54 x 10-12J, Ans. (C) 54 x 10°J, , Four equal charges 4 are placed at four, , 103., , corners of a square of each side a each. Work, done in carrying a charge -q from its centre, , (Diksha), , t oinfinity is:, , (C)2a)/(mega), , positive, , (A) 54 x 10J, , (B) VA = Vc# VB, , (A) zero, , required to carry 64C, , How much work, , charge, , of the three, , Ve=Vp=Va, V=Vc* Vs, Vc= Va* Va, Ve=Va* Vs, , Ans. (C) (V2a ) /(mega), , point,, , from a charge q varies as, , (B) /r, , (A), (B), (C), (D), 96., , (Diksha), , 1S, , (A) 9x 10 volt, , (A) q/, , shells, then, for, , Ans., , of 9m is:, , (D) 0° to 180" always, , Vg, , (Diksha), , (D) may increase or decrease, , distance, , 101. Electrostatic potential, , densities o, - a and+ a respectively. If Va, , Ans. (D) may increase or decrease, 90. A dipole is, placed parallel to the electric, field. If W is the work done in, rotating the, dipole by 60°, then the work done in, , a, , (B) 10 V, , Ans., , 95. Three concentric spherical shells have radii, a, b and c (a <b <c) and have surface charge, , (B) take shelter under a tree, , of 100uC at, , (A) 10 v, , 94. What is the angle between electric field and, (Diksha), equipotential surface?, , (B) O, (D) CO, , (A) remain in the car, , charged., , charge, , Ans. (A) Equidistant planes parallel to YZ-plane., , from, (Diksha), , 4C, , Ans. (B) zero, 99. The potential at a point, due to a positive, , around the X-axis., , (A) increases, (B) decreases, (C) remains the same, , (D), , (D) 180 V, , (C) surface charge density, , charges, , (C) 2C, , (D) 0.1J, , (B) zero, (C) Infinite, , (Diksha), , Ans. (A) remain in the car, 89. When the separation between two, charges, is increased, the electric, potential of the, , Ans. (B) C, 83. A parallel plate, capacitor is, plates are pulled apart, (A) the capacitance increases, , (B) 1.1J, , (C) 0.01J, , then the, (Diksha), , (A) Equidistant planes parallel to YZ-plane, , storm. In order to protect yourself, lightening, would you prefer to, , (B)C, , (A) 11J, , at, , (D) density, , (D) touch, , (A), , equilateral triangle of side 0.5 m,, , kept, , Ans., 98., , surfaces associated with this field will be, , 88. You are travelling in a car during a thunder, , of the, , are, , Ans. (D) 0.1J, 93. In a certain range, a uniform electric field, exists along X-direction. The equipotential, , (A) polarisation, (B) susceptibility, , combination shown in fig. ?, , charges 1uC, 2uC, 34C, , work done is, , Ans. (C) H,o, , (D) 4C, () 2C, Ans. (B) C, 82. What is equivalent capacitance, , (D) None of these, , (A) 1 V, , (B) 13 x 10* V/m, , (B) C, , (C), , (D) 27, , If they are brought nearer, so they now form, an, , (A) H2, (C) H,O, , (A), , B) 1/(4ms). p/, , vertices of an equilateral triangle of side lm., , (A) 3x 10° V/m, , Ans. (A) polarisation, 87. Which of the following is not a non-polar, molecule?, (Diksha), , (Diksha), , (A) zero, Potentail on the equatorial line of a dipole, (Diksha), 1S, , Three, , (Diksha), , Ans. (A) 3 x 10° V/m, 86. The dipole moment per unit volume is :, (Diksha), , equatorial line, , (A) zero, , (B) t, , zero, , (C) /2, Ans. (A) zero, , (A) 9 km, , 85. The dielectric strength of, , 97. The ratio of potential on the, and on the axial line is:, , (Diksha), , (A), , 92., , (D) 2000 NC-, , Ans. (C) 1000 NC-1, 81. What is the equivalent capacitance of the, combination shown in the figure?, , potential difference, increases, , (B) 1012, (D) more than 1012, , Ans. (D) more than 10, , and, , difference, (B) the potential, metallic sphere will be, of, The, 84., capacitance a, is, radius, nearly, (Diksha), 1uE if its, , be, (A) zero, , charge, , Ans., , Ans. (B) 8 V, 79. One of the plates of capacitor is connected to, , the electrons accumulated on its are 10, When the other plate is earthed, the number, of electrons n o w present o n the plate wil, , the, , 37, , Electrostatlc Potential and Capactance, , increases, the total charges, , (B) (24 (T Ega), (D) I2m6a), , 5 cm and, The radii of two metallic sphere are, 10 cm and both carry equal charge of 75uC., If the, , two, , spheres, , are, , shorted then, , will be transferred :, , (A), (B), (C), (D), , from smaller to bigger, from bigger to smaller, , 254C, 25uC, 50uC from smaller to bigger, smaller, 504C from bigger to, , Ans. (A) 25uC from smaller to bigger, , charges, (DIksha)

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VIDYA MaKmarks, 38, , PHYSIcs | CLASs 12, , of capacitance, 104. A parallel plate air capacitor, then, Cis connected to a cell of emf V and, dielectric slab of, disconnected from it. A, fill the, dielectric constant K, which can just, it., n o w inserted in, is, of the capacitor,, air gap of, the following is incorrect? (Diksha), Which, the capacitor, (A) The energy stored in, decreases K times, , Explanation: Let us, , The, , (C), , charge, , the, , capacitor, , is, , the, , potential differençe, plates decreaes K times, charge, , on, , the, , capacitor, , is, , not, , Assertion-Reasoning, , V, a, , V2 and, , consequently, , difference, , potential, , there will be, , between, , the, , 3. Assertion: When a dielectric slab is gradually, inserted between the plates of an isolated, capacitor, the energy of the, , below., , (A) Both Assertion and Reason are true and, Reason is the correct explanation of Assertion, (B) Both Assertion and Reason are true but, Reason is not the correct explanation of, Assertion, (C) Assertion is true but Reason is false, , (D) Assertion is false but Reason is true, 1. Assertion: Electric field is always normal to, equipotential surfaces and along the direction of decreasing order of potential., Reason: Negative gradient of electric potential is electric field., ICBSE SQP 2021], Ans. (A) Both Assertion and Reason are true and, Reason is the correct explanation of Assertion, , Explanation Electric lines of force are, normal to any equipotential surface at all, points on the surface. Electric field is strong, at the points where equipotential surfaces are, , crowded and vice versa., 2. Assertion: Two, , adjacent conductors of une, qual dimensions, carrying the same positive, , charge have a potential difference between, them., Reason: The potential of a, conductor, depends upon the charge given to it., , (B) Both Assertion and Reason are true but, Reason is not the correct, explanation of, Assertion, , decreases., Ans., , cv, , Both Assertion and Reason are true and, Reason is the correct explanation of Assertion, , Explanation : When dielectric is inserted, between the plates of capacitor, then the, capacitance becomes k times, then energy, between the plates increases., , 7. Assertion: Two equipotential surfaces cannot, Reason: Equipotential surfaces, each other, , (C), , Assertion is, , true, , are, , there is, , parallel to each other because, direction, potential gradient along any, is no, there, thus, and, surface, the, parallel to, , Explanation, =, , KC and U, , electric field parallel to the surface., , =, , *, , 2KC, , 8. Assertion: The capacity of a given conductor, remains, , 4. Assertion: Polar molecules have temporary, , Reason, , dipole moment., Reason: In polar molecule, the centres of, positive and negative charges coincide even, when there is no external field., Ans. (D) Assertion is false but Reason is true, , Explanation: The molecules of a substance, may be polar or non-polar. In a non-polar, molecule, the centres of positive and, negative charges coincide. This molecule has, no permanent dipole moment.On the other, hand, a polar molecule is one in which the, centres of positive and, are, negative, , charges, , separated, even when there is no external, field. Such molecules have a, permanent, , dipole moment., , 5. Assertion: Electric, , potential and electric, potential energy are different quantities., Reason: For a, system of positive tést 'charge, and point charge, electric potential energy, electric potential., , Ans. (C) Assertion is true but, Reason is, , Explanation, potential, , false, , Electric potential and, energy are different, quantiies anda, , cannot be equated., , nearly, , same even, , :, , if, , charge is varied, , Capacitance, , medium, , as, , well, , as, , depends, size and, , on, , it., , upon, , shape, , (B), , Ans., , Ans., , (A), , Reason is the, , correct, , are true, , (), , (A), (B), (C), , and, , geometric, , are, , Ans. (D) Assertion is false but Reason is, , Case/Source Based Type, , high voltage of few million volts, , Graaff generator generates:, current, , does not need to be, needs, can, , to, , be, , never, , be, , (D) None of these, Ans., , (iv), , orthogonal., Reason : Electric field lines, equipotential surface., , normal to, , (A) does not need to be, One end of the discharge tube in, Graff generator is, (B) covered, (A) earthed, , (D), , (C) isolated, true, , like, , shaped to work., , of, , quantity., 9. Assertion: Two equipotential surface can be, , of few million, , (A) High resistance (B) High, D) High power, (C) High voltage, Ans. (C) High voltage, terminal sphere(ii) A Van de Graaff generator, , explanation of Assertion, , Explanation: Capacitance is a, , Build up, , Van de, , conductors., Both Assertion and Reason, , high voltage, , (C)Deaccelerate charged particle, electrons, (D) Both (A) and (B) are correct, , but Reason is false, , no, , Build up, volts, , B), , parallel to, , be, , Graaff generator is used to:, , (A) Store'électrical energy, , Explanation: wo equipotential can never, , (C) Assertion is true but Reason is false, , C, , Van de, , (i), , cut each other, , Ans., , The force between the plates, , Reason, , Energy of the capacitor, U=, , (A), , parallel plate, , Type 1Mark, , from the codes (A), (B), (C) and (D) as given, , Reason:, , two, , system decreases., , Select the correct answer to these question5, , energy of the capacitor increases., , Ans., , V=and V, =, , conservedd., , Ans., , on, , inserted between, , the plates of a battery connected capacitor,, , will be,, , not, , between the, , 6. Assertion: A dielectric is, , the surface of each conductor, , conductors., , The, , Ans. (C) The, , same, , potential, , conserved, , (D), , spherical, , which a r e possessing, r and ra, Therefore the, positive charge Q., , shells of radii, , is, (B) The change in energy stored, 1/2 CV (1/K-1), on, , consider two, , 39, , Electrostatic Potentlal and Capacitance, , a, , Van de, , None of these, , Ans. (A) earthed, , that the sphere of a Van de Graaff, Then the motor, generator gathers a charge., is allowed to, and, the, off, turned, sphere, is, , () Suppose, , 1 Mark, , reach electrostatic equilibrium. The charge, , 1. A Van de Graaff generator is an electrostatic, generator, invented by an American physicist, , (A), , its, on, both, resides, throughout its volume, , Robert J. Van de Graaff. It uses a moving belt, , (B), , resides, , that accumulates charge on a hollow metal, structure designed like a globe, placed on the, in nature and, top of a column that is insulating, , thus, creating a very high electric potential in, the order of a few million volts. This results, in a very large electric field that is used to, accelerate charged particles., , (C), (D), Ans., , surface, , and, , inside the sphere and, when touched, outside, only emerges, on the surface of the sphere, resides, , mostly, , only, , None of these, (C) resides only on the surface of the sphere., devices which store electrical, the basic component, are, of electronics and have a host of various, , 2. Capacitors, , are, , charge. They

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40, , IPHYSICs | CLASS, , 12, , applications. The most common use for, uses, capadtors is energy storage. Additional, , include power conditioning, signal coupling8, , or decoupling, electronic noise filtering and, remote sensing. Because of its varied applications, capacitors are used in a wide range, of industries and have become a vital part of, everyday life., , enVIDYA MaK marksElectrostatle Potentlal, equal charge, (A) They, will have, , same, , potential, , (B) They, (C) Both A and B, D) None of these, Ans. (A) They will have equal charge, , When 3 capacitors are, , Explanation, connected in series then the charge in each, , electronic component with 2 terminals. The, , capacitor ?, , (A) AC, , (B) DC, (C)Both AC and DC (D) Neither AC nor DC, Ans. (D) DC, , (B) Mica, (D) Metal, , (C) Water, , energy in an electric field. It is a passive, , Now, answer the following questions:, , Air, , effect of a capacitor is known as capacitance, It has its wide application. Its simple use is in, our ceiling fan. Capacitor is not only used to, start the fan but also to run it. The fan won't, work without a capacitor, even if you rotate, it manually because capacitor is needed to, create magnetic flux, which makes the fan, rotate. In simple words, a capacitor acts as, a different phase for the single-phase motor, including that in your fan., , Explanation: Asf= 0(for DC), , assumed to have, high value of dielectric constant so have higha, capacitance., are, , (iv) Sixty four (64) drops each having the, capacity C and potential V are combined to, form a big drop. It the charge on the small, drop is q, then the charge on big drop will, be:, , (A) 24, (C) 16, , (B) 44, (D) 64q, , Ans. (D) 64, , Explanation: Since Q= nq, Q, , 64 q, , mm is introduced between them, then the, , capacity will become., (A) 2 times, , (B) the same, (D) 4 times, , (C)3 times, Ans. (C) 3 times, , d-t+, k, A parallel plate, capacitor has a, of 50pF in air and 105, when, , pF, , oil. The dielectric, (A) 5.1, (C) 2.1, Ans. (C) 2.1, , CV,we can see that energy of system, will be half the original. This half energy, lost while charge flowing from charged to, , capacitance, , capacitance, immersed in, , constant of the oil is:, (B) 1, , (C), , (B) 4F, (D) 8F, , 6F, , are, , connected in, , V. The constant of proportionality, is C, i.e., the, , Hence,, , 4. A capacitor is device which can store energy., , The process of charging a capacitor involves, , capacitance, , in this case, , Q CV, C, , W-, , (D) Insufficient, , Ans. (A) When they are connected in parallel, , Explanation : We get maximum energy, , (A) 2J, , (D)116J, , 8, , (B) 4J, , Ans. (B) 4J, , Explanation : Expression for finding value, of energy is:, , v--4x-4], 2C 2x2, (v) Calculate the energy in the 2F capacitor, , the transferring of electric charges in capacitor, is stored as its potential energy. If q is the, , HA, , Vis the potential difference across, a capacitor at any instant during its charging, , charge and, , 80V, , small charge dq against the repulsion of, , (A) 8.6 kJ, , charge q already stored in it is, , (C) 64 kJ, , W, , =, , ;, , (B) 64k, (D) 6.4k, , Ans. (D) 6.4kj, , va-, , Explanation: Qis directly proportional to, , Explanation:k -5021, , C= QV, , then small work done in storing an addition, , Ans. (B) 4F, , (D), , (iv) Three different capacitors, , capacitor which has voltage of 4V and has, , 16C of charge?, (A) 2F, , Put, , uncharged capacitor., , charge. It stores electrical energy between the, plates., (i) What is the value of, of a, , 105, , series.Then:, , (B) Vary the resistance, , Explanation: Capacitor is used to store the, , C, , medium, air, , (ii), , Explanation: Charge willflow, , (C) Store magnetic energy, , Since, work done = Q2C, , energy stored in it., , till p.d. of, both becomes same. Using, ener8y formula, , (D) Dissipate energy., Ans. (A) Store electrical, energy, , Explanation:, Since, , (D) increases by factor of 2, , Ans. (D) decreases by factor of 2, , (A) Store electrical energy, , Explanation:, , when capacitors are connected in paralel, as equivalent capacitance is greater then, the largest individual capacitance when, connected in parallel., (i) If the charge stored in a capacitor is 4C and, the value of capacitance is 2F, calculate the, , (C) remains the sanme., , () Capacitor is a device used to, , Ans. (B)ov, , C) Both in series and parallel, , (v) 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, , (B) decreases by factor of 2., (i) A parallel plate condenser is connected, with the terminals of a battery. The distance, between the plates is 6 mm. If a glass plate, dielectric constant k = 9 of thickness 4.5, , (D) 202, , (i) When do we get maximum energy from the, set of capacitors ?, (A) When they are connected in parallel, (B) When they are connected in series, , system, (A) increases by factor of 4., , 1, , (0) Work done is charging a capacitor is:, , (C) 2Qv, , Explanation: Metals, , 41, , (A) QV, , Ans. (D) Metal, , capacitor is same., , Which of the following is blocked by a, , 4, , (H) For which medium capacitance is high ?, , (A), , 3. A capacitor is a device that stores electrical, , ), , Capacitance, , will have, , -, , Explanation, Work done =, =6.4 k, , 16/4, , 4F, , =6400J

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42, , VIDYA MaKmark, , PHYSIcs| CLASS 12, , (V), , the, Calculate, energy stored, combination of the capacitors, , in, , the, , the, , cut, , Potentlal and, , Ectrosiac, , 43, , Capacitance, , equipotential surfaces orthogonall, , therefore, equipotential surtace must, , CHAPTER, , plane surface., , the diagram, the equipotentia, (ii) According to, are the directio, are ., Thearrows, points, , ASSESSMENT", , of electric field., , 80V, , R, , (A) 192 k, , (B) 1.92 k, , ()19.2kJ, , (D) 1920J, , Bxplanation: Ceq=4 +2, , =, , 2, , 5. Any surface over which the poterntial is, , constant is called an equipotential surfae., In other words, the potential surface is zero., , The equipotential surfaces of a single charge, are concentric shells with their centres at, , the point charge. As the lines of force point, radially outwords, so they are perpendicular, to the equipotenital surfaces all points., , (B) S and Q, , (A) P and Q, , fields., (B) Will be, , Explanation: Equipotential surface is, always perpendicular to the electric field, lines. Electric field lines are horizontal and, parallel to each other. Equipotential lines, must be vertical and the points laving equal, potential must be on same vertical line., , (D), 3., , 4., , (C) Va=Vp, , (P) None of these, , Ans. (C) Va=Vs, , Explanation : As both points Aand B are, , An electric field is, , scalar, , a, , (B) Electric field lines are at 45° to the, , potenial will be equal., What will be the nature of, equipotential, surfaces due to a point charge, situated at, , (C) The surface of a charged capacitor 15, , infinity?, (A) Plane surface, , (B) Spherical, , (C) Elliptical, , (D) Cylindrical, , Ans. (A) Plane surface, , Explanation : If a point charge is situated, at, , infinity,, , the electric field lines, coming, an +ve form of, parallel, are known that, field lines, , out of it will be, lines. As, , straight, , equally, , 3 min. for each question, , for, , correct, , a, , metal is, , (C)1, , (D) 10, , is a basic storage device to store, charges. Capacitors have many uses, in electronics and electrical systems. They a r e, , :, , O Capacitor, electric, , A proton and a n electron are released, infinite distance apart and are attracted, towards each other. Which of the following, ?, statement about their kinetic energy is true, Kinetic energy of electron is, , more, , so a, , cal, , (C), , Kinetic, , energy, , electron, , =, , are, , at, , 45° to the, , electrione, , for, , are, , through capacitor,, block any further current from following, , None of the above, , (A) n /, , an, , least, , also used in smoothening, filtering,, If you pass DC, bypassing etc. in a circuit., will, it, a, charge and then, , They, , energy of proton, , (D), , that, at, , capacitor., , kinetic, , 5. Two conducting spheres of radii r and r2, are charged such that they have the same, electric field on their surfaces. The ratio of, , product, , rare, , does not include, , In electric power distribution, capacitors are, the, used for power factor correction. This is, ofa, used, application, easiest and very widely, , than, , Kinetic energy of electron is less than, of, , ubiquitous that it is, , some purpose., , 7., , Capacitor is a device used for:, (A) Store electrical energy, , the electrie potential at their centres is:, , Ans. (B) Electric field lines, , (B) 2, , (B) Vary the resistance, (C) Store magnetic energy, , (D) 2, , (D) dissipate energy, on a, , In, , conductors,, , to, time that, need spend, E.AT(Estimated Average Time) is given to help you understand the amount of maximum of latestyou, sQP and previous year, of question. E.A.T IS designed by a team of subject experts after a thorough analysis, type, particular, well in time and revise, is a, method, , charge>, , distributed over the, surfac, conductor. Therefore, the, potentia, throughout the surface is same 1., are, , (B), , constant, , are, , 1 Mark, , Estimated Average Time, , that of proton, , equipotential., , of, , and, , Electric field lines are normal to the, , Case/Source Based Type, , sharp edges, , (B) infinite, , D) Field lines due to a point charge are, circular, , Explanation, , near, , (A) Zero, , (B), , equipotential sufaces., , equipotential sufaces., , (A), , Dielectric, , quantity., , at the equipotential surface. Therefore, their, , crowded, , that of proton, , generated radially from a (+)ve point, charge. And the electric field lines cross the, equipotential surfaces perpendicularly., (v) Which of the following statement is correct?, , (A), , both, , (A), , Explanation : Electric field lines are, (B) Va<Vg, , Reason, , of a conductor, , Ans. (B) Spherical, , (A) Va> V, , more, , equipotential surfaces c a n be, , equipotential surface., , (C) will always be equally spaced, , (D) Cylindrical, , Assertion: Two, , orthogonal., , fields, (A) Closer in regions of large electric, electric, lower, of, to, regions, compared, , Ans. (C) S and R, , (C) Cubical, , 6., , Equipotential surface:, , (D) P and S, , S and R, , (C), , 2., , (iv) What is the nature of equipotential surface, in case of a positive point charge?, (A) Circular, (B) Spherical, , () Which is true?, , 1 min. for each question, , 1. 1 Voltis equivalent to, (A) Newton/seond (B) Newton/coulomb, (C) Joule/coulomb, (D) Joule/second, , v-CV6x80x80, 19200J =19.2 kJ, , Estimated Average Time, , 1 min. for each question, , 6F, , 1Mark, , For instruction and code refer page 16, , Estimated Average Time, , Ans. (C) 19.2 kJ, , (), , Assertion-Reasoning Type, , 1Mark, , Choice Questions, , Multiple, , The, , board 'examination papers. E.A.T, , a, , **, , pragmatic, , that will, , For Detailed Solutions Scan, , equipotential., , Note: For Answers, use OMR sheet provided at the end of this book., , help, , you, , finish, , it ds, , your, , paper, , weu.