Page images
PDF
EPUB

45. A spherical air-condenser, the coatings of which have radii of 16 and 17.5 cm. respectively, is charged to a potential 12, its outer coating being in contact with earth. Calculate its energy.

46. Two insulated spheres, of 12 cm. and 3 cm. radius, are charged respectively with 36 and 24 units of electricity compare their potentials, and the energies of their charges.

47. Compare the work done in charging a Leyden jar of capacity 30 to potential 15 with that required to charge a jar of capacity 20 to potential 45.

48. The armatures of a condenser are concentric spheres of diameter 20 and 24 cm. respectively, and the space between them is filled with shellac of S.I.C. = 3. The condenser has a charge of 7560 units. If it is discharged in such a way that all the energy is converted into heat, how much heat will be produced? 4.2 x 107.]

[J =

The capacity of the condenser is 3 × 10 × 12/2 = 180. The energy of its charge is Q22 C = (7560)2/360=158760 ergs. Let H denote the amount of heat (in terms of the calorie or gramme-degree) resulting from the discharge: then JH = E, or

[blocks in formation]

49. The capacity of a condenser is 700; to what potential must it be charged in order that the energy of its discharge may be equivalent to one heat-unit?

50. Two equal and similar Leyden jars have their outer coatings connected to earth: one is uncharged, the other is charged to potential V. Find the energy of each after the charge has been shared, and show that one-half of the energy of the charged jar is dissipated in the spark which passes when their knobs are connected.

51. The coatings of a charged Leyden jar are connected with those of an uncharged jar of double the

capacity. Compare the energy of the system with that of the original charged jar.

52. What would be the solution of the preceding example if the linear dimensions of the uncharged jar were double those of the charged jar, other things being equal?

53. A charged sphere of radius r is made to share its charge with an uncharged sphere of radius r': prove that the energy of the original distribution is to that of the final distribution as (r+r): r.

54. A Leyden jar is charged and then connected up with nine uncharged jars so as to form a battery of ten equal jars: show that the energy of the whole battery is only one-tenth that of the single jar.

55. A condenser is charged to a given potential and then discharged. It is again charged to the same potential, and made to share its charge with another condenser of half its capacity, after which the jars are separately discharged. Compare the energy of discharge in each case.

56. A Leyden jar is charged with electricity; an equal charge is imparted to a battery consisting of four equal and similar jars, the inner coatings of which are connected together. Compare the energies of the two charges.

57. The outer armatures of two spherical air-condensers are of the same radius, viz. 20 cm. The first is charged, and the radius of its inner armature is 15 cm.: the second is uncharged, and its inner armature has a radius of 18 cm. Prove that if the first condenser is made to share its charge with the second, three-fourths of its energy will be lost.

58. A given quantity of electricity is to be shared between a number of conductors of different capacities. Prove that the energy of the system is a minimum when all the conductors are charged to the same potential.

EXAMINATION QUESTIONS.

59. Define the potential and the capacity of a charged conductor. Two insulated hollow conducting spheres of radii a and b (a>b) are charged at a considerable distance from one another to potentials A and B. The larger is then opened and the other is put inside and allowed to touch. Determine the potentials of the spheres and the quantities of electricity in each.

Edinb. M.A. 1884.

60. Of two similar metal discs A and B, placed parallel to each other, A is connected with a gold-leaf electroscope, and B with the gas-pipes. A small charge of electricity is given to A, and the leaves of the electroscope diverge. When a slab of sulphur is introduced between the discs, the divergence diminishes. But if B be insulated and charged, while A is charged only by induction, the introduction of the sulphur causes an increase of the divergence. Explain these experiments. Prel. Sc. 1887.

61. Two small equal spheres, A and B, placed with their centres at a distance of 1 metre apart, are charged with 25 and - 25 units of electricity respectively. Find the direction and magnitude of the resultant electric force at a point I metre from each of the spheres. Find also the electric potential at the same point.

Prel. Sc. 1888.

62. Assuming that the quantity of electricity produced by a plate machine is proportional to the number of turns of the disc, explain how the capacities of two condensers may be compared. Int. Sc. 1883.

63. A, B, and C are three Leyden jars, equal in all respects. A is charged, made to share its charge with B, and afterwards share the remainder with C, both B and C being previously without charge. The three jars are now separately discharged. Compare the quantity

of heat resulting from each discharge with what would have been produced by the discharge of A before any sharing of its charge. Int. Sc. 1884.

64. What must be the velocity of a bullet of 15 gm. that its kinetic energy may be equal to the electric energy of a globular flask of 8 cm. radius, half filled with oil of vitriol and half immersed in oil of vitriol, the glass being 0.05 cm. thick, its specific inductive capacity = 6, the liquid inside being at potential 300, and the liquid outside at potential 700?

meter.

Int. Sc. Honours 1884.

65. Explain the action of the attracted disc electroA circular plate connected with the earth, 5 cm. in radius, hangs from a balance at a distance of .5 cm. above an equal horizontal disc which is insulated. On electrifying the lower disc, a mass of 8 gm. has to be placed in the other pan of the balance to maintain equilibrium. Find the potential of the lower disc. In what units is your answer expressed? Int. Sc. Honours 1887.

CHAPTER X

CURRENT ELECTRICITY

Ohm's Law.-The current which flows along any conductor is directly proportional to the electromotive force (or difference of potential) between its ends, and is inversely proportional to its resistance. Thus if C denote the current and E the electromotive force (or E.M.F.),

[blocks in formation]

R being the resistance of the conductor, and k a constant.

If we agree to define the resistance of a conductor as being the ratio between the E.M.F. along it and the current thereby produced (R = E/C), the constant k becomes equal to unity, and Ohm's law may be expressed by the equation

[blocks in formation]

This equation holds good when C, E, and R are expressed in terms of the C.G.S. electromagnetic units defined on p. 5, and also when these three quantities are expressed in terms of the so-called practical units (current in ampères, E.M.F. in volts, and resistance in ohms).

1. An incandescent lamp takes a current of 0.7 ampère, and the E. M. F. between its terminals is found to be 98 volts: what is its resistance?

« PreviousContinue »