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 ?

Int. Sc. Honours 1884.

65. Explain the action of the attracted disc electrometer. A 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.

Ohm's Law.

CURRENT ELECTRICITY

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.),

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

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?

Since C is expressed in ampères and E in volts, the resistance of the lamp, in ohms, will be given by the equation

RE/C=98/0.7 = 140.

2. The E.M.F. of a battery (or difference of potential between its poles on open circuit) is 15 volts: when the poles are connected by a copper wire a current of 1.5 ampère is produced, and the potential difference between the battery poles falls to 9 volts. Find the resistance

of the wire and the internal resistance of the battery.

The resistance (R) of the wire is the ratio of the difference of potential between its ends (9 volts) to the current thereby produced (1.5 ampère),

i.e. R=V/C=9/1.5=6 ohms.

Notice that 9 volts is the potential difference causing the flow of current through the wire of resistance to 6 ohms; the total E.M.F. acting round the circuit is 15 volts. Call this E, and the resistance of the battery B: applying Ohm's law to the complete circuit, we have E=C(B+R),

3. The wire used on Indian telegraph lines is iron wire of No. 2 B.W.G., having a resistance of 4.6 ohms per mile. The batteries consist of Minotto cells of 1.04 volt E.M.F. and 30 ohms resistance per cell. Assuming that the resistance of the instruments is 80 ohms, and that a current of 8 milli-ampères is required to work them, find how many cells should be employed on a line 200 miles in length.

If n be the number of cells required, the E.M.F. of the battery is 1.04 volt, and its internal resistance is 30 n ohms. The resistance of the line is 4.6 × 200 = 920 ohms, and that of the instruments is 80 ohms; the total external resistance (assuming that of the return circuit through the earth to be negligible) is 1000 ohms.

A milli-ampère is one-thousandth of an ampère, so that the required current is 0.008 ampère. By Ohm's law,

C = 1.04 n/(30 n + 1000), and this = 0.008,

.. 1.04 n=0.24n+8,

i.e. 0.8n=8, and n = 10.

4. A current of 8.5 ampères flows through a conductor, the ends of which are found to have a difference of potential of 24 volts: what is its resistance?

5. If an incandescent lamp of 80 ohms resistance takes a current of 0.75 ampère, what E.M.F. is required to work it?

6. A glow lamp takes a current of 1.32 ampère and the E.M.F. between its terminals is found to be 66 volts: what is its resistance while hot?

7. A battery consists of 5 Daniell cells, each having an E.M.F. of 1.08 volt and an internal resistance of 4 ohms: what current will the battery produce with an external resistance of 7 ohms?

8. You are required to send a current of 2 ampères through an electromagnet of 3.5 ohms resistance, and are supplied with a number of Grove cells each of 1.9 volt E.M.F. and 0.25 ohm internal resistance: how many cells are required?

9. One end (A) of a wire ABC is connected to earth; the other end (C) is kept at a constant potential of 100 volts. If the resistance of the portion AB is 9.6 ohms and that of BC 2.4 ohms, what current will flow along the wire, and what will be the potential of the point B ?

10. A Bunsen cell has an internal resistance of 0.3 ohm and its E.M.F. on open circuit is 1.8 volt. The circuit is completed by an external resistance of 1.2 ohm : find the current produced and the difference of potential which now exists between the terminals of the cell. [See Ex. 2.]

11. On adding 3 ohms to the resistance of a certain